DSpace Community:
http://hdl.handle.net/10023/95
Thu, 28 May 2015 16:09:16 GMT2015-05-28T16:09:16ZDSpace Community:http://research-repository.st-andrews.ac.uk:80/retrieve/30/Mathematics and statistics.gif
http://hdl.handle.net/10023/95
Using accelerometers to determine the calling behavior of tagged baleen whales
http://hdl.handle.net/10023/6623
Abstract: Low-frequency acoustic signals generated by baleen whales can propagate over vast distances, making the assignment of calls to specific individuals problematic. Here, we report the novel use of acoustic recording tags equipped with high-resolution accelerometers to detect vibrations from the surface of two tagged fin whales that directly match the timing of recorded acoustic signals. A tag deployed on a buoy in the vicinity of calling fin whales and a recording from a tag that had just fallen off a whale were able to detect calls acoustically but did not record corresponding accelerometer signals that were measured on calling individuals. Across the hundreds of calls measured on two tagged fin whales, the accelerometer response was generally anisotropic across all three axes, appeared to depend on tag placement and increased with the level of received sound. These data demonstrate that high-sample rate accelerometry can provide important insights into the acoustic behavior of baleen whales that communicate at low frequencies. This method helps identify vocalizing whales, which in turn enables the quantification of call rates, a fundamental component of models used to estimate baleen whale abundance and distribution from passive acoustic monitoring.Tue, 15 Jul 2014 00:00:00 GMThttp://hdl.handle.net/10023/66232014-07-15T00:00:00ZGoldbogen, JeremyDe Ruiter, Stacy LynnStimpert, AlisonCalambokidis, JohnFriedlaender, AriSchorr, GregMoretti, DavidTyack, Peter LloydSouthall, BrandonLow-frequency acoustic signals generated by baleen whales can propagate over vast distances, making the assignment of calls to specific individuals problematic. Here, we report the novel use of acoustic recording tags equipped with high-resolution accelerometers to detect vibrations from the surface of two tagged fin whales that directly match the timing of recorded acoustic signals. A tag deployed on a buoy in the vicinity of calling fin whales and a recording from a tag that had just fallen off a whale were able to detect calls acoustically but did not record corresponding accelerometer signals that were measured on calling individuals. Across the hundreds of calls measured on two tagged fin whales, the accelerometer response was generally anisotropic across all three axes, appeared to depend on tag placement and increased with the level of received sound. These data demonstrate that high-sample rate accelerometry can provide important insights into the acoustic behavior of baleen whales that communicate at low frequencies. This method helps identify vocalizing whales, which in turn enables the quantification of call rates, a fundamental component of models used to estimate baleen whale abundance and distribution from passive acoustic monitoring.Nested row-column designs for near-factorial experiments with two treatment factors and one control treatment
http://hdl.handle.net/10023/6556
Abstract: This paper presents some methods of designing experiments in a block design with nested rows and columns. The treatments consist of all combinations of levels of two treatment factors, with an additional control treatment.
Description: The authors also thank Queen Mary, University of London, the University of St Andrews and the Poznan University of Life Sciences for financial support. The second author was also supported by the British-Polish Young Scientists Programme, grant WAR/342/116. Date of Acceptance: 07/04/2015Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10023/65562015-01-01T00:00:00ZBailey, Rosemary AnneLacka, AgnieszkaThis paper presents some methods of designing experiments in a block design with nested rows and columns. The treatments consist of all combinations of levels of two treatment factors, with an additional control treatment.The effect of animal movement on line transect estimates of abundance
http://hdl.handle.net/10023/6466
Abstract: Line transect sampling is a distance sampling method for estimating the abundance of wild animal populations. One key assumption of this method is that all animals are detected at their initial location. Animal movement independent of the transect and observer can thus cause substantial bias. We present an analytic expression for this bias when detection within the transect is certain (strip transect sampling) and use simulation to quantify bias when detection falls off with distance from the line (line transect sampling). We also explore the non-linear relationship between bias, detection, and animal movement by varying detectability and movement type. We consider animals that move in randomly orientated straight lines, which provides an upper bound on bias, and animals that are constrained to a home range of random radius. We find that bias is reduced when animal movement is constrained, and bias is considerably smaller in line transect sampling than strip transect sampling provided that mean animal speed is less than observer speed. By contrast, when mean animal speed exceeds observer speed the bias in line transect sampling becomes comparable with, and may exceed, that of strip transect sampling. Bias from independent animal movement is reduced by the observer searching further perpendicular to the transect, searching a shorter distance ahead and by ignoring animals that may overtake the observer from behind. However, when animals move in response to the observer, the standard practice of searching further ahead should continue as the bias from responsive movement is often greater than that from independent movement.
Description: This work was supported by the University of St Andrews (http://www.st-andrews.ac.uk/; RG, STB, LT) and by a summer scholarship and PhD grant from The Carnegie Trust for the Universities of Scotland (http://www.carnegie-trust.org/) to RG. Date of Acceptance: 10/02/2015Mon, 23 Mar 2015 00:00:00 GMThttp://hdl.handle.net/10023/64662015-03-23T00:00:00ZGlennie, R.Buckland, S.T.Thomas, L.Line transect sampling is a distance sampling method for estimating the abundance of wild animal populations. One key assumption of this method is that all animals are detected at their initial location. Animal movement independent of the transect and observer can thus cause substantial bias. We present an analytic expression for this bias when detection within the transect is certain (strip transect sampling) and use simulation to quantify bias when detection falls off with distance from the line (line transect sampling). We also explore the non-linear relationship between bias, detection, and animal movement by varying detectability and movement type. We consider animals that move in randomly orientated straight lines, which provides an upper bound on bias, and animals that are constrained to a home range of random radius. We find that bias is reduced when animal movement is constrained, and bias is considerably smaller in line transect sampling than strip transect sampling provided that mean animal speed is less than observer speed. By contrast, when mean animal speed exceeds observer speed the bias in line transect sampling becomes comparable with, and may exceed, that of strip transect sampling. Bias from independent animal movement is reduced by the observer searching further perpendicular to the transect, searching a shorter distance ahead and by ignoring animals that may overtake the observer from behind. However, when animals move in response to the observer, the standard practice of searching further ahead should continue as the bias from responsive movement is often greater than that from independent movement.Mixture models for distance sampling detection functions
http://hdl.handle.net/10023/6463
Abstract: We present a new class of models for the detection function in distance sampling surveys of wildlife populations, based on finite mixtures of simple parametric key functions such as the half-normal. The models share many of the features of the widely-used “key function plus series adjustment” (K+A) formulation: they are flexible, produce plausible shapes with a small number of parameters, allow incorporation of covariates in addition to distance and can be fitted using maximum likelihood. One important advantage over the K+A approach is that the mixtures are automatically monotonic non-increasing and non-negative, so constrained optimization is not required to ensure distance sampling assumptions are honoured. We compare the mixture formulation to the K+A approach using simulations to evaluate its applicability in a wide set of challenging situations. We also re-analyze four previously problematic real-world case studies. We find mixtures outperform K+A methods in many cases, particularly spiked line transect data (i.e., where detectability drops rapidly at small distances) and larger sample sizes. We recommend that current standard model selection methods for distance sampling detection functions are extended to include mixture models in the candidate set.
Description: Funding: EPSRC DTG Date of Acceptance: 15/01/2015Fri, 20 Mar 2015 00:00:00 GMThttp://hdl.handle.net/10023/64632015-03-20T00:00:00ZMiller, David LawrenceThomas, LenWe present a new class of models for the detection function in distance sampling surveys of wildlife populations, based on finite mixtures of simple parametric key functions such as the half-normal. The models share many of the features of the widely-used “key function plus series adjustment” (K+A) formulation: they are flexible, produce plausible shapes with a small number of parameters, allow incorporation of covariates in addition to distance and can be fitted using maximum likelihood. One important advantage over the K+A approach is that the mixtures are automatically monotonic non-increasing and non-negative, so constrained optimization is not required to ensure distance sampling assumptions are honoured. We compare the mixture formulation to the K+A approach using simulations to evaluate its applicability in a wide set of challenging situations. We also re-analyze four previously problematic real-world case studies. We find mixtures outperform K+A methods in many cases, particularly spiked line transect data (i.e., where detectability drops rapidly at small distances) and larger sample sizes. We recommend that current standard model selection methods for distance sampling detection functions are extended to include mixture models in the candidate set.Most switching classes with primitive automorphism groups contain graphs with trivial groups
http://hdl.handle.net/10023/6429
Abstract: The operation of switching a graph Gamma with respect to a subset X of the vertex set interchanges edges and non-edges between X and its complement, leaving the rest of the graph unchanged. This is an equivalence relation on the set of graphs on a given vertex set, so we can talk about the automorphism group of a switching class of graphs. It might be thought that switching classes with many automorphisms would have the property that all their graphs also have many automorphisms. But the main theorem of this paper shows a different picture: with finitely many exceptions, if a non-trivial switching class S has primitive automorphism group, then it contains a graph whose automorphism group is trivial. We also find all the exceptional switching classes; up to complementation, there are just six.
Description: Date of Acceptance: 20/02/2015Mon, 01 Jun 2015 00:00:00 GMThttp://hdl.handle.net/10023/64292015-06-01T00:00:00ZCameron, Peter JephsonSpiga, PabloThe operation of switching a graph Gamma with respect to a subset X of the vertex set interchanges edges and non-edges between X and its complement, leaving the rest of the graph unchanged. This is an equivalence relation on the set of graphs on a given vertex set, so we can talk about the automorphism group of a switching class of graphs. It might be thought that switching classes with many automorphisms would have the property that all their graphs also have many automorphisms. But the main theorem of this paper shows a different picture: with finitely many exceptions, if a non-trivial switching class S has primitive automorphism group, then it contains a graph whose automorphism group is trivial. We also find all the exceptional switching classes; up to complementation, there are just six.Random coeffcient models for complex longitudinal data
http://hdl.handle.net/10023/6386
Abstract: Longitudinal data are common in biological research. However, real data sets vary considerably in terms of their structure and complexity and present many challenges for statistical modelling. This thesis proposes a series of methods using random coefficients for modelling two broad types of longitudinal response: normally distributed measurements and binary recapture data.
Biased inference can occur in linear mixed-effects modelling if subjects are drawn from a number of unknown sub-populations, or if the residual covariance is poorly specified. To address some of the shortcomings of previous approaches in terms of model selection and flexibility, this thesis presents methods for: (i) determining the presence of latent grouping structures using a two-step approach, involving regression splines for modelling functional random effects and mixture modelling of the fitted random effects; and (ii) flexible of modelling of the residual covariance matrix using regression splines to specify smooth and potentially non-monotonic variance and correlation functions.
Spatially explicit capture-recapture methods for estimating the density of animal populations have shown a rapid increase in popularity over recent years. However, further refinements to existing theory and fitting software are required to apply these methods in many situations. This thesis presents: (i) an analysis of recapture data from an acoustic survey of gibbons using supplementary data in the form of estimated angles to detections, (ii) the development of a multi-occasion likelihood including a model for stochastic availability using a partially observed random effect (interpreted in terms of calling behaviour in the case of gibbons), and (iii) an analysis of recapture data from a population of radio-tagged skates using a conditional likelihood that allows the density of animal activity centres to be modelled as functions of time, space and animal-level covariates.Fri, 27 Jun 2014 00:00:00 GMThttp://hdl.handle.net/10023/63862014-06-27T00:00:00ZKidney, DarrenLongitudinal data are common in biological research. However, real data sets vary considerably in terms of their structure and complexity and present many challenges for statistical modelling. This thesis proposes a series of methods using random coefficients for modelling two broad types of longitudinal response: normally distributed measurements and binary recapture data.
Biased inference can occur in linear mixed-effects modelling if subjects are drawn from a number of unknown sub-populations, or if the residual covariance is poorly specified. To address some of the shortcomings of previous approaches in terms of model selection and flexibility, this thesis presents methods for: (i) determining the presence of latent grouping structures using a two-step approach, involving regression splines for modelling functional random effects and mixture modelling of the fitted random effects; and (ii) flexible of modelling of the residual covariance matrix using regression splines to specify smooth and potentially non-monotonic variance and correlation functions.
Spatially explicit capture-recapture methods for estimating the density of animal populations have shown a rapid increase in popularity over recent years. However, further refinements to existing theory and fitting software are required to apply these methods in many situations. This thesis presents: (i) an analysis of recapture data from an acoustic survey of gibbons using supplementary data in the form of estimated angles to detections, (ii) the development of a multi-occasion likelihood including a model for stochastic availability using a partially observed random effect (interpreted in terms of calling behaviour in the case of gibbons), and (iii) an analysis of recapture data from a population of radio-tagged skates using a conditional likelihood that allows the density of animal activity centres to be modelled as functions of time, space and animal-level covariates.Statistical ecology comes of age
http://hdl.handle.net/10023/6128
Abstract: The desire to predict the consequences of global environmental change has been the driver towards more realistic models embracing the variability and uncertainties inherent in ecology. Statistical ecology has gelled over the past decade as a discipline that moves away from describing patterns towards modelling the ecological processes that generate these patterns. Following the fourth International Statistical Ecology Conference (1 –4 July 2014) in Montpellier, France, we analyse current trends in statistical ecology. Important advances in the analysis of individual movement, and in the modelling of population dynamics and species distributions, are made possible by the increasing use of hierarchical and hidden process models. Exciting research perspectives include the development of methods to interpret citizen science data and of efficient, flexible computational algorithms for model fitting. Statistical ecology has come of age: it now provides a general and mathematically rigorous framework linking ecological theory and empirical data.
Description: Date of Acceptance: 04/12/2015Wed, 24 Dec 2014 00:00:00 GMThttp://hdl.handle.net/10023/61282014-12-24T00:00:00ZGimenez, OlivierBuckland, Stephen TerrenceMorgan, Byron J. T.Bez, NicolasBertrand, SophieChoquet, RemiDray, StephaneEtienne, Marie-PierreFewster, RachelGosselin, FredericMerigot, BastienMonestiez, PascalMorales, Juan M.Mortier, FredericMunoz, FrancoisOvaskainen, OtsoPavoine, SandrinePradel, RogerSchurr, Frank M.Thomas, LenThuiller, WilfriedTrenkel, Verenade Valpine, PerryRexstad, EricThe desire to predict the consequences of global environmental change has been the driver towards more realistic models embracing the variability and uncertainties inherent in ecology. Statistical ecology has gelled over the past decade as a discipline that moves away from describing patterns towards modelling the ecological processes that generate these patterns. Following the fourth International Statistical Ecology Conference (1 –4 July 2014) in Montpellier, France, we analyse current trends in statistical ecology. Important advances in the analysis of individual movement, and in the modelling of population dynamics and species distributions, are made possible by the increasing use of hierarchical and hidden process models. Exciting research perspectives include the development of methods to interpret citizen science data and of efficient, flexible computational algorithms for model fitting. Statistical ecology has come of age: it now provides a general and mathematically rigorous framework linking ecological theory and empirical data.Inter-annual and seasonal trends in cetacean distribution, density and abundance off southern California
http://hdl.handle.net/10023/6088
Abstract: Trends in cetacean density and distribution off southern California were assessed through visual line-transect surveys during thirty-seven California Cooperative Oceanic Fisheries Investigations (CalCOFI) cruises from July 2004–November 2013. From sightings of the six most commonly encountered cetacean species, seasonal, annual and overall density estimates were calculated. Blue whales (Balaenoptera musculus), fin whales (Balaenoptera physalus) and humpback whales (Megaptera novaeangliae) were the most frequently sighted baleen whales with overall densities of 0.91/1000 km2 (CV=0.27), 2.73/1000 km2 (CV=0.19), and 1.17/1000 km2 (CV=0.21) respectively. Species specific density estimates, stratified by cruise, were analyzed using a generalized additive model to estimate long-term trends and correct for seasonal imbalances. Variances were estimated using a non-parametric bootstrap with one day of effort as the sampling unit. Blue whales were primarily observed during summer and fall while fin and humpback whales were observed year-round with peaks in density during summer and spring respectively. Short-beaked common dolphins (Delphinus delphis), Pacific white-sided dolphins (Lagenorhynchus obliquidens) and Dall’s porpoise (Phocoenoidesdalli) were the most frequently encountered small cetaceans with overall densities of 705.83/1000 km2 (CV=0.22), 51.98/1000 km2 (CV=0.27), and 21.37/1000 km2 (CV=0.19) respectively. Seasonally, short-beaked common dolphins were most abundant in winter whereas Pacific white-sided dolphins and Dall’s porpoise were most abundant during spring. There were no significant long-term changes in blue whale, fin whale, humpback whale, short-beaked common dolphin or Dall’s porpoise densities while Pacific white-sided dolphins exhibited a significant decrease in density across the ten-year study. The results from this study were fundamentally consistent with earlier studies, but provide greater temporal and seasonal resolution
Description: Funding was provided by the Chief of Naval Operations Environmental Readiness Division, the United States Navy’s Pacific Fleet, the Naval Postgraduate School Grant #N00244-11-1-027, and the Naval Facilities Engineering Command Living Marine Resources Program.Sun, 01 Feb 2015 00:00:00 GMThttp://hdl.handle.net/10023/60882015-02-01T00:00:00ZCampbell, G.S.Thomas, L.Whitaker, K.Douglas, A.B.Calambokidis, J.Hildebrand, J.A.Trends in cetacean density and distribution off southern California were assessed through visual line-transect surveys during thirty-seven California Cooperative Oceanic Fisheries Investigations (CalCOFI) cruises from July 2004–November 2013. From sightings of the six most commonly encountered cetacean species, seasonal, annual and overall density estimates were calculated. Blue whales (Balaenoptera musculus), fin whales (Balaenoptera physalus) and humpback whales (Megaptera novaeangliae) were the most frequently sighted baleen whales with overall densities of 0.91/1000 km2 (CV=0.27), 2.73/1000 km2 (CV=0.19), and 1.17/1000 km2 (CV=0.21) respectively. Species specific density estimates, stratified by cruise, were analyzed using a generalized additive model to estimate long-term trends and correct for seasonal imbalances. Variances were estimated using a non-parametric bootstrap with one day of effort as the sampling unit. Blue whales were primarily observed during summer and fall while fin and humpback whales were observed year-round with peaks in density during summer and spring respectively. Short-beaked common dolphins (Delphinus delphis), Pacific white-sided dolphins (Lagenorhynchus obliquidens) and Dall’s porpoise (Phocoenoidesdalli) were the most frequently encountered small cetaceans with overall densities of 705.83/1000 km2 (CV=0.22), 51.98/1000 km2 (CV=0.27), and 21.37/1000 km2 (CV=0.19) respectively. Seasonally, short-beaked common dolphins were most abundant in winter whereas Pacific white-sided dolphins and Dall’s porpoise were most abundant during spring. There were no significant long-term changes in blue whale, fin whale, humpback whale, short-beaked common dolphin or Dall’s porpoise densities while Pacific white-sided dolphins exhibited a significant decrease in density across the ten-year study. The results from this study were fundamentally consistent with earlier studies, but provide greater temporal and seasonal resolutionHigher biodiversity is required to sustain multiple ecosystem processes across temperature regimes
http://hdl.handle.net/10023/5975
Abstract: Biodiversity loss is occurring rapidly worldwide, yet it is uncertain whether few or many species are required to sustain ecosystem functioning in the face of environmental change. The importance of biodiversity might be enhanced when multiple ecosystem processes (termed multifunctionality) and environmental contexts are considered, yet no studies have quantified this explicitly to date. We measured five key processes and their combined multifunctionality at three temperatures (5, 10 and 15 °C) in freshwater aquaria containing different animal assemblages (1-4 benthic macroinvertebrate species). For single processes, biodiversity effects were weak and were best predicted by additive-based models, i.e. polyculture performances represented the sum of their monoculture parts. There were, however, significant effects of biodiversity on multifunctionality at the low and the high (but not the intermediate) temperature. Variation in the contribution of species to processes across temperatures meant that greater biodiversity was required to sustain multifunctionality across different temperatures than was the case for single processes. This suggests that previous studies might have underestimated the importance of biodiversity in sustaining ecosystem functioning in a changing environment.
Description: The authors thank the Natural Environment Research Council for financial support awarded to G. W. (Grant reference: NE/D013305/1) that funded D. M. P.'s research. Accepted 11 July 2014.Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10023/59752015-01-01T00:00:00ZPerkins, D.M.Bailey, R.A.Dossena, M.Gamfeldt, L.Reiss, J.Trimmer, M.Woodward, G.Biodiversity loss is occurring rapidly worldwide, yet it is uncertain whether few or many species are required to sustain ecosystem functioning in the face of environmental change. The importance of biodiversity might be enhanced when multiple ecosystem processes (termed multifunctionality) and environmental contexts are considered, yet no studies have quantified this explicitly to date. We measured five key processes and their combined multifunctionality at three temperatures (5, 10 and 15 °C) in freshwater aquaria containing different animal assemblages (1-4 benthic macroinvertebrate species). For single processes, biodiversity effects were weak and were best predicted by additive-based models, i.e. polyculture performances represented the sum of their monoculture parts. There were, however, significant effects of biodiversity on multifunctionality at the low and the high (but not the intermediate) temperature. Variation in the contribution of species to processes across temperatures meant that greater biodiversity was required to sustain multifunctionality across different temperatures than was the case for single processes. This suggests that previous studies might have underestimated the importance of biodiversity in sustaining ecosystem functioning in a changing environment.A unifying model for capture-recapture and distance sampling surveys of wildlife populations
http://hdl.handle.net/10023/5797
Abstract: Spatially explicit capture-recapture (SECR) methods extend traditional capture-recapture methods for estimating population density by using information contained in the location of traps. The The central feature of the improvement is estimation from the locations of traps at which animals were and were not captured to estimate of the distance over which animals are susceptible to capture. We show that standard SECR models are a special case of a more general class of model in which animal detection is not certain, but some information is available about the location of detected animals. The model class accommodates a range of spatial data types and includes as a special case mark-recapture distance sampling, where distances to detected animals are recorded by multiple observers. Other examples of additional information that can be included are bearing to detected animals, strength of acoustic signals received from detected animals, and time of arrival of acoustic signals at detectors. Errors in variables are easily incorporated. We illustrate the versatility of the model and method through a number of applications, in each case using real and simulated data, and comparing our results with those from previous studies where these are available.
Description: Funding: Part-funded by Fundacao Nacional para a Cienca e Technologia, Portugal (FCT) under the project PEst OE/MAT/UI0006/2011 (Marques) and the UK Engineering and Physical Sciences Research Council EP/I000917/1Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10023/57972015-01-01T00:00:00ZBorchers, D. L.Stevenson, B.C.Kidney, D.Thomas, L.Marques, T.A.Spatially explicit capture-recapture (SECR) methods extend traditional capture-recapture methods for estimating population density by using information contained in the location of traps. The The central feature of the improvement is estimation from the locations of traps at which animals were and were not captured to estimate of the distance over which animals are susceptible to capture. We show that standard SECR models are a special case of a more general class of model in which animal detection is not certain, but some information is available about the location of detected animals. The model class accommodates a range of spatial data types and includes as a special case mark-recapture distance sampling, where distances to detected animals are recorded by multiple observers. Other examples of additional information that can be included are bearing to detected animals, strength of acoustic signals received from detected animals, and time of arrival of acoustic signals at detectors. Errors in variables are easily incorporated. We illustrate the versatility of the model and method through a number of applications, in each case using real and simulated data, and comparing our results with those from previous studies where these are available.Acoustic and foraging behavior of a Baird’s beaked whale, Berardius bairdii, exposed to simulated sonar
http://hdl.handle.net/10023/5787
Abstract: Beaked whales are hypothesized to be particularly sensitive to anthropogenic noise, based on previous strandings and limited experimental and observational data. However, few species have been studied in detail. We describe the underwater behavior of a Baird's beaked whale (Berardius bairdii) from the first deployment of a multi-sensor acoustic tag on this species. The animal exhibited shallow (23 ± 15 m max depth), intermediate (324 ± 49 m), and deep (1138 ± 243 m) dives. Echolocation clicks were produced with a mean inter-click interval of approximately 300 ms and peak frequency of 25 kHz. Two deep dives included presumed foraging behavior, with echolocation pulsed sounds (presumed prey capture attempts) associated with increased maneuvering, and sustained inverted swimming during the bottom phase of the dive. A controlled exposure to simulated mid-frequency active sonar (3.5–4 kHz) was conducted 4 hours after tag deployment, and within 3 minutes of exposure onset, the tagged whale increased swim speed and body movement, and continued to show unusual dive behavior for each of its next three dives, one of each type. These are the first data on the acoustic foraging behavior in this largest beaked whale species, and the first experimental demonstration of a response to simulated sonar.
Description: Research was supported by the US Navy Chief of Naval Operations, Environmental Readiness Program, the Office of Naval Research, the Naval Postgraduate School, and the National Research Council.Thu, 13 Nov 2014 00:00:00 GMThttp://hdl.handle.net/10023/57872014-11-13T00:00:00ZStimpert, AlisonDe Ruiter, Stacy LynnSouthall, BrandonMoretti, DavidFalcone, ErinGoldbogen, JeremyFriedlaender, AriSchorr, GregCalambokidis, JohnBeaked whales are hypothesized to be particularly sensitive to anthropogenic noise, based on previous strandings and limited experimental and observational data. However, few species have been studied in detail. We describe the underwater behavior of a Baird's beaked whale (Berardius bairdii) from the first deployment of a multi-sensor acoustic tag on this species. The animal exhibited shallow (23 ± 15 m max depth), intermediate (324 ± 49 m), and deep (1138 ± 243 m) dives. Echolocation clicks were produced with a mean inter-click interval of approximately 300 ms and peak frequency of 25 kHz. Two deep dives included presumed foraging behavior, with echolocation pulsed sounds (presumed prey capture attempts) associated with increased maneuvering, and sustained inverted swimming during the bottom phase of the dive. A controlled exposure to simulated mid-frequency active sonar (3.5–4 kHz) was conducted 4 hours after tag deployment, and within 3 minutes of exposure onset, the tagged whale increased swim speed and body movement, and continued to show unusual dive behavior for each of its next three dives, one of each type. These are the first data on the acoustic foraging behavior in this largest beaked whale species, and the first experimental demonstration of a response to simulated sonar.Optimal cross-over designs for full interaction models
http://hdl.handle.net/10023/5768
Abstract: We consider repeated measurement designs when a residual or carry-over effect may be present in at most one later period. Since assuming an additive model may be unrealistic for some applications and leads to biased estimation of treatment effects, we consider a model with interactions between carry-over and direct treatment effects. When the aim of the experiment is to study the effects of a treatment used alone, we obtain universally optimal approximate designs. We also propose some efficient designs with a reduced number of subjects.
Description: July 2014Sat, 01 Nov 2014 00:00:00 GMThttp://hdl.handle.net/10023/57682014-11-01T00:00:00ZBailey, Rosemary AnneDruilhet, PierreWe consider repeated measurement designs when a residual or carry-over effect may be present in at most one later period. Since assuming an additive model may be unrealistic for some applications and leads to biased estimation of treatment effects, we consider a model with interactions between carry-over and direct treatment effects. When the aim of the experiment is to study the effects of a treatment used alone, we obtain universally optimal approximate designs. We also propose some efficient designs with a reduced number of subjects.Computing in permutation groups without memory
http://hdl.handle.net/10023/5727
Abstract: Memoryless computation is a new technique to compute any function of a set of registers by updating one register at a time while using no memory. Its aim is to emulate how computations are performed in modern cores, since they typically involve updates of single registers. The memoryless computation model can be fully expressed in terms of transformation semigroups, or in the case of bijective functions, permutation groups. In this paper, we consider how efficiently permutations can be computed without memory. We determine the minimum number of basic updates required to compute any permutation, or any even permutation. The small number of required instructions shows that very small instruction sets could be encoded on cores to perform memoryless computation. We then start looking at a possible compromise between the size of the instruction set and the length of the resulting programs. We consider updates only involving a limited number of registers. In particular, we show that binary instructions are not enough to compute all permutations without memory when the alphabet size is even. These results, though expressed as properties of special generating sets of the symmetric or alternating groups, provide guidelines on the implementation of memoryless computation.
Description: Funding: UK Engineering and Physical Sciences Research Council (EP/K033956/1)Sun, 02 Nov 2014 00:00:00 GMThttp://hdl.handle.net/10023/57272014-11-02T00:00:00ZCameron, Peter JephsonFairbairn, BenGadouleau, MaximilienMemoryless computation is a new technique to compute any function of a set of registers by updating one register at a time while using no memory. Its aim is to emulate how computations are performed in modern cores, since they typically involve updates of single registers. The memoryless computation model can be fully expressed in terms of transformation semigroups, or in the case of bijective functions, permutation groups. In this paper, we consider how efficiently permutations can be computed without memory. We determine the minimum number of basic updates required to compute any permutation, or any even permutation. The small number of required instructions shows that very small instruction sets could be encoded on cores to perform memoryless computation. We then start looking at a possible compromise between the size of the instruction set and the length of the resulting programs. We consider updates only involving a limited number of registers. In particular, we show that binary instructions are not enough to compute all permutations without memory when the alphabet size is even. These results, though expressed as properties of special generating sets of the symmetric or alternating groups, provide guidelines on the implementation of memoryless computation.Computing in matrix groups without memory
http://hdl.handle.net/10023/5715
Abstract: Memoryless computation is a novel means of computing any function of a set of registers by updating one register at a time while using no memory. We aim to emulate how computations are performed on modern cores, since they typically involve updates of single registers. The computation model of memoryless computation can be fully expressed in terms of transformation semigroups, or in the case of bijective functions, permutation groups. In this paper, we view registers as elements of a finite field and we compute linear permutations without memory. We first determine the maximum complexity of a linear function when only linear instructions are allowed. We also determine which linear functions are hardest to compute when the field in question is the binary field and the number of registers is even. Secondly, we investigate some matrix groups, thus showing that the special linear group is internally computable but not fast. Thirdly, we determine the smallest set of instructions required to generate the special and general linear groups. These results are important for memoryless computation, for they show that linear functions can be computed very fast or that very few instructions are needed to compute any linear function. They thus indicate new advantages of using memoryless computation.
Description: Funding: UK Engineering and Physical Sciences Research Council award EP/K033956/1Sun, 02 Nov 2014 00:00:00 GMThttp://hdl.handle.net/10023/57152014-11-02T00:00:00ZCameron, Peter JephsonFairbairn, BenGadouleau, MaximilienMemoryless computation is a novel means of computing any function of a set of registers by updating one register at a time while using no memory. We aim to emulate how computations are performed on modern cores, since they typically involve updates of single registers. The computation model of memoryless computation can be fully expressed in terms of transformation semigroups, or in the case of bijective functions, permutation groups. In this paper, we view registers as elements of a finite field and we compute linear permutations without memory. We first determine the maximum complexity of a linear function when only linear instructions are allowed. We also determine which linear functions are hardest to compute when the field in question is the binary field and the number of registers is even. Secondly, we investigate some matrix groups, thus showing that the special linear group is internally computable but not fast. Thirdly, we determine the smallest set of instructions required to generate the special and general linear groups. These results are important for memoryless computation, for they show that linear functions can be computed very fast or that very few instructions are needed to compute any linear function. They thus indicate new advantages of using memoryless computation.Most primitive groups are full automorphism groups of edge-transitive hypergraphs
http://hdl.handle.net/10023/5580
Abstract: We prove that, for a primitive permutation group G acting on a set of size n, other than the alternating group, the probability that Aut(X,YG) = G for a random subset Y of X, tends to 1 as n tends to infinity. So the property of the title holds for all primitive groups except the alternating groups and finitely many others. This answers a question of M. Klin. Moreover, we give an upper bound n1/2+ε for the minimum size of the edges in such a hypergraph. This is essentially best possible.Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10023/55802015-01-01T00:00:00ZBabai, LaszloCameron, Peter JephsonWe prove that, for a primitive permutation group G acting on a set of size n, other than the alternating group, the probability that Aut(X,YG) = G for a random subset Y of X, tends to 1 as n tends to infinity. So the property of the title holds for all primitive groups except the alternating groups and finitely many others. This answers a question of M. Klin. Moreover, we give an upper bound n1/2+ε for the minimum size of the edges in such a hypergraph. This is essentially best possible.The effects of acoustic misclassification on cetacean species abundance estimation
http://hdl.handle.net/10023/5163
Abstract: To estimate the density or abundance of a cetacean species using acoustic detection data, it is necessary to correctly identify the species that are detected. Developing an automated species classifier with 100% correct classification rate for any species is likely to stay out of reach. It is therefore necessary to consider the effect of misidentified detections on the number of observed data and consequently on abundance or density estimation, and develop methods to cope with these misidentifications. If misclassification rates are known, it is possible to estimate the true numbers of detected calls without bias. However, misclassification and uncertainties in the level of misclassification increase the variance of the estimates. If the true numbers of calls from different species are similar, then a small amount of misclassification between species and a small amount of uncertainty around the classification probabilities does not have an overly detrimental effect on the overall variance. However, if there is a difference in the encounter rate between species calls and/or a large amount of uncertainty in misclassification rates, then the variance of the estimates becomes very large and this dramatically increases the variance of the final abundance estimate.
Description: This work was funded through the Natural Environment Research Council and SMRU Ltd.Wed, 25 Dec 2013 00:00:00 GMThttp://hdl.handle.net/10023/51632013-12-25T00:00:00ZCaillat, Marjolaine AnnieThomas, LenGillespie, Douglas MichaelTo estimate the density or abundance of a cetacean species using acoustic detection data, it is necessary to correctly identify the species that are detected. Developing an automated species classifier with 100% correct classification rate for any species is likely to stay out of reach. It is therefore necessary to consider the effect of misidentified detections on the number of observed data and consequently on abundance or density estimation, and develop methods to cope with these misidentifications. If misclassification rates are known, it is possible to estimate the true numbers of detected calls without bias. However, misclassification and uncertainties in the level of misclassification increase the variance of the estimates. If the true numbers of calls from different species are similar, then a small amount of misclassification between species and a small amount of uncertainty around the classification probabilities does not have an overly detrimental effect on the overall variance. However, if there is a difference in the encounter rate between species calls and/or a large amount of uncertainty in misclassification rates, then the variance of the estimates becomes very large and this dramatically increases the variance of the final abundance estimate.Dose-response relationships for the onset of avoidance of sonar by free-ranging killer whales
http://hdl.handle.net/10023/5092
Abstract: Eight experimentally controlled exposures to 1−2 kHz or 6−7 kHz sonar signals were conducted with four killer whale groups. The source level and proximity of the source were increased during each exposure in order to reveal response thresholds. Detailed inspection of movements during each exposure session revealed sustained changes in speed and travel direction judged to be avoidance responses during six of eight sessions. Following methods developed for Phase-I clinical trials in human medicine, response thresholds ranging from 94 to 164 dB re 1 μPa received sound pressure level (SPL) were fitted to Bayesian dose-response functions. Thresholds did not consistently differ by sonar frequency or whether a group had previously been exposed, with a mean SPL response threshold of 142 ± 15 dB (mean ± s.d.). High levels of between- and within-individual variability were identified, indicating that thresholds depended upon other undefined contextual variables. The dose-response functions indicate that some killer whales started to avoid sonar at received SPL below thresholds assumed by the U.S. Navy. The predicted extent of habitat over which avoidance reactions occur depends upon whether whales responded to proximity or received SPL of the sonar or both, but was large enough to raise concerns about biological consequences to the whales.
Description: The authors acknowledge the support of the MASTS pooling initiative (The Marine Alliance for Science and Technology for Scotland) in the completion of this study. MASTS is funded by the Scottish Funding Council (grant reference HR09011) and contributing institutions.Sat, 01 Feb 2014 00:00:00 GMThttp://hdl.handle.net/10023/50922014-02-01T00:00:00ZMiller, PatrickAntunes, Ricardo NunoWensveen, Paulus JacobusSamarra, Filipa Isabel PereiraAlves, Ana Catarina De CarvalhoTyack, Peter LloydKvadsheim, Petter H.Kleivane, LarsLam, Frans-Peter A.Ainslie, Michael A.Thomas, LenEight experimentally controlled exposures to 1−2 kHz or 6−7 kHz sonar signals were conducted with four killer whale groups. The source level and proximity of the source were increased during each exposure in order to reveal response thresholds. Detailed inspection of movements during each exposure session revealed sustained changes in speed and travel direction judged to be avoidance responses during six of eight sessions. Following methods developed for Phase-I clinical trials in human medicine, response thresholds ranging from 94 to 164 dB re 1 μPa received sound pressure level (SPL) were fitted to Bayesian dose-response functions. Thresholds did not consistently differ by sonar frequency or whether a group had previously been exposed, with a mean SPL response threshold of 142 ± 15 dB (mean ± s.d.). High levels of between- and within-individual variability were identified, indicating that thresholds depended upon other undefined contextual variables. The dose-response functions indicate that some killer whales started to avoid sonar at received SPL below thresholds assumed by the U.S. Navy. The predicted extent of habitat over which avoidance reactions occur depends upon whether whales responded to proximity or received SPL of the sonar or both, but was large enough to raise concerns about biological consequences to the whales.Using hidden Markov models to deal with availability bias on line transect surveys
http://hdl.handle.net/10023/5017
Abstract: We develop estimators for line transect surveys of animals that are stochastically unavailable for detection while within detection range. The detection process is formulated as a hidden Markov model with a binary state-dependent observation model that depends on both perpendicular and forward distances. This provides a parametric method of dealing with availability bias when estimates of availability process parameters are available even if series of availability events themselves are not. We apply the estimators to an aerial and a shipboard survey of whales, and investigate their properties by simulation. They are shown to be more general and more flexible than existing estimators based on parametric models of the availability process. We also find that methods using availability correction factors can be very biased when surveys are not close to being instantaneous, as can estimators that assume temporal independence in availability when there is temporal dependence.
Description: This work was supported by EPSRC grant EP/I000917/1Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10023/50172013-01-01T00:00:00ZBorchers, David LouisZucchini, WalterHeide-Jørgensen, M.P.Cañadas, A.Langrock, RolandWe develop estimators for line transect surveys of animals that are stochastically unavailable for detection while within detection range. The detection process is formulated as a hidden Markov model with a binary state-dependent observation model that depends on both perpendicular and forward distances. This provides a parametric method of dealing with availability bias when estimates of availability process parameters are available even if series of availability events themselves are not. We apply the estimators to an aerial and a shipboard survey of whales, and investigate their properties by simulation. They are shown to be more general and more flexible than existing estimators based on parametric models of the availability process. We also find that methods using availability correction factors can be very biased when surveys are not close to being instantaneous, as can estimators that assume temporal independence in availability when there is temporal dependence.An approximate Bayesian method applied to estimating the trajectories of four British grey seal (Halichoerus grypus) populations from pup counts.
http://hdl.handle.net/10023/4688
Abstract: 1. For British grey seals, as with many pinniped species, population monitoring is implemented by aerial surveys of pups at breeding colonies. Scaling pup counts up to population estimates requires assumptions about population structure; this is straightforward when populations are growing exponentially, but not when growth slows, since it is unclear whether density dependence affects pup survival or fecundity. 2. We present an approximate Bayesian method for fitting pup trajectories, estimating adult population size and investigating alternative biological models. The method is equivalent to fitting a density dependent Leslie matrix model, within a Bayesian framework, but with the forms of the density dependent effects as outputs rather than assumptions. 3. This approach requires fewer assumptions than the state space models currently used, and produces similar estimates. The simplifications made the models easier to fit, reducing their computational intensity and allowing regional differences in demographic parameters to be considered. 4. The approach is not restricted to situations where only a single component of the population is observable, but, particularly in those cases, provides a practical method for extracting information from limited datasets. 5. We discuss the potential and limitations of the method and suggest that this approach provides a useful tool for at least the preliminary analysis of similar datasets.Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10023/46882011-01-01T00:00:00ZLonergan, Michael EdwardThompson, DavidThomas, Leonard JosephDuck, Callan David1. For British grey seals, as with many pinniped species, population monitoring is implemented by aerial surveys of pups at breeding colonies. Scaling pup counts up to population estimates requires assumptions about population structure; this is straightforward when populations are growing exponentially, but not when growth slows, since it is unclear whether density dependence affects pup survival or fecundity. 2. We present an approximate Bayesian method for fitting pup trajectories, estimating adult population size and investigating alternative biological models. The method is equivalent to fitting a density dependent Leslie matrix model, within a Bayesian framework, but with the forms of the density dependent effects as outputs rather than assumptions. 3. This approach requires fewer assumptions than the state space models currently used, and produces similar estimates. The simplifications made the models easier to fit, reducing their computational intensity and allowing regional differences in demographic parameters to be considered. 4. The approach is not restricted to situations where only a single component of the population is observable, but, particularly in those cases, provides a practical method for extracting information from limited datasets. 5. We discuss the potential and limitations of the method and suggest that this approach provides a useful tool for at least the preliminary analysis of similar datasets.Modelling group dynamic animal movement
http://hdl.handle.net/10023/4555
Abstract: 1). Group dynamics are a fundamental aspect of many species' movements. The need to adequately model individuals' interactions with other group members has been recognized, particularly in order to differentiate the role of social forces in individual movement from environmental factors. However, to date, practical statistical methods, which can include group dynamics in animal movement models, have been lacking. 2). We consider a flexible modelling framework that distinguishes a group-level model, describing the movement of the group's centre, and an individual-level model, such that each individual makes its movement decisions relative to the group centroid. The basic idea is framed within the flexible class of hidden Markov models, extending previous work on modelling animal movement by means of multistate random walks. 3). While in simulation experiments parameter estimators exhibit some bias in non-ideal scenarios, we show that generally the estimation of models of this type is both feasible and ecologically informative. 4). We illustrate the approach using real movement data from 11 reindeer (Rangifer tarandus). Results indicate a directional bias towards a group centroid for reindeer in an encamped state. Though the attraction to the group centroid is relatively weak, our model successfully captures group-influenced movement dynamics. Specifically, as compared to a regular mixture of correlated random walks, the group dynamic model more accurately predicts the non-diffusive behaviour of a cohesive mobile group. 5). As technology continues to develop, it will become easier and less expensive to tag multiple individuals within a group in order to follow their movements. Our work provides a first inferential framework for understanding the relative influences of individual versus group-level movement decisions. This framework can be extended to include covariates corresponding to environmental influences or body condition. As such, this framework allows for a broader understanding of the many internal and external factors that can influence an individual's movement.Sat, 01 Feb 2014 00:00:00 GMThttp://hdl.handle.net/10023/45552014-02-01T00:00:00ZLangrock, RolandHopcraft, GrantBlackwell, PaulGoodall, VictoriaKing, RuthNiu, MuPatterson, TobyPedersen, MartinSkarin, AnnaSchick, Robert Schilling1). Group dynamics are a fundamental aspect of many species' movements. The need to adequately model individuals' interactions with other group members has been recognized, particularly in order to differentiate the role of social forces in individual movement from environmental factors. However, to date, practical statistical methods, which can include group dynamics in animal movement models, have been lacking. 2). We consider a flexible modelling framework that distinguishes a group-level model, describing the movement of the group's centre, and an individual-level model, such that each individual makes its movement decisions relative to the group centroid. The basic idea is framed within the flexible class of hidden Markov models, extending previous work on modelling animal movement by means of multistate random walks. 3). While in simulation experiments parameter estimators exhibit some bias in non-ideal scenarios, we show that generally the estimation of models of this type is both feasible and ecologically informative. 4). We illustrate the approach using real movement data from 11 reindeer (Rangifer tarandus). Results indicate a directional bias towards a group centroid for reindeer in an encamped state. Though the attraction to the group centroid is relatively weak, our model successfully captures group-influenced movement dynamics. Specifically, as compared to a regular mixture of correlated random walks, the group dynamic model more accurately predicts the non-diffusive behaviour of a cohesive mobile group. 5). As technology continues to develop, it will become easier and less expensive to tag multiple individuals within a group in order to follow their movements. Our work provides a first inferential framework for understanding the relative influences of individual versus group-level movement decisions. This framework can be extended to include covariates corresponding to environmental influences or body condition. As such, this framework allows for a broader understanding of the many internal and external factors that can influence an individual's movement.A risk function for behavioral disruption of Blainville’s beaked whales (Mesoplodon densirostris) from mid-frequency active sonar
http://hdl.handle.net/10023/4522
Abstract: There is increasing concern about the potential effects of noise pollution on marine life in the world’s oceans. For marine mammals, anthropogenic sounds may cause behavioral disruption, and this can be quantified using a risk function that relates sound exposure to a measured behavioral response. Beaked whales are a taxon of deep diving whales that may be particularly susceptible to naval sonar as the species has been associated with sonar-related mass stranding events. Here we derive the first empirical risk function for Blainville’s beaked whales (Mesoplodon densirostris) by combining in situ data from passive acoustic monitoring of animal vocalizations and navy sonar operations with precise ship tracks and sound field modeling. The hydrophone array at the Atlantic Undersea Test and Evaluation Center, Bahamas, was used to locate vocalizing groups of Blainville’s beaked whales and identify sonar transmissions before, during, and after Mid-Frequency Active (MFA) sonar operations. Sonar transmission times and source levels were combined with ship tracks using a sound propagation model to estimate the received level (RL) at each hydrophone. A generalized additive model was fitted to data to model the presence or absence of the start of foraging dives in 30-minute periods as a function of the corresponding sonar RL at the hydrophone closest to the center of each group. This model was then used to construct a risk function that can be used to estimate the probability of a behavioral change (cessation of foraging) the individual members of a Blainville’s beaked whale population might experience as a function of sonar RL. The function predicts a 0.5 probability of disturbance at a RL of 150dBrms re µPa (CI: 144 to 155) This is 15dB lower than the level used historically by the US Navy in their risk assessments but 10 dB higher than the current 140 dB step-functionWed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10023/45222014-01-01T00:00:00ZMoretti, DavidThomas, LenMarques, Tiago A.Harwood, JohnDilley, AshleyNeales, BertShaffer, JessicaMccarthy, ENew, Leslie FrancesJarvis, SMorrissey, RonThere is increasing concern about the potential effects of noise pollution on marine life in the world’s oceans. For marine mammals, anthropogenic sounds may cause behavioral disruption, and this can be quantified using a risk function that relates sound exposure to a measured behavioral response. Beaked whales are a taxon of deep diving whales that may be particularly susceptible to naval sonar as the species has been associated with sonar-related mass stranding events. Here we derive the first empirical risk function for Blainville’s beaked whales (Mesoplodon densirostris) by combining in situ data from passive acoustic monitoring of animal vocalizations and navy sonar operations with precise ship tracks and sound field modeling. The hydrophone array at the Atlantic Undersea Test and Evaluation Center, Bahamas, was used to locate vocalizing groups of Blainville’s beaked whales and identify sonar transmissions before, during, and after Mid-Frequency Active (MFA) sonar operations. Sonar transmission times and source levels were combined with ship tracks using a sound propagation model to estimate the received level (RL) at each hydrophone. A generalized additive model was fitted to data to model the presence or absence of the start of foraging dives in 30-minute periods as a function of the corresponding sonar RL at the hydrophone closest to the center of each group. This model was then used to construct a risk function that can be used to estimate the probability of a behavioral change (cessation of foraging) the individual members of a Blainville’s beaked whale population might experience as a function of sonar RL. The function predicts a 0.5 probability of disturbance at a RL of 150dBrms re µPa (CI: 144 to 155) This is 15dB lower than the level used historically by the US Navy in their risk assessments but 10 dB higher than the current 140 dB step-functionNovel methods for species distribution mapping including spatial models in complex regions
http://hdl.handle.net/10023/4514
Abstract: Species Distribution Modelling (SDM) plays a key role in a number of biological applications: assessment of temporal trends in distribution, environmental impact assessment and spatial conservation planning. From a statistical perspective, this thesis develops two methods for increasing the accuracy and reliability of maps of density surfaces and provides a solution to the problem of how to collate multiple density maps of the same region, obtained from differing sources. From a biological perspective, these statistical methods are used to analyse two marine mammal datasets to produce accurate maps for use in spatial conservation planning and temporal trend assessment.
The first new method, Complex Region Spatial Smoother [CReSS; Scott-Hayward et al., 2013], improves smoothing in areas where the real distance an animal must travel (`as the animal swims') between two points may be greater than the straight line distance between them, a problem that occurs in complex domains with coastline or islands. CReSS uses estimates of the geodesic distance between points, model averaging and local radial smoothing. Simulation is used to compare its performance with other traditional and recently-developed smoothing techniques: Thin Plate Splines (TPS, Harder and Desmarais [1972]), Geodesic Low rank TPS (GLTPS; Wang and Ranalli [2007]) and the Soap lm smoother (SOAP; Wood et al. [2008]). GLTPS cannot be used in areas with islands and SOAP can be very hard to parametrise. CReSS outperforms all of the other methods on a range of simulations, based on their fit to the underlying function as measured by mean squared error, particularly for sparse data sets.
Smoothing functions need to be flexible when they are used to model density surfaces that are highly heterogeneous, in order to avoid biases due to under- or over-fitting. This issue was addressed using an adaptation of a Spatially Adaptive Local Smoothing Algorithm (SALSA, Walker et al. [2010]) in combination with the CReSS method (CReSS-SALSA2D). Unlike traditional methods, such as Generalised Additive Modelling, the adaptive knot selection approach used in SALSA2D naturally accommodates local changes in the smoothness of the density surface that is being modelled. At the time of writing, there are no other methods available to deal with this issue in topographically complex regions. Simulation results show that CReSS-SALSA2D performs better than CReSS (based on MSE scores), except at very high noise levels where there is an issue with over-fitting.
There is an increasing need for a facility to combine multiple density surface maps of individual species in order to make best use of meta-databases, to maintain existing maps, and to extend their geographical coverage. This thesis develops a framework and methods for combining species distribution maps as new information becomes available. The methods use Bayes Theorem to combine density surfaces, taking account of the levels of precision associated with the different sets of estimates, and kernel smoothing to alleviate artefacts that may be created where pairs of surfaces join. The methods were used as part of an algorithm (the Dynamic Cetacean Abundance Predictor) designed for BAE Systems to aid in risk mitigation for naval exercises.
Two case studies show the capabilities of CReSS and CReSS-SALSA2D when applied to real ecological data. In the first case study, CReSS was used in a Generalised Estimating Equation framework to identify a candidate Marine Protected Area for the Southern Resident Killer Whale population to the south of San Juan Island, off the Pacific coast of the United States. In the second case study, changes in the spatial and temporal distribution of harbour porpoise and minke whale in north-western European waters over a period of 17 years (1994-2010) were modelled. CReSS and CReSS-SALSA2D performed well in a large, topographically complex study area. Based on simulation results, maps produced using these methods are more accurate than if a traditional GAM-based method is used. The resulting maps identified particularly high densities of both harbour porpoise and minke whale in an area off the west coast of Scotland in 2010, that might be a candidate for inclusion into the
Scottish network of Nature Conservation Marine Protected Areas.Tue, 05 Nov 2013 00:00:00 GMThttp://hdl.handle.net/10023/45142013-11-05T00:00:00ZScott-Hayward, Lindesay Alexandra SarahSpecies Distribution Modelling (SDM) plays a key role in a number of biological applications: assessment of temporal trends in distribution, environmental impact assessment and spatial conservation planning. From a statistical perspective, this thesis develops two methods for increasing the accuracy and reliability of maps of density surfaces and provides a solution to the problem of how to collate multiple density maps of the same region, obtained from differing sources. From a biological perspective, these statistical methods are used to analyse two marine mammal datasets to produce accurate maps for use in spatial conservation planning and temporal trend assessment.
The first new method, Complex Region Spatial Smoother [CReSS; Scott-Hayward et al., 2013], improves smoothing in areas where the real distance an animal must travel (`as the animal swims') between two points may be greater than the straight line distance between them, a problem that occurs in complex domains with coastline or islands. CReSS uses estimates of the geodesic distance between points, model averaging and local radial smoothing. Simulation is used to compare its performance with other traditional and recently-developed smoothing techniques: Thin Plate Splines (TPS, Harder and Desmarais [1972]), Geodesic Low rank TPS (GLTPS; Wang and Ranalli [2007]) and the Soap lm smoother (SOAP; Wood et al. [2008]). GLTPS cannot be used in areas with islands and SOAP can be very hard to parametrise. CReSS outperforms all of the other methods on a range of simulations, based on their fit to the underlying function as measured by mean squared error, particularly for sparse data sets.
Smoothing functions need to be flexible when they are used to model density surfaces that are highly heterogeneous, in order to avoid biases due to under- or over-fitting. This issue was addressed using an adaptation of a Spatially Adaptive Local Smoothing Algorithm (SALSA, Walker et al. [2010]) in combination with the CReSS method (CReSS-SALSA2D). Unlike traditional methods, such as Generalised Additive Modelling, the adaptive knot selection approach used in SALSA2D naturally accommodates local changes in the smoothness of the density surface that is being modelled. At the time of writing, there are no other methods available to deal with this issue in topographically complex regions. Simulation results show that CReSS-SALSA2D performs better than CReSS (based on MSE scores), except at very high noise levels where there is an issue with over-fitting.
There is an increasing need for a facility to combine multiple density surface maps of individual species in order to make best use of meta-databases, to maintain existing maps, and to extend their geographical coverage. This thesis develops a framework and methods for combining species distribution maps as new information becomes available. The methods use Bayes Theorem to combine density surfaces, taking account of the levels of precision associated with the different sets of estimates, and kernel smoothing to alleviate artefacts that may be created where pairs of surfaces join. The methods were used as part of an algorithm (the Dynamic Cetacean Abundance Predictor) designed for BAE Systems to aid in risk mitigation for naval exercises.
Two case studies show the capabilities of CReSS and CReSS-SALSA2D when applied to real ecological data. In the first case study, CReSS was used in a Generalised Estimating Equation framework to identify a candidate Marine Protected Area for the Southern Resident Killer Whale population to the south of San Juan Island, off the Pacific coast of the United States. In the second case study, changes in the spatial and temporal distribution of harbour porpoise and minke whale in north-western European waters over a period of 17 years (1994-2010) were modelled. CReSS and CReSS-SALSA2D performed well in a large, topographically complex study area. Based on simulation results, maps produced using these methods are more accurate than if a traditional GAM-based method is used. The resulting maps identified particularly high densities of both harbour porpoise and minke whale in an area off the west coast of Scotland in 2010, that might be a candidate for inclusion into the
Scottish network of Nature Conservation Marine Protected Areas.Modelling catch sampling uncertainty in fisheries stock assessment : the Atlantic-Iberian sardine case
http://hdl.handle.net/10023/4474
Abstract: The statistical assessment of harvested fish populations, such as the Atlantic-Iberian sardine (AIS)
stock, needs to deal with uncertainties inherent in fisheries systems. Uncertainties arising from
sampling errors and stochasticity in stock dynamics must be incorporated in stock assessment
models so that management decisions are based on realistic evaluation of the uncertainty about
the status of the stock. The main goal of this study is to develop a stock assessment framework
that accounts for some of the uncertainties associated with the AIS stock that are currently not
integrated into stock assessment models. In particular, it focuses on accounting for the uncertainty
arising from the catch data sampling process.
The central innovation the thesis is the development of a Bayesian integrated stock assessment
(ISA) model, in which an observation model explicitly links stock dynamics parameters
with statistical models for the various types of data observed from catches of the AIS stock.
This allows for systematic and statistically consistent propagation of the uncertainty inherent in
the catch sampling process across the whole stock assessment model, through to estimates of
biomass and stock parameters. The method is tested by simulations and found to provide reliable
and accurate estimates of stock parameters and associated uncertainty, while also outperforming
existing designed-based and model-based estimation approaches.
The method is computationally very demanding and this is an obstacle to its adoption
by fisheries bodies. Once this obstacle is overcame, the ISA modelling framework developed
and presented in this thesis could provide an important contribution to the improvement in the
evaluation of uncertainty in fisheries stock assessments, not only of the AIS stock, but of any other
fish stock with similar data and dynamics structure. Furthermore, the models developed in this
study establish a solid conceptual platform to allow future development of more complex models
of fish population dynamics.Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10023/44742013-01-01T00:00:00ZCaneco, BrunoThe statistical assessment of harvested fish populations, such as the Atlantic-Iberian sardine (AIS)
stock, needs to deal with uncertainties inherent in fisheries systems. Uncertainties arising from
sampling errors and stochasticity in stock dynamics must be incorporated in stock assessment
models so that management decisions are based on realistic evaluation of the uncertainty about
the status of the stock. The main goal of this study is to develop a stock assessment framework
that accounts for some of the uncertainties associated with the AIS stock that are currently not
integrated into stock assessment models. In particular, it focuses on accounting for the uncertainty
arising from the catch data sampling process.
The central innovation the thesis is the development of a Bayesian integrated stock assessment
(ISA) model, in which an observation model explicitly links stock dynamics parameters
with statistical models for the various types of data observed from catches of the AIS stock.
This allows for systematic and statistically consistent propagation of the uncertainty inherent in
the catch sampling process across the whole stock assessment model, through to estimates of
biomass and stock parameters. The method is tested by simulations and found to provide reliable
and accurate estimates of stock parameters and associated uncertainty, while also outperforming
existing designed-based and model-based estimation approaches.
The method is computationally very demanding and this is an obstacle to its adoption
by fisheries bodies. Once this obstacle is overcame, the ISA modelling framework developed
and presented in this thesis could provide an important contribution to the improvement in the
evaluation of uncertainty in fisheries stock assessments, not only of the AIS stock, but of any other
fish stock with similar data and dynamics structure. Furthermore, the models developed in this
study establish a solid conceptual platform to allow future development of more complex models
of fish population dynamics.Using energetic models to investigate the survival and reproduction of beaked whales (family Ziphiidae)
http://hdl.handle.net/10023/4053
Abstract: Mass stranding of several species of beaked whales (family Ziphiidae) associated with exposure to anthropogenic sounds has raised concern for the conservation of these species. However, little is known about the species’ life histories, prey or habitat requirements. Without this knowledge, it becomes difficult to assess the effects of anthropogenic sound, since there is no way to determine whether the disturbance is impacting the species’ physical or environmental requirements. Here we take a bioenergetics approach to address this gap in our knowledge, as the elusive, deep-diving nature of beaked whales has made it hard to study these effects directly. We develop a model for Ziphiidae linking feeding energetics to the species’ requirements for survival and reproduction, since these life history traits would be the most likely to be impacted by non-lethal disturbances. Our models suggest that beaked whale reproduction requires energy dense prey, and that poor resource availability would lead to an extension of the inter-calving interval. Further, given current information, it seems that some beaked whale species require relatively high quality habitat in order to meet their requirements for survival and reproduction. As a result, even a small non-lethal disturbance that results in displacement of whales from preferred habitats could potentially impact a population if a significant proportion of that population was affected. We explored the impact of varying ecological parameters and model assumptions on survival and reproduction, and find that calf and fetus survival appear more readily affected than the survival of adult females.Wed, 17 Jul 2013 00:00:00 GMThttp://hdl.handle.net/10023/40532013-07-17T00:00:00ZNew, Leslie FrancesMoretti, DavidHooker, Sascha KateCosta, Daniel P.Simmons, Samantha E.Mass stranding of several species of beaked whales (family Ziphiidae) associated with exposure to anthropogenic sounds has raised concern for the conservation of these species. However, little is known about the species’ life histories, prey or habitat requirements. Without this knowledge, it becomes difficult to assess the effects of anthropogenic sound, since there is no way to determine whether the disturbance is impacting the species’ physical or environmental requirements. Here we take a bioenergetics approach to address this gap in our knowledge, as the elusive, deep-diving nature of beaked whales has made it hard to study these effects directly. We develop a model for Ziphiidae linking feeding energetics to the species’ requirements for survival and reproduction, since these life history traits would be the most likely to be impacted by non-lethal disturbances. Our models suggest that beaked whale reproduction requires energy dense prey, and that poor resource availability would lead to an extension of the inter-calving interval. Further, given current information, it seems that some beaked whale species require relatively high quality habitat in order to meet their requirements for survival and reproduction. As a result, even a small non-lethal disturbance that results in displacement of whales from preferred habitats could potentially impact a population if a significant proportion of that population was affected. We explored the impact of varying ecological parameters and model assumptions on survival and reproduction, and find that calf and fetus survival appear more readily affected than the survival of adult females.Spatial models for distance sampling data : recent developments and future directions
http://hdl.handle.net/10023/4046
Abstract: Our understanding of a biological population can be greatly enhanced by modelling their distribution in space and as a function of environmental covariates. Density surface models consist of a spatial model of the abundance of a biological population which has been corrected for uncertain detection via distance sampling methods. We offer a comparison of recent advances in the field and consider the likely directions of future research. In particular we consider spatial modelling techniques that may be advantageous to applied ecologists such as quantification of uncertainty in a two-stage model and smoothing in areas with complex boundaries. The methods discussed are available in an \textsf{R} package developed by the authors and are largely implemented in the popular Windows package Distance (or are soon to be incorporated). Density surface modelling enables applied ecologists to reliably estimate abundances and create maps of animal/plant distribution. Such models can also be used to investigate the relationships between distribution and environmental covariates.Fri, 01 Nov 2013 00:00:00 GMThttp://hdl.handle.net/10023/40462013-11-01T00:00:00ZMiller, David LawrenceBurt, M LouiseRexstad, EricThomas, LenOur understanding of a biological population can be greatly enhanced by modelling their distribution in space and as a function of environmental covariates. Density surface models consist of a spatial model of the abundance of a biological population which has been corrected for uncertain detection via distance sampling methods. We offer a comparison of recent advances in the field and consider the likely directions of future research. In particular we consider spatial modelling techniques that may be advantageous to applied ecologists such as quantification of uncertainty in a two-stage model and smoothing in areas with complex boundaries. The methods discussed are available in an \textsf{R} package developed by the authors and are largely implemented in the popular Windows package Distance (or are soon to be incorporated). Density surface modelling enables applied ecologists to reliably estimate abundances and create maps of animal/plant distribution. Such models can also be used to investigate the relationships between distribution and environmental covariates.Estimating resource acquisition and at-sea body condition of a marine predator
http://hdl.handle.net/10023/3867
Abstract: (1) Body condition plays a fundamental role in many ecological and evolutionary processes at a variety of scales and across a broad range of animal taxa. An understanding of how body condition changes at fine spatial and temporal scales as a result of interaction with the environment provides necessary information about how animals acquire resources. (2) However, comparatively little is known about intra- and interindividual variation of condition in marine systems. Where condition has been studied, changes typically are recorded at relatively coarse time-scales. By quantifying how fine-scale interaction with the environment influences condition, we can broaden our understanding of how animals acquire resources and allocate them to body stores. (3) Here we used a hierarchical Bayesian state-space model to estimate the body condition as measured by the size of an animal's lipid store in two closely related species of marine predator that occupy different hemispheres: northern elephant seals (Mirounga angustirostris) and southern elephant seals (Mirounga leonina). The observation model linked drift dives to lipid stores. The process model quantified daily changes in lipid stores as a function of the physiological condition of the seal (lipid:lean tissue ratio, departure lipid and departure mass), its foraging location, two measures of behaviour and environmental covariates. (4) We found that physiological condition significantly impacted lipid gain at two time-scales – daily and at departure from the colony – that foraging location was significantly associated with lipid gain in both species of elephant seals and that long-term behavioural phase was associated with positive lipid gain in northern and southern elephant seals. In northern elephant seals, the occurrence of short-term behavioural states assumed to represent foraging were correlated with lipid gain. Lipid gain was a function of covariates in both species. Southern elephant seals performed fewer drift dives than northern elephant seals and gained lipids at a lower rate. (5) We have demonstrated a new way to obtain time series of body condition estimates for a marine predator at fine spatial and temporal scales. This modelling approach accounts for uncertainty at many levels and has the potential to integrate physiological and movement ecology of top predators. The observation model we used was specific to elephant seals, but the process model can readily be applied to other species, providing an opportunity to understand how animals respond to their environment at a fine spatial scale.
Description: This article was made open access through BIS OA funding.Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10023/38672013-01-01T00:00:00ZSchick, Robert SchillingNew, LeslieThomas, LenCosta, DanielHindell, MarkMcMahon, CliveRobinson, PatrickSimmons, SamanthaThums, MicheleHarwood, JohnClark, James(1) Body condition plays a fundamental role in many ecological and evolutionary processes at a variety of scales and across a broad range of animal taxa. An understanding of how body condition changes at fine spatial and temporal scales as a result of interaction with the environment provides necessary information about how animals acquire resources. (2) However, comparatively little is known about intra- and interindividual variation of condition in marine systems. Where condition has been studied, changes typically are recorded at relatively coarse time-scales. By quantifying how fine-scale interaction with the environment influences condition, we can broaden our understanding of how animals acquire resources and allocate them to body stores. (3) Here we used a hierarchical Bayesian state-space model to estimate the body condition as measured by the size of an animal's lipid store in two closely related species of marine predator that occupy different hemispheres: northern elephant seals (Mirounga angustirostris) and southern elephant seals (Mirounga leonina). The observation model linked drift dives to lipid stores. The process model quantified daily changes in lipid stores as a function of the physiological condition of the seal (lipid:lean tissue ratio, departure lipid and departure mass), its foraging location, two measures of behaviour and environmental covariates. (4) We found that physiological condition significantly impacted lipid gain at two time-scales – daily and at departure from the colony – that foraging location was significantly associated with lipid gain in both species of elephant seals and that long-term behavioural phase was associated with positive lipid gain in northern and southern elephant seals. In northern elephant seals, the occurrence of short-term behavioural states assumed to represent foraging were correlated with lipid gain. Lipid gain was a function of covariates in both species. Southern elephant seals performed fewer drift dives than northern elephant seals and gained lipids at a lower rate. (5) We have demonstrated a new way to obtain time series of body condition estimates for a marine predator at fine spatial and temporal scales. This modelling approach accounts for uncertainty at many levels and has the potential to integrate physiological and movement ecology of top predators. The observation model we used was specific to elephant seals, but the process model can readily be applied to other species, providing an opportunity to understand how animals respond to their environment at a fine spatial scale.Evidence for density-dependent changes in body condition and pregnancy rate of North Atlantic fin whales over four decades of varying environmental conditions
http://hdl.handle.net/10023/3854
Abstract: A central theme in ecology is the search for pattern in the response of a species to changing environmental conditions. Natural resource management and endangered species conservation require an understanding of density-dependent and density-independent factors that regulate populations. Marine mammal populations are expected to express density dependence in the same way as terrestrial mammals, but logistical difficulties in data acquisition for many large whale species have hindered attempts to identify population-regulation mechanisms. We explored relationships between body condition (inferred from patterns in blubber thickness) and per capita prey abundance, and between pregnancy rate and body condition in North Atlantic fin whales as environmental conditions and population size varied between 1967 and 2010. Blubber thickness in both males and females declined at low per capita prey availability, and in breeding-age females, pregnancy rate declined at low blubber thickness, demonstrating a density-dependent response of pregnancy to prey limitation mediated through body condition. To the best of our knowledge, this is the first time a quantitative relationship among per capita prey abundance, body condition, and pregnancy rate has been documented for whales. As long-lived predators, marine mammals can act as indicators of the state of marine ecosystems. Improving our understanding of the relationships that link prey, body condition, and population parameters such as pregnancy rate and survival will become increasingly useful as these systems are affected by natural and anthropogenic change. Quantifying linkages among prey, fitness and vital rates will improve our ability to predict population consequences of subtle, sublethal impacts of ocean noise and other anthropogenic stressors.Fri, 01 Mar 2013 00:00:00 GMThttp://hdl.handle.net/10023/38542013-03-01T00:00:00ZWilliams, RobertVikingsson, Gisli A.Gislason, AstthorLockyer, ChristinaNew, LeslieThomas, LenHammond, Philip StevenA central theme in ecology is the search for pattern in the response of a species to changing environmental conditions. Natural resource management and endangered species conservation require an understanding of density-dependent and density-independent factors that regulate populations. Marine mammal populations are expected to express density dependence in the same way as terrestrial mammals, but logistical difficulties in data acquisition for many large whale species have hindered attempts to identify population-regulation mechanisms. We explored relationships between body condition (inferred from patterns in blubber thickness) and per capita prey abundance, and between pregnancy rate and body condition in North Atlantic fin whales as environmental conditions and population size varied between 1967 and 2010. Blubber thickness in both males and females declined at low per capita prey availability, and in breeding-age females, pregnancy rate declined at low blubber thickness, demonstrating a density-dependent response of pregnancy to prey limitation mediated through body condition. To the best of our knowledge, this is the first time a quantitative relationship among per capita prey abundance, body condition, and pregnancy rate has been documented for whales. As long-lived predators, marine mammals can act as indicators of the state of marine ecosystems. Improving our understanding of the relationships that link prey, body condition, and population parameters such as pregnancy rate and survival will become increasingly useful as these systems are affected by natural and anthropogenic change. Quantifying linkages among prey, fitness and vital rates will improve our ability to predict population consequences of subtle, sublethal impacts of ocean noise and other anthropogenic stressors.First direct measurements of behavioural responses by Cuvier's beaked whales to mid-frequency active sonar
http://hdl.handle.net/10023/3836
Abstract: Most marine mammal strandings coincident with naval sonar exercises have involved Cuvier's beaked whales (Ziphius cavirostris). We recorded animal movement and acoustic data on two tagged Ziphius and obtained the first direct measurements of behavioural responses of this species to mid-frequency active (MFA) sonar signals. Each recording included a 30-min playback (one 1.6-s simulated MFA sonar signal repeated every 25 s); one whale was also incidentally exposed to MFA sonar from distant naval exercises. Whales responded strongly to playbacks at low received levels (RLs; 89–127 dB re 1 µPa): after ceasing normal fluking and echolocation, they swam rapidly, silently away, extending both dive duration and subsequent non-foraging interval. Distant sonar exercises (78–106 dB re 1 µPa) did not elicit such responses, suggesting that context may moderate reactions. The observed responses to playback occurred at RLs well below current regulatory thresholds; equivalent responses to operational sonars could elevate stranding risk and reduce foraging efficiency.Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10023/38362013-01-01T00:00:00ZDe Ruiter, Stacy LynnSouthall, Brandon L.Calambokidis, JohnZimmer, Walter M. X.Sadykova, DinaraFalcone, Erin A.Friedlaender, Ari S.Joseph, John E.Moretti, DavidSchorr, Gregory S.Thomas, LenTyack, Peter LloydMost marine mammal strandings coincident with naval sonar exercises have involved Cuvier's beaked whales (Ziphius cavirostris). We recorded animal movement and acoustic data on two tagged Ziphius and obtained the first direct measurements of behavioural responses of this species to mid-frequency active (MFA) sonar signals. Each recording included a 30-min playback (one 1.6-s simulated MFA sonar signal repeated every 25 s); one whale was also incidentally exposed to MFA sonar from distant naval exercises. Whales responded strongly to playbacks at low received levels (RLs; 89–127 dB re 1 µPa): after ceasing normal fluking and echolocation, they swam rapidly, silently away, extending both dive duration and subsequent non-foraging interval. Distant sonar exercises (78–106 dB re 1 µPa) did not elicit such responses, suggesting that context may moderate reactions. The observed responses to playback occurred at RLs well below current regulatory thresholds; equivalent responses to operational sonars could elevate stranding risk and reduce foraging efficiency.Estimating wildlife distribution and abundance from line transect surveys conducted from platforms of opportunity
http://hdl.handle.net/10023/3727
Abstract: Line transect data obtained from 'platforms of opportunity' are useful for the monitoring
of long term trends in dolphin populations which occur over vast areas, yet analyses of
such data axe problematic due to violation of fundamental assumptions of line transect
methodology. In this thesis we develop methods which allow estimates of dolphin relative
abundance to be obtained when certain assumptions of line transect sampling are violated.
Generalised additive models are used to model encounter rate and mean school size as
a function of spatially and temporally referenced covariates. The estimated relationship
between the response and the environmental and locational covariates is then used to
obtain a predicted surface for the response over the entire survey region. Given those
predicted surfaces, a density surface can then be obtained and an estimate of abundance
computed by numerically integrating over the entire survey region. This approach is
particularly useful when search effort is not random, in which case standard line transect
methods would yield biased estimates.
Estimates of f (0) (the inverse of the effective strip (half-)width), an essential component
of the line transect estimator, may also be biased due to heterogeneity in detection probabilities.
We developed a conditional likelihood approach in which covariate effects are
directly incorporated into the estimation procedure. Simulation results indicated that the
method performs well in the presence of size-bias. When multiple covariates are used, it
is important that covariate selection be carried out.
As an example we applied the methods described above to eastern tropical Pacific dolphin
stocks. However, uncertainty in stock identification has never been directly incorporated
into methods used to obtain estimates of relative or absolute abundance. Therefore we
illustrate an approach in which trends in dolphin relative abundance axe monitored by
small areas, rather than stocks.Mon, 01 Jan 2001 00:00:00 GMThttp://hdl.handle.net/10023/37272001-01-01T00:00:00ZMarques, Fernanda F. C.Line transect data obtained from 'platforms of opportunity' are useful for the monitoring
of long term trends in dolphin populations which occur over vast areas, yet analyses of
such data axe problematic due to violation of fundamental assumptions of line transect
methodology. In this thesis we develop methods which allow estimates of dolphin relative
abundance to be obtained when certain assumptions of line transect sampling are violated.
Generalised additive models are used to model encounter rate and mean school size as
a function of spatially and temporally referenced covariates. The estimated relationship
between the response and the environmental and locational covariates is then used to
obtain a predicted surface for the response over the entire survey region. Given those
predicted surfaces, a density surface can then be obtained and an estimate of abundance
computed by numerically integrating over the entire survey region. This approach is
particularly useful when search effort is not random, in which case standard line transect
methods would yield biased estimates.
Estimates of f (0) (the inverse of the effective strip (half-)width), an essential component
of the line transect estimator, may also be biased due to heterogeneity in detection probabilities.
We developed a conditional likelihood approach in which covariate effects are
directly incorporated into the estimation procedure. Simulation results indicated that the
method performs well in the presence of size-bias. When multiple covariates are used, it
is important that covariate selection be carried out.
As an example we applied the methods described above to eastern tropical Pacific dolphin
stocks. However, uncertainty in stock identification has never been directly incorporated
into methods used to obtain estimates of relative or absolute abundance. Therefore we
illustrate an approach in which trends in dolphin relative abundance axe monitored by
small areas, rather than stocks.Bayesian point process modelling of ecological communities
http://hdl.handle.net/10023/3710
Abstract: The modelling of biological communities is important to further the understanding
of species coexistence and the mechanisms involved in maintaining
biodiversity. This involves considering not only interactions between individual
biological organisms, but also the incorporation of covariate information,
if available, in the modelling process. This thesis explores the use
of point processes to model interactions in bivariate point patterns within
a Bayesian framework, and, where applicable, in conjunction with covariate
data. Specifically, we distinguish between symmetric and asymmetric species
interactions and model these using appropriate point processes. In this thesis
we consider both pairwise and area interaction point processes to allow for
inhibitory interactions and both inhibitory and attractive interactions.
It is envisaged that the analyses and innovations presented in this thesis
will contribute to the parsimonious modelling of biological communities.Fri, 28 Jun 2013 00:00:00 GMThttp://hdl.handle.net/10023/37102013-06-28T00:00:00ZNightingale, Glenna FaithThe modelling of biological communities is important to further the understanding
of species coexistence and the mechanisms involved in maintaining
biodiversity. This involves considering not only interactions between individual
biological organisms, but also the incorporation of covariate information,
if available, in the modelling process. This thesis explores the use
of point processes to model interactions in bivariate point patterns within
a Bayesian framework, and, where applicable, in conjunction with covariate
data. Specifically, we distinguish between symmetric and asymmetric species
interactions and model these using appropriate point processes. In this thesis
we consider both pairwise and area interaction point processes to allow for
inhibitory interactions and both inhibitory and attractive interactions.
It is envisaged that the analyses and innovations presented in this thesis
will contribute to the parsimonious modelling of biological communities.Animal population estimation using mark-recapture and plant-capture
http://hdl.handle.net/10023/3655
Abstract: Mark-recapture is a method of population estimation that involves capturing a number
of animals from a population of unknown size on several occasions, and marking
those animals that are caught each time. By observing the number of marked
animals that are subsequently seen, estimates of the total population size can be
made. There are various subclasses of the mark-recapture method called the Otis-class
of models (Otis, Burnham, White & Anderson 1978). These relate to the
assumed behaviour of the individuals in the target population.
More recent work has generalised the theory of mark-recapture to the so-called
plant-capture, where a known number of animals are pre-inserted into the target
population. Sampling is then carried out as normal, but with additional information
coming from knowledge of the number of planted individuals.
The theory underpinning plant-capture is less well-developed than mark-recapture,
with the difference on population estimation of the former over the latter not often
tested. This thesis shows that, under fixed and random sample-size models, the
inclusion of plants can improve the mean point population estimation of various
estimators. The estimator of Pathak (1964) is generalised to allow for the inclusion
of plants into the target population. The results show that mean estimates from
most estimators, under most models, can be improved with the inclusion of plants,
and the sample standard deviations of the simulations can be reduced. This improvement
in mean point population estimation is particularly pronounced when
the number of animals captured is low.
Sample coverage, which is the proportion of distinct animals caught during sampling,
is also often sought by practitioners. Given here is a generalisation of the
inverse population estimator of Pathak (1964) to plant-capture and a proposed new
inverse population estimator, which can be used as estimates of the coverage of a
sample.Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10023/36552012-01-01T00:00:00ZGormley, RichardMark-recapture is a method of population estimation that involves capturing a number
of animals from a population of unknown size on several occasions, and marking
those animals that are caught each time. By observing the number of marked
animals that are subsequently seen, estimates of the total population size can be
made. There are various subclasses of the mark-recapture method called the Otis-class
of models (Otis, Burnham, White & Anderson 1978). These relate to the
assumed behaviour of the individuals in the target population.
More recent work has generalised the theory of mark-recapture to the so-called
plant-capture, where a known number of animals are pre-inserted into the target
population. Sampling is then carried out as normal, but with additional information
coming from knowledge of the number of planted individuals.
The theory underpinning plant-capture is less well-developed than mark-recapture,
with the difference on population estimation of the former over the latter not often
tested. This thesis shows that, under fixed and random sample-size models, the
inclusion of plants can improve the mean point population estimation of various
estimators. The estimator of Pathak (1964) is generalised to allow for the inclusion
of plants into the target population. The results show that mean estimates from
most estimators, under most models, can be improved with the inclusion of plants,
and the sample standard deviations of the simulations can be reduced. This improvement
in mean point population estimation is particularly pronounced when
the number of animals captured is low.
Sample coverage, which is the proportion of distinct animals caught during sampling,
is also often sought by practitioners. Given here is a generalisation of the
inverse population estimator of Pathak (1964) to plant-capture and a proposed new
inverse population estimator, which can be used as estimates of the coverage of a
sample.Estimating anglerfish abundance from trawl surveys, and related problems
http://hdl.handle.net/10023/3652
Abstract: The content of this thesis was motivated by the need to estimate anglerfish abundance
from stratified random trawl surveys of the anglerfish stock which occupies
the northern European shelf (Fernandes et al., 2007). The survey was conducted
annually from 2005 to 2010 in order to obtain age-structured estimates of absolute
abundance for this stock. An estimation method is considered to incorporate statistical models for herding, length-based net retention probability and missing age data and uncertainty from all of these sources in variance estimation.
A key component of abundance estimation is the estimation of capture probability.
Capture probability is estimated from the experimental survey data using various
logistic regression models with haul as a random effect. Conditional on the estimated
capture probability, a number of abundance estimators are developed and applied to
the anglerfish data. The abundance estimators differ in the way that the haul effect is incorporated. The performance of these estimators is investigated by simulation. An estimator with form similar to that conventionally used to estimate abundance from distance sampling surveys is found to perform best.
The estimators developed for the anglerfish survey data which incorporate random
effects in capture probability have wider application than trawl surveys. We examine
the analytic properties of these estimators when the capture/detection probability is
known. We apply these estimators to three different types of survey data in addition
to the anglerfish data, with different forms of random effects and investigate their
performance by simulation. We find that a generalization of the form of estimator
typically used on line transect surveys performs best overall. It has low bias, and
also the lowest bias and mean squared error among all the estimators we considered.Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10023/36522012-01-01T00:00:00ZYuan, YuanThe content of this thesis was motivated by the need to estimate anglerfish abundance
from stratified random trawl surveys of the anglerfish stock which occupies
the northern European shelf (Fernandes et al., 2007). The survey was conducted
annually from 2005 to 2010 in order to obtain age-structured estimates of absolute
abundance for this stock. An estimation method is considered to incorporate statistical models for herding, length-based net retention probability and missing age data and uncertainty from all of these sources in variance estimation.
A key component of abundance estimation is the estimation of capture probability.
Capture probability is estimated from the experimental survey data using various
logistic regression models with haul as a random effect. Conditional on the estimated
capture probability, a number of abundance estimators are developed and applied to
the anglerfish data. The abundance estimators differ in the way that the haul effect is incorporated. The performance of these estimators is investigated by simulation. An estimator with form similar to that conventionally used to estimate abundance from distance sampling surveys is found to perform best.
The estimators developed for the anglerfish survey data which incorporate random
effects in capture probability have wider application than trawl surveys. We examine
the analytic properties of these estimators when the capture/detection probability is
known. We apply these estimators to three different types of survey data in addition
to the anglerfish data, with different forms of random effects and investigate their
performance by simulation. We find that a generalization of the form of estimator
typically used on line transect surveys performs best overall. It has low bias, and
also the lowest bias and mean squared error among all the estimators we considered.Mixed effect models in distance sampling
http://hdl.handle.net/10023/3618
Abstract: Recently, much effort has been expended for improving conventional distance sampling methods, e.g. by replacing the design-based approach with a model-based approach where observed counts are related to environmental covariates (Hedley and Buckland, 2004) or by incorporating covariates in the detection function model (Marques and Buckland, 2003).
While these models have generally been limited to include fixed effects, we propose
four different methods for analysing distance sampling data using mixed effects models. These include an extension of the two-stage approach (Buckland et al., 2009),
where we include site random effects in the second-stage count model to account for
correlated counts at the same sites. We also present two integrated approaches which
include site random effects in the count model. These approaches combine the analysis stages for the detection and count models and allow simultaneous estimation of all
parameters. Furthermore, we develop a detection function model that incorporates
random effects. We also propose a novel Bayesian approach to analysing distance sampling data which uses a Metropolis-Hastings algorithm for updating model parameters and a reversible jump Markov chain Monte Carlo (RJMCMC) algorithm for assessing model uncertainty. Lastly, we propose using hierarchical centering as a novel technique for improving model mixing and hence facilitating an RJMCMC algorithm for mixed models.
We analyse two case studies, both large-scale point transect surveys, where the interest lies in establishing the effects of conservation buffers on agricultural fields. For each case study, we compare the results from one integrated approach to those from
the extended two-stage approach. We find that these may differ in parameter estimates for covariates that were both in the detection and the count model and in model probabilities when model uncertainty was included in inference. The performance of the random effects based detection function is assessed via simulation and when heterogeneity in the data is present, one of the new estimators yields improved results compared to conventional distance sampling estimators.Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10023/36182013-01-01T00:00:00ZOedekoven, Cornelia SabrinaRecently, much effort has been expended for improving conventional distance sampling methods, e.g. by replacing the design-based approach with a model-based approach where observed counts are related to environmental covariates (Hedley and Buckland, 2004) or by incorporating covariates in the detection function model (Marques and Buckland, 2003).
While these models have generally been limited to include fixed effects, we propose
four different methods for analysing distance sampling data using mixed effects models. These include an extension of the two-stage approach (Buckland et al., 2009),
where we include site random effects in the second-stage count model to account for
correlated counts at the same sites. We also present two integrated approaches which
include site random effects in the count model. These approaches combine the analysis stages for the detection and count models and allow simultaneous estimation of all
parameters. Furthermore, we develop a detection function model that incorporates
random effects. We also propose a novel Bayesian approach to analysing distance sampling data which uses a Metropolis-Hastings algorithm for updating model parameters and a reversible jump Markov chain Monte Carlo (RJMCMC) algorithm for assessing model uncertainty. Lastly, we propose using hierarchical centering as a novel technique for improving model mixing and hence facilitating an RJMCMC algorithm for mixed models.
We analyse two case studies, both large-scale point transect surveys, where the interest lies in establishing the effects of conservation buffers on agricultural fields. For each case study, we compare the results from one integrated approach to those from
the extended two-stage approach. We find that these may differ in parameter estimates for covariates that were both in the detection and the count model and in model probabilities when model uncertainty was included in inference. The performance of the random effects based detection function is assessed via simulation and when heterogeneity in the data is present, one of the new estimators yields improved results compared to conventional distance sampling estimators.Estimating animal population density using passive acoustics
http://hdl.handle.net/10023/3496
Abstract: Reliable estimation of the size or density of wild animal populations is very important for effective wildlife management, conservation and ecology. Currently, the most widely used methods for obtaining such estimates involve either sighting animals from transect lines or some form of capture-recapture on marked or uniquely identifiable individuals. However, many species are difficult to sight, and cannot be easily marked or recaptured. Some of these species produce readily identifiable sounds, providing an opportunity to use passive acoustic data to estimate animal density. In addition, even for species for which other visually based methods are feasible, passive acoustic methods offer the potential for greater detection ranges in some environments (e.g. underwater or in dense forest), and hence potentially better precision. Automated data collection means that surveys can take place at times and in places where it would be too expensive or dangerous to send human observers. Here, we present an overview of animal density estimation using passive acoustic data, a relatively new and fast-developing field. We review the types of data and methodological approaches currently available to researchers and we provide a framework for acoustics-based density estimation, illustrated with examples from real-world case studies. We mention moving sensor platforms (e.g. towed acoustics), but then focus on methods involving sensors at fixed locations, particularly hydrophones to survey marine mammals, as acoustic-based density estimation research to date has been concentrated in this area. Primary among these are methods based on distance sampling and spatially explicit capture-recapture. The methods are also applicable to other aquatic and terrestrial sound-producing taxa. We conclude that, despite being in its infancy, density estimation based on passive acoustic data likely will become an important method for surveying a number of diverse taxa, such as sea mammals, fish, birds, amphibians, and insects, especially in situations where inferences are required over long periods of time. There is considerable work ahead, with several potentially fruitful research areas, including the development of (i) hardware and software for data acquisition, (ii) efficient, calibrated, automated detection and classification systems, and (iii) statistical approaches optimized for this application. Further, survey design will need to be developed, and research is needed on the acoustic behaviour of target species. Fundamental research on vocalization rates and group sizes, and the relation between these and other factors such as season or behaviour state, is critical. Evaluation of the methods under known density scenarios will be important for empirically validating the approaches presented hereWed, 01 May 2013 00:00:00 GMThttp://hdl.handle.net/10023/34962013-05-01T00:00:00ZMarques, Tiago A.Thomas, LenMartin, StephenMellinger, DavidWard, JessicaMoretti, DavidHarris, Danielle VeronicaTyack, Peter LloydReliable estimation of the size or density of wild animal populations is very important for effective wildlife management, conservation and ecology. Currently, the most widely used methods for obtaining such estimates involve either sighting animals from transect lines or some form of capture-recapture on marked or uniquely identifiable individuals. However, many species are difficult to sight, and cannot be easily marked or recaptured. Some of these species produce readily identifiable sounds, providing an opportunity to use passive acoustic data to estimate animal density. In addition, even for species for which other visually based methods are feasible, passive acoustic methods offer the potential for greater detection ranges in some environments (e.g. underwater or in dense forest), and hence potentially better precision. Automated data collection means that surveys can take place at times and in places where it would be too expensive or dangerous to send human observers. Here, we present an overview of animal density estimation using passive acoustic data, a relatively new and fast-developing field. We review the types of data and methodological approaches currently available to researchers and we provide a framework for acoustics-based density estimation, illustrated with examples from real-world case studies. We mention moving sensor platforms (e.g. towed acoustics), but then focus on methods involving sensors at fixed locations, particularly hydrophones to survey marine mammals, as acoustic-based density estimation research to date has been concentrated in this area. Primary among these are methods based on distance sampling and spatially explicit capture-recapture. The methods are also applicable to other aquatic and terrestrial sound-producing taxa. We conclude that, despite being in its infancy, density estimation based on passive acoustic data likely will become an important method for surveying a number of diverse taxa, such as sea mammals, fish, birds, amphibians, and insects, especially in situations where inferences are required over long periods of time. There is considerable work ahead, with several potentially fruitful research areas, including the development of (i) hardware and software for data acquisition, (ii) efficient, calibrated, automated detection and classification systems, and (iii) statistical approaches optimized for this application. Further, survey design will need to be developed, and research is needed on the acoustic behaviour of target species. Fundamental research on vocalization rates and group sizes, and the relation between these and other factors such as season or behaviour state, is critical. Evaluation of the methods under known density scenarios will be important for empirically validating the approaches presented hereDecomposition tables for experiments : II. Two–one randomizations
http://hdl.handle.net/10023/3479
Abstract: We investigate structure for pairs of randomizations that do not follow each other in a chain. These are unrandomized-inclusive, independent, coincident or double randomizations. This involves taking several structures that satisfy particular relations and combining them to form the appropriate orthogonal decomposition of the data space for the experiment. We show how to establish the decomposition table giving the sources of variation, their relationships and their degrees of freedom, so that competing designs can be evaluated. This leads to recommendations for when the different types of multiple randomization should be used.Fri, 01 Oct 2010 00:00:00 GMThttp://hdl.handle.net/10023/34792010-10-01T00:00:00ZBrien, C. J.Bailey, Rosemary AnneWe investigate structure for pairs of randomizations that do not follow each other in a chain. These are unrandomized-inclusive, independent, coincident or double randomizations. This involves taking several structures that satisfy particular relations and combining them to form the appropriate orthogonal decomposition of the data space for the experiment. We show how to establish the decomposition table giving the sources of variation, their relationships and their degrees of freedom, so that competing designs can be evaluated. This leads to recommendations for when the different types of multiple randomization should be used.Decomposition tables for experiments : I. A chain of randomizations
http://hdl.handle.net/10023/3478
Abstract: One aspect of evaluating the design for an experiment is the discovery of the relationships between subspaces of the data space. Initially we establish the notation and methods for evaluating an experiment with a single randomization. Starting with two structures, or orthogonal decompositions of the data space, we describe how to combine them to form the overall decomposition for a single-randomization experiment that is "structure balanced." The relationships between the two structures are characterized using efficiency factors. The decomposition is encapsulated in a decomposition table. Then, for experiments that involve multiple randomizations forming a chain, we take several structures that pairwise are structure balanced and combine them to establish the form of the orthogonal decomposition for the experiment. In particular, it is proven that the properties of the design for Such an experiment are derived in a straightforward manner from those of the individual designs. We show how to formulate an extended decomposition table giving the sources of variation, their relationships and their degrees of freedom, so that competing designs can be evaluated.Tue, 01 Dec 2009 00:00:00 GMThttp://hdl.handle.net/10023/34782009-12-01T00:00:00ZBrien, C. J.Bailey, Rosemary AnneOne aspect of evaluating the design for an experiment is the discovery of the relationships between subspaces of the data space. Initially we establish the notation and methods for evaluating an experiment with a single randomization. Starting with two structures, or orthogonal decompositions of the data space, we describe how to combine them to form the overall decomposition for a single-randomization experiment that is "structure balanced." The relationships between the two structures are characterized using efficiency factors. The decomposition is encapsulated in a decomposition table. Then, for experiments that involve multiple randomizations forming a chain, we take several structures that pairwise are structure balanced and combine them to establish the form of the orthogonal decomposition for the experiment. In particular, it is proven that the properties of the design for Such an experiment are derived in a straightforward manner from those of the individual designs. We show how to formulate an extended decomposition table giving the sources of variation, their relationships and their degrees of freedom, so that competing designs can be evaluated.Quantifying biodiversity trends in time and space
http://hdl.handle.net/10023/3414
Abstract: The global loss of biodiversity calls for robust large-scale diversity assessment. Biological diversity is a multi-faceted concept; defined as the “variety of life”, answering questions such as “How much is there?” or more precisely “Have we succeeded in reducing the rate of its decline?” is not straightforward. While various aspects of biodiversity give rise to numerous ways of quantification, we focus on temporal (and spatial) trends and their changes in species diversity.
Traditional diversity indices summarise information contained in the species abundance distribution, i.e. each species' proportional contribution to total abundance. Estimated from data, these indices can be biased if variation in detection probability is ignored. We discuss differences between diversity indices and demonstrate possible adjustments for detectability.
Additionally, most indices focus on the most abundant species in ecological communities. We introduce a new set of diversity measures, based on a family of goodness-of-fit statistics. A function of a free parameter, this family allows us to vary the sensitivity of these measures to dominance and rarity of species.
Their performance is studied by assessing temporal trends in diversity for five communities of British breeding birds based on 14 years of survey data, where they are applied alongside the current headline index, a geometric mean of relative abundances. Revealing the contributions of both rare and common species to biodiversity trends, these "goodness-of-fit" measures provide novel insights into how ecological communities change over time.
Biodiversity is not only subject to temporal changes, but it also varies across space. We take first steps towards estimating spatial diversity trends. Finally, processes maintaining biodiversity act locally, at specific spatial scales. Contrary to abundance-based summary statistics, spatial characteristics of ecological communities may distinguish these processes. We suggest a generalisation to a spatial summary, the cross-pair overlap distribution, to render it more flexible to spatial scale.Fri, 30 Nov 2012 00:00:00 GMThttp://hdl.handle.net/10023/34142012-11-30T00:00:00ZStudeny, Angelika C.The global loss of biodiversity calls for robust large-scale diversity assessment. Biological diversity is a multi-faceted concept; defined as the “variety of life”, answering questions such as “How much is there?” or more precisely “Have we succeeded in reducing the rate of its decline?” is not straightforward. While various aspects of biodiversity give rise to numerous ways of quantification, we focus on temporal (and spatial) trends and their changes in species diversity.
Traditional diversity indices summarise information contained in the species abundance distribution, i.e. each species' proportional contribution to total abundance. Estimated from data, these indices can be biased if variation in detection probability is ignored. We discuss differences between diversity indices and demonstrate possible adjustments for detectability.
Additionally, most indices focus on the most abundant species in ecological communities. We introduce a new set of diversity measures, based on a family of goodness-of-fit statistics. A function of a free parameter, this family allows us to vary the sensitivity of these measures to dominance and rarity of species.
Their performance is studied by assessing temporal trends in diversity for five communities of British breeding birds based on 14 years of survey data, where they are applied alongside the current headline index, a geometric mean of relative abundances. Revealing the contributions of both rare and common species to biodiversity trends, these "goodness-of-fit" measures provide novel insights into how ecological communities change over time.
Biodiversity is not only subject to temporal changes, but it also varies across space. We take first steps towards estimating spatial diversity trends. Finally, processes maintaining biodiversity act locally, at specific spatial scales. Contrary to abundance-based summary statistics, spatial characteristics of ecological communities may distinguish these processes. We suggest a generalisation to a spatial summary, the cross-pair overlap distribution, to render it more flexible to spatial scale.Finite and infinite ergodic theory for linear and conformal dynamical systems
http://hdl.handle.net/10023/3220
Abstract: The first main topic of this thesis is the thorough analysis of two families of piecewise linear
maps on the unit interval, the α-Lüroth and α-Farey maps. Here, α denotes a countably infinite
partition of the unit interval whose atoms only accumulate at the origin. The basic properties
of these maps will be developed, including that each α-Lüroth map (denoted Lα) gives rise to a
series expansion of real numbers in [0,1], a certain type of Generalised Lüroth Series. The first
example of such an expansion was given by Lüroth. The map Lα is the jump transformation
of the corresponding α-Farey map Fα. The maps Lα and Fα share the same relationship as the
classical Farey and Gauss maps which give rise to the continued fraction expansion of a real
number. We also consider the topological properties of Fα and some Diophantine-type sets of
numbers expressed in terms of the α-Lüroth expansion.
Next we investigate certain ergodic-theoretic properties of the maps Lα and Fα. It will turn
out that the Lebesgue measure λ is invariant for every map Lα and that there exists a unique
Lebesgue-absolutely continuous invariant measure for Fα. We will give a precise expression for
the density of this measure. Our main result is that both Lα and Fα are exact, and thus ergodic.
The interest in the invariant measure for Fα lies in the fact that under a particular condition on
the underlying partition α, the invariant measure associated to the map Fα is infinite.
Then we proceed to introduce and examine the sequence of α-sum-level sets arising from
the α-Lüroth map, for an arbitrary given partition α. These sets can be written dynamically in
terms of Fα. The main result concerning the α-sum-level sets is to establish weak and strong
renewal laws. Note that for the Farey map and the Gauss map, the analogue of this result has
been obtained by Kesseböhmer and Stratmann. There the results were derived by using advanced
infinite ergodic theory, rather than the strong renewal theorems employed here. This underlines
the fact that one of the main ingredients of infinite ergodic theory is provided by some delicate
estimates in renewal theory.
Our final main result concerning the α-Lüroth and α-Farey systems is to provide a fractal-geometric
description of the Lyapunov spectra associated with each of the maps Lα and Fα.
The Lyapunov spectra for the Farey map and the Gauss map have been investigated in detail by
Kesseböhmer and Stratmann. The Farey map and the Gauss map are non-linear, whereas the
systems we consider are always piecewise linear. However, since our analysis is based on a large
family of different partitions of U , the class of maps which we consider in this paper allows us
to detect a variety of interesting new phenomena, including that of phase transitions.
Finally, we come to the conformal systems of the title. These are the limit sets of discrete
subgroups of the group of isometries of the hyperbolic plane. For these so-called Fuchsian
groups, our first main result is to establish the Hausdorff dimension of some Diophantine-type
sets contained in the limit set that are similar to those considered for the maps Lα. These sets
are then used in our second main result to analyse the more geometrically defined strict-Jarník
limit set of a Fuchsian group. Finally, we obtain a “weak multifractal spectrum” for the Patterson
measure associated to the Fuchsian group.Wed, 30 Nov 2011 00:00:00 GMThttp://hdl.handle.net/10023/32202011-11-30T00:00:00ZMunday, SaraThe first main topic of this thesis is the thorough analysis of two families of piecewise linear
maps on the unit interval, the α-Lüroth and α-Farey maps. Here, α denotes a countably infinite
partition of the unit interval whose atoms only accumulate at the origin. The basic properties
of these maps will be developed, including that each α-Lüroth map (denoted Lα) gives rise to a
series expansion of real numbers in [0,1], a certain type of Generalised Lüroth Series. The first
example of such an expansion was given by Lüroth. The map Lα is the jump transformation
of the corresponding α-Farey map Fα. The maps Lα and Fα share the same relationship as the
classical Farey and Gauss maps which give rise to the continued fraction expansion of a real
number. We also consider the topological properties of Fα and some Diophantine-type sets of
numbers expressed in terms of the α-Lüroth expansion.
Next we investigate certain ergodic-theoretic properties of the maps Lα and Fα. It will turn
out that the Lebesgue measure λ is invariant for every map Lα and that there exists a unique
Lebesgue-absolutely continuous invariant measure for Fα. We will give a precise expression for
the density of this measure. Our main result is that both Lα and Fα are exact, and thus ergodic.
The interest in the invariant measure for Fα lies in the fact that under a particular condition on
the underlying partition α, the invariant measure associated to the map Fα is infinite.
Then we proceed to introduce and examine the sequence of α-sum-level sets arising from
the α-Lüroth map, for an arbitrary given partition α. These sets can be written dynamically in
terms of Fα. The main result concerning the α-sum-level sets is to establish weak and strong
renewal laws. Note that for the Farey map and the Gauss map, the analogue of this result has
been obtained by Kesseböhmer and Stratmann. There the results were derived by using advanced
infinite ergodic theory, rather than the strong renewal theorems employed here. This underlines
the fact that one of the main ingredients of infinite ergodic theory is provided by some delicate
estimates in renewal theory.
Our final main result concerning the α-Lüroth and α-Farey systems is to provide a fractal-geometric
description of the Lyapunov spectra associated with each of the maps Lα and Fα.
The Lyapunov spectra for the Farey map and the Gauss map have been investigated in detail by
Kesseböhmer and Stratmann. The Farey map and the Gauss map are non-linear, whereas the
systems we consider are always piecewise linear. However, since our analysis is based on a large
family of different partitions of U , the class of maps which we consider in this paper allows us
to detect a variety of interesting new phenomena, including that of phase transitions.
Finally, we come to the conformal systems of the title. These are the limit sets of discrete
subgroups of the group of isometries of the hyperbolic plane. For these so-called Fuchsian
groups, our first main result is to establish the Hausdorff dimension of some Diophantine-type
sets contained in the limit set that are similar to those considered for the maps Lα. These sets
are then used in our second main result to analyse the more geometrically defined strict-Jarník
limit set of a Fuchsian group. Finally, we obtain a “weak multifractal spectrum” for the Patterson
measure associated to the Fuchsian group.Workshop on new developments in cetacean survey methods
http://hdl.handle.net/10023/3216
Abstract: This report contains the slides from a workshop on New Developments in Cetacean Survey Methods held on 27th November 2011 at the 19th Biennial Conference on the Biology of Marine Mammals, Tampa, Florida. Review talks were given on Passive Acoustic Density Estimation (Len Thomas); Dealing with g(0)<1: Perception Bias (Stephen Buckland); Dealing with g(0)<1: Availability Bias (Hans Skaug); Dealing with Measurement Error (David Borchers); and Density Surface Modelling (Jay Barlow). The sessions were followed by a discussion, and this is summarized at the end of the report.Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10023/32162011-01-01T00:00:00ZBorchers, David LouisThomas, LenBuckland, Stephen TerrenceSkaug, HansBarlow, JayThis report contains the slides from a workshop on New Developments in Cetacean Survey Methods held on 27th November 2011 at the 19th Biennial Conference on the Biology of Marine Mammals, Tampa, Florida. Review talks were given on Passive Acoustic Density Estimation (Len Thomas); Dealing with g(0)<1: Perception Bias (Stephen Buckland); Dealing with g(0)<1: Availability Bias (Hans Skaug); Dealing with Measurement Error (David Borchers); and Density Surface Modelling (Jay Barlow). The sessions were followed by a discussion, and this is summarized at the end of the report.Spatial patterns and species coexistence : using spatial statistics to identify underlying ecological processes in plant communities
http://hdl.handle.net/10023/3084
Abstract: The use of spatial statistics to investigate ecological processes in plant communities is becoming increasingly widespread. In diverse communities such as tropical rainforests, analysis of spatial structure may help to unravel the various processes that act and interact to maintain high levels of diversity. In particular, a number of contrasting mechanisms have been suggested to explain species coexistence, and these differ greatly in their practical implications for the ecology and conservation of tropical forests. Traditional first-order measures of community structure have proved unable to distinguish these mechanisms in practice, but statistics that describe spatial structure may be able to do so. This is of great interest and relevance as spatially explicit data become available for a range of ecological communities and analysis methods for these data become more accessible.
This thesis investigates the potential for inference about underlying ecological processes in plant communities using spatial statistics. Current methodologies for spatial analysis are reviewed and extended, and are used to characterise the spatial signals of the principal theorised mechanisms of coexistence. The sensitivity of a range of spatial statistics to these signals is assessed, and the strength of such signals in natural communities is investigated.
The spatial signals of the processes considered here are found to be strong and robust to modelled stochastic variation. Several new and existing spatial statistics are found to be sensitive to these signals, and offer great promise for inference about underlying processes from empirical data. The relative strengths of particular processes are found to vary between natural communities, with any one theory being insufficient to explain observed patterns. This thesis extends both understanding of species coexistence in diverse plant communities and the methodology for assessing underlying process in particular cases. It demonstrates that the potential of spatial statistics in ecology is great and largely unexplored.Thu, 01 Nov 2012 00:00:00 GMThttp://hdl.handle.net/10023/30842012-11-01T00:00:00ZBrown, CalumThe use of spatial statistics to investigate ecological processes in plant communities is becoming increasingly widespread. In diverse communities such as tropical rainforests, analysis of spatial structure may help to unravel the various processes that act and interact to maintain high levels of diversity. In particular, a number of contrasting mechanisms have been suggested to explain species coexistence, and these differ greatly in their practical implications for the ecology and conservation of tropical forests. Traditional first-order measures of community structure have proved unable to distinguish these mechanisms in practice, but statistics that describe spatial structure may be able to do so. This is of great interest and relevance as spatially explicit data become available for a range of ecological communities and analysis methods for these data become more accessible.
This thesis investigates the potential for inference about underlying ecological processes in plant communities using spatial statistics. Current methodologies for spatial analysis are reviewed and extended, and are used to characterise the spatial signals of the principal theorised mechanisms of coexistence. The sensitivity of a range of spatial statistics to these signals is assessed, and the strength of such signals in natural communities is investigated.
The spatial signals of the processes considered here are found to be strong and robust to modelled stochastic variation. Several new and existing spatial statistics are found to be sensitive to these signals, and offer great promise for inference about underlying processes from empirical data. The relative strengths of particular processes are found to vary between natural communities, with any one theory being insufficient to explain observed patterns. This thesis extends both understanding of species coexistence in diverse plant communities and the methodology for assessing underlying process in particular cases. It demonstrates that the potential of spatial statistics in ecology is great and largely unexplored.Vessel noise affects beaked whale behavior : Results of a dedicated acoustic response study
http://hdl.handle.net/10023/3078
Abstract: Some beaked whale species are susceptible to the detrimental effects of anthropogenic noise. Most studies have concentrated on the effects of military sonar, but other forms of acoustic disturbance (e.g. shipping noise) may disrupt behavior. An experiment involving the exposure of target whale groups to intense vessel-generated noise tested how these exposures influenced the foraging behavior of Blainville’s beaked whales (Mesoplodon densirostris) in the Tongue of the Ocean (Bahamas). A military array of bottom-mounted hydrophones was used to measure the response based upon changes in the spatial and temporal pattern of vocalizations. The archived acoustic data were used to compute metrics the echolocation-based foraging behavior for 16 targeted groups, 10 groups further away on the range, and 26 nonexposed groups. The duration of foraging bouts was not significantly affected by the exposure. Changes in the hydrophone over which the group was most frequently detected occurred as the animals moved around within a foraging bout, and their number was significantly less the closer the whales were to the sound source. Non-exposed groups also had significantly more changes in the primary hydrophone than exposed groups irrespective of distance. Our results suggested that broadband ship noise caused a significant change in beaked whale behavior up to at least 5.2 kilometers away from the vessel. The observed change could potentially correspond to a restriction in the movement of groups, a period of more directional travel, a reduction in the number of individuals clicking within the group, or a response to changes in prey movement.Fri, 03 Aug 2012 00:00:00 GMThttp://hdl.handle.net/10023/30782012-08-03T00:00:00ZPirotta, EnricoMilor, RachelQuick, Nicola JaneMoretti, DavidDimarzio, NancyTyack, Peter LloydBoyd, IanHastie, Gordon DrummondSome beaked whale species are susceptible to the detrimental effects of anthropogenic noise. Most studies have concentrated on the effects of military sonar, but other forms of acoustic disturbance (e.g. shipping noise) may disrupt behavior. An experiment involving the exposure of target whale groups to intense vessel-generated noise tested how these exposures influenced the foraging behavior of Blainville’s beaked whales (Mesoplodon densirostris) in the Tongue of the Ocean (Bahamas). A military array of bottom-mounted hydrophones was used to measure the response based upon changes in the spatial and temporal pattern of vocalizations. The archived acoustic data were used to compute metrics the echolocation-based foraging behavior for 16 targeted groups, 10 groups further away on the range, and 26 nonexposed groups. The duration of foraging bouts was not significantly affected by the exposure. Changes in the hydrophone over which the group was most frequently detected occurred as the animals moved around within a foraging bout, and their number was significantly less the closer the whales were to the sound source. Non-exposed groups also had significantly more changes in the primary hydrophone than exposed groups irrespective of distance. Our results suggested that broadband ship noise caused a significant change in beaked whale behavior up to at least 5.2 kilometers away from the vessel. The observed change could potentially correspond to a restriction in the movement of groups, a period of more directional travel, a reduction in the number of individuals clicking within the group, or a response to changes in prey movement.Global analysis of cetacean line-transect surveys : detecting trends in cetacean density
http://hdl.handle.net/10023/2747
Abstract: Measuring the effect of anthropogenic change on cetacean populations is hampered by our lack of understanding about population status and a lack of power in the available data to detect trends in abundance. Often long-term data from repeated surveys are lacking, and alternative approaches to trend detection must be considered. We utilised an existing database of line transect survey records to determine whether temporal trends could be detected when survey effort from around the world was combined. We extracted density estimates for 25 species and fitted generalised additive models (GAMs) to investigate whether taxonomic, spatial or methodological differences among systematic line-transect surveys affect estimates of density and whether we can identify temporal trends in the data once these factors are accounted for. The selected GAM consisted of 2 parts: an intercept term that was a complex interaction of taxonomic, spatial and methodological factors and a smooth temporal term with trends varying by family and ocean basin. We discuss the trends found and assess the suitability of published density estimates for detecting temporal trends using retrospective power analysis. In conclusion, increasing sample size through combining survey effort across a global scale does not necessarily result in sufficient power to detect trends because of the extent of variability across surveys, species and oceans. Instead, results from repeated dedicated surveys designed specifically for the species and geographical region of interest should be used to inform conservation and management.Mon, 07 May 2012 00:00:00 GMThttp://hdl.handle.net/10023/27472012-05-07T00:00:00ZJewell, Rebecca LucyThomas, LenHarris, Catriona MKaschner, KristinWiff, Rodrigo AlexisHammond, Philip StevenQuick, Nicola JaneMeasuring the effect of anthropogenic change on cetacean populations is hampered by our lack of understanding about population status and a lack of power in the available data to detect trends in abundance. Often long-term data from repeated surveys are lacking, and alternative approaches to trend detection must be considered. We utilised an existing database of line transect survey records to determine whether temporal trends could be detected when survey effort from around the world was combined. We extracted density estimates for 25 species and fitted generalised additive models (GAMs) to investigate whether taxonomic, spatial or methodological differences among systematic line-transect surveys affect estimates of density and whether we can identify temporal trends in the data once these factors are accounted for. The selected GAM consisted of 2 parts: an intercept term that was a complex interaction of taxonomic, spatial and methodological factors and a smooth temporal term with trends varying by family and ocean basin. We discuss the trends found and assess the suitability of published density estimates for detecting temporal trends using retrospective power analysis. In conclusion, increasing sample size through combining survey effort across a global scale does not necessarily result in sufficient power to detect trends because of the extent of variability across surveys, species and oceans. Instead, results from repeated dedicated surveys designed specifically for the species and geographical region of interest should be used to inform conservation and management.A critical review of the literature on population modelling
http://hdl.handle.net/10023/2241
Abstract: The 2005 report of the National Research Council’s ‘Committee on Characterizing Biologically Significant Marine Mammal Behavior’ proposed a framework, which they called PCAD - Population Consequences of Acoustic Disturbance, that uses a series of transfer functions to link behavioural responses to sound with life functions, vital rates, and population change. The Committee suggested that the best understood transfer functions are those linking vital rates to population change. One of the main aims of this report is to document that understanding. However, we also show how the existing frameworks for modelling the dynamics of marine mammal populations can be extended to include the effects of behavioural responses on vital rates. In Chapter 1 we introduce the central concept of the rate of increase (lambda) of a population, which we believe is the most useful measure of the effects of behavioural responses on the dynamics of a population. If the value of lambda exceeds one, then thepopulation will increase over time; if it is less than one it will decrease. We show how changes in lambda provide a measure of the impact of human activities (such as exploitation, conservation, or disturbance) on a population. We also introduce structured population models, which take account of the fact that all individuals in a population are not identical, and show how the dynamics of different parts of a population can be modelled using a population projection matrix. The mathematical properties of this projection matrix can be used to determine the sensitivity of lambda to small changes in vital rates. Finally, we provide a very brief introduction to the concept of stochasticity, and the use of lambda to predict when (and if) a population might be driven to extinction. Chapter 2 describes how lambda also provides a measure of the Darwinian fitness of the individual members of a population. An individual’s fitness, the contribution it will make to future generations, depends to a large extent on its body condition and on the risks of mortality to which it is exposed. Both of these could be affected by behaviour responses to sound. We also explain current theories about the relationship between an individual’s feeding behaviour and the abundance and distribution of prey, and how this can affect body condition. Chapter 3 provides a more detailed description of how elasticity analysis can be used to investigate the impact of changes in vital rates on lambda . Elasticity analysis is a useful tool for detecting which vital rates are most important in determining the dynamics of a population. However, its value is limited because it does not take account of random variations (stochasticity) and, in theory, it can only predict the effect of small changes in vital rates. Chapter 4 describes the fundamental concept of density dependence: the way in which vital rates change with population size or the availability of resources, such as prey. Not only is density dependence an essential prerequisite for population stability and sustainable use, but the form it takes will also determine how a population responds to behavioural changes. This is because behaviour, and particularly the effect of behavioural change on body condition, plays a central role in many of the mechanistic models of density dependence. Chapters 5 and 6 explore the way in which additional complexities, such as social structure and the way in which populations are distributed in space, can affect the dynamics of populations. Models that account for these complexities behave in a much less predictable way than the relatively simple structured models that form the core of Chapters 1-4. So far, the models of population dynamics that we have reviewed have been deterministic. That is, they have assumed that the only way in which vital rates can vary is in response to a change in abundance, via density dependent mechanisms. In Chapters 7 and 8 we investigate the effect of random variation (stochasticity) on population dynamics. We distinguish the effects of demographic stochasticity, chance variations in the number of animals that die or give birth in a time interval that occur even if vital rates do not vary over time, and environmental stochasticity, which is the result of variations in vital rates across years. Variation in abundance may also occur as a result of environmental change and changes in the ecological community of which a population is a part. The effect of all these sources of variation is to reduce the realised growth rate of a population, and therefore its risk of extinction. In Chapter 9 we consider how the basic population modelling framework described in Chapters 1-8 might be extended to take account of the life functions identified by the NRC Committee. We suggest that these life functions are useful for defining the context in which behavioural responses might affect vital rates, but that they do not need to be modelled explicitly. Removing vital functions from the PCAD framework results in a much simpler structure, which is compatible with existing population modelling frameworks. However, these will have to be extended to allow population states, like body condition, that vary continuously to be modelled. Chapter 10 describes how changes in lambda can be detected. The simple analytical frameworks that are available for this are all vulnerable to the effects of variability that we introduced in Chapter 7. However, there is a framework (state-space and hidden Markov process modelling) that can account for the effects of this variability, and we recommend its use for detecting trends. The additional benefit of this approach is that its use results in a detailed model of the dynamics of the population that is under investigation. Chapter 11 reviews the different model structures that can be used to describe the dynamics of a population, and explains when different forms of population models (e.g. discrete vs. continuous time, deterministic vs. stochastic) are most appropriate. We also discuss how these different frameworks can be extended to account for continuous population states, as recommended in Chapter 8. The final focus is on how state-space models can be fitted to time series of abundance estimates and information on vital rates. Chapter 12 looks at the relevance of the different modelling approaches described in the previous chapters for analysing the potential effects of behavioural responses to sound on population dynamics, particularly the kinds of sounds that may be generated by the oil and gas industry. We conclude that lambda , the population rate of increase, and its variation provides a useful measure of these effects. We also believe that the models used for this purpose will certainly have to account for the effects of variability and density dependence. They will probably also have to account for the effects of social structure and the way in which populations use space. The state-space modelling framework outlined in Chapter 11 can, in principle, be extended to capture all of these features although work on this is still in its infancy.
Description: Final Report to the Joint Industry Project of the International Association of Oil & Gas Producers on contract JIP22 07_20Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10023/22412009-01-01T00:00:00ZCabrelli, AbigailHarwood, JohnMatthiopoulos, JasonNew, Leslie FrancesThomas, LenThe 2005 report of the National Research Council’s ‘Committee on Characterizing Biologically Significant Marine Mammal Behavior’ proposed a framework, which they called PCAD - Population Consequences of Acoustic Disturbance, that uses a series of transfer functions to link behavioural responses to sound with life functions, vital rates, and population change. The Committee suggested that the best understood transfer functions are those linking vital rates to population change. One of the main aims of this report is to document that understanding. However, we also show how the existing frameworks for modelling the dynamics of marine mammal populations can be extended to include the effects of behavioural responses on vital rates. In Chapter 1 we introduce the central concept of the rate of increase (lambda) of a population, which we believe is the most useful measure of the effects of behavioural responses on the dynamics of a population. If the value of lambda exceeds one, then thepopulation will increase over time; if it is less than one it will decrease. We show how changes in lambda provide a measure of the impact of human activities (such as exploitation, conservation, or disturbance) on a population. We also introduce structured population models, which take account of the fact that all individuals in a population are not identical, and show how the dynamics of different parts of a population can be modelled using a population projection matrix. The mathematical properties of this projection matrix can be used to determine the sensitivity of lambda to small changes in vital rates. Finally, we provide a very brief introduction to the concept of stochasticity, and the use of lambda to predict when (and if) a population might be driven to extinction. Chapter 2 describes how lambda also provides a measure of the Darwinian fitness of the individual members of a population. An individual’s fitness, the contribution it will make to future generations, depends to a large extent on its body condition and on the risks of mortality to which it is exposed. Both of these could be affected by behaviour responses to sound. We also explain current theories about the relationship between an individual’s feeding behaviour and the abundance and distribution of prey, and how this can affect body condition. Chapter 3 provides a more detailed description of how elasticity analysis can be used to investigate the impact of changes in vital rates on lambda . Elasticity analysis is a useful tool for detecting which vital rates are most important in determining the dynamics of a population. However, its value is limited because it does not take account of random variations (stochasticity) and, in theory, it can only predict the effect of small changes in vital rates. Chapter 4 describes the fundamental concept of density dependence: the way in which vital rates change with population size or the availability of resources, such as prey. Not only is density dependence an essential prerequisite for population stability and sustainable use, but the form it takes will also determine how a population responds to behavioural changes. This is because behaviour, and particularly the effect of behavioural change on body condition, plays a central role in many of the mechanistic models of density dependence. Chapters 5 and 6 explore the way in which additional complexities, such as social structure and the way in which populations are distributed in space, can affect the dynamics of populations. Models that account for these complexities behave in a much less predictable way than the relatively simple structured models that form the core of Chapters 1-4. So far, the models of population dynamics that we have reviewed have been deterministic. That is, they have assumed that the only way in which vital rates can vary is in response to a change in abundance, via density dependent mechanisms. In Chapters 7 and 8 we investigate the effect of random variation (stochasticity) on population dynamics. We distinguish the effects of demographic stochasticity, chance variations in the number of animals that die or give birth in a time interval that occur even if vital rates do not vary over time, and environmental stochasticity, which is the result of variations in vital rates across years. Variation in abundance may also occur as a result of environmental change and changes in the ecological community of which a population is a part. The effect of all these sources of variation is to reduce the realised growth rate of a population, and therefore its risk of extinction. In Chapter 9 we consider how the basic population modelling framework described in Chapters 1-8 might be extended to take account of the life functions identified by the NRC Committee. We suggest that these life functions are useful for defining the context in which behavioural responses might affect vital rates, but that they do not need to be modelled explicitly. Removing vital functions from the PCAD framework results in a much simpler structure, which is compatible with existing population modelling frameworks. However, these will have to be extended to allow population states, like body condition, that vary continuously to be modelled. Chapter 10 describes how changes in lambda can be detected. The simple analytical frameworks that are available for this are all vulnerable to the effects of variability that we introduced in Chapter 7. However, there is a framework (state-space and hidden Markov process modelling) that can account for the effects of this variability, and we recommend its use for detecting trends. The additional benefit of this approach is that its use results in a detailed model of the dynamics of the population that is under investigation. Chapter 11 reviews the different model structures that can be used to describe the dynamics of a population, and explains when different forms of population models (e.g. discrete vs. continuous time, deterministic vs. stochastic) are most appropriate. We also discuss how these different frameworks can be extended to account for continuous population states, as recommended in Chapter 8. The final focus is on how state-space models can be fitted to time series of abundance estimates and information on vital rates. Chapter 12 looks at the relevance of the different modelling approaches described in the previous chapters for analysing the potential effects of behavioural responses to sound on population dynamics, particularly the kinds of sounds that may be generated by the oil and gas industry. We conclude that lambda , the population rate of increase, and its variation provides a useful measure of these effects. We also believe that the models used for this purpose will certainly have to account for the effects of variability and density dependence. They will probably also have to account for the effects of social structure and the way in which populations use space. The state-space modelling framework outlined in Chapter 11 can, in principle, be extended to capture all of these features although work on this is still in its infancy.An update to the methods in Endangered Species Research 2011 paper "Estimating North Pacific right whale Eubalaena japonica density using passive acoustic cue counting"
http://hdl.handle.net/10023/2158
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10023/21582012-01-01T00:00:00ZMarques, Tiago A.Munger, LisaThomas, LenWiggins, SeanHildebrand, JohnEstimating abundance of rare, small mammals: A case study of the Key Largo woodrat (Neotoma floridana smalli)
http://hdl.handle.net/10023/2068
Abstract: Estimates of animal abundance or density are fundamental quantities in ecology and conservation, but for many species such as rare, small mammals, obtaining robust estimates is problematic. In this thesis, I combine elements of two standard abundance estimation methods, capture-recapture and distance sampling, to develop a method called trapping point transects (TPT). In TPT, a "detection function", g(r) (i.e. the probability of capturing an animal, given it is r m from a trap when the trap is set) is estimated using a subset of animals whose locations are known prior to traps being set. Generalised linear models are used to estimate the detection function, and the model can be extended to include random effects to allow for heterogeneity in capture probabilities. Standard point transect methods are modified to estimate abundance. Two abundance estimators are available. The first estimator is based on the reciprocal of the expected probability of detecting an animal, ^P, where the expectation is over r;
whereas the second estimator is the expectation of the reciprocal of ^P.
Performance of the TPT method under various sampling efforts and underlying true detection probabilities of individuals in the population was investigated in a simulation study. When underlying probability of detection was high (g(0) = 0:88) and between-individual variation was small, survey effort could be surprisingly low (c. 510 trap nights) to yield low bias (c. 4%) in the two estimators;
but under certain situations, the second estimator can be extremely biased. Uncertainty and relative bias in population estimates increased with decreasing detectability and increasing between-individual variation.
Abundance of the Key Largo woodrat (Neotoma floridana smalli), an endangered rodent with a restricted geographic range, was estimated using TPT. The TPT method compared well to other viable methods (capture-recapture and spatially-explicit capture-recapture), in terms of both field practicality and cost. The TPT method may generally be useful in estimating animal abundance in trapping studies and variants of the TPT method are presented.Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10023/20682011-01-01T00:00:00ZPotts, Joanne M.Estimates of animal abundance or density are fundamental quantities in ecology and conservation, but for many species such as rare, small mammals, obtaining robust estimates is problematic. In this thesis, I combine elements of two standard abundance estimation methods, capture-recapture and distance sampling, to develop a method called trapping point transects (TPT). In TPT, a "detection function", g(r) (i.e. the probability of capturing an animal, given it is r m from a trap when the trap is set) is estimated using a subset of animals whose locations are known prior to traps being set. Generalised linear models are used to estimate the detection function, and the model can be extended to include random effects to allow for heterogeneity in capture probabilities. Standard point transect methods are modified to estimate abundance. Two abundance estimators are available. The first estimator is based on the reciprocal of the expected probability of detecting an animal, ^P, where the expectation is over r;
whereas the second estimator is the expectation of the reciprocal of ^P.
Performance of the TPT method under various sampling efforts and underlying true detection probabilities of individuals in the population was investigated in a simulation study. When underlying probability of detection was high (g(0) = 0:88) and between-individual variation was small, survey effort could be surprisingly low (c. 510 trap nights) to yield low bias (c. 4%) in the two estimators;
but under certain situations, the second estimator can be extremely biased. Uncertainty and relative bias in population estimates increased with decreasing detectability and increasing between-individual variation.
Abundance of the Key Largo woodrat (Neotoma floridana smalli), an endangered rodent with a restricted geographic range, was estimated using TPT. The TPT method compared well to other viable methods (capture-recapture and spatially-explicit capture-recapture), in terms of both field practicality and cost. The TPT method may generally be useful in estimating animal abundance in trapping studies and variants of the TPT method are presented.Complex Region Spatial Smoother (CReSS)
http://hdl.handle.net/10023/2048
Abstract: Conventional smoothing over complicated coastal and island regions may result in errors across boundaries, due to the use of Euclidean distances to represent inter-point similarity. The new Complex Region Spatial Smoother (CReSS) method presented here, uses estimated geodesic distances, model averaging and a local radial basis function to provide improved smoothing over complex domains. CReSS is compared, via simulation, to recent related smoothing techniques, Thin Plate Splines (TPS, Harder and Desmarais, 1972), geodesic low rank TPS [Wang and Ranalli, 2007] and the Soap film smoother [Wood et al., 2008]. The GLTPS method cannot be used in areas with islands and SOAP can be hard to parameterize. CReSS is comparable with, if not better than, all considered methods on a range of simulations. Supplementary materials for this article are available online.
Description: This work is supported with funding from NERC UKSat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10023/20482011-01-01T00:00:00ZScott Hayward, Lindesay Alexandra SarahMacKenzie, Monique LeaDonovan, Carl RobertWalker, CameronAshe, ErinConventional smoothing over complicated coastal and island regions may result in errors across boundaries, due to the use of Euclidean distances to represent inter-point similarity. The new Complex Region Spatial Smoother (CReSS) method presented here, uses estimated geodesic distances, model averaging and a local radial basis function to provide improved smoothing over complex domains. CReSS is compared, via simulation, to recent related smoothing techniques, Thin Plate Splines (TPS, Harder and Desmarais, 1972), geodesic low rank TPS [Wang and Ranalli, 2007] and the Soap film smoother [Wood et al., 2008]. The GLTPS method cannot be used in areas with islands and SOAP can be hard to parameterize. CReSS is comparable with, if not better than, all considered methods on a range of simulations. Supplementary materials for this article are available online.Bayesian modelling of integrated data and its application to seabird populations
http://hdl.handle.net/10023/1635
Abstract: Integrated data analyses are becoming increasingly popular in studies of wild animal populations where two or more separate sources of data contain information about common parameters. Here we develop an integrated population model using abundance and demographic data from a study of common guillemots (Uria aalge) on the Isle of May, southeast Scotland. A state-space model for the count data is supplemented by three demographic time series (productivity and two mark-recapture-recovery (MRR)), enabling the estimation of prebreeder emigration rate - a parameter for which there is no direct observational data, and which is unidentifiable in the separate analysis of MRR data. A Bayesian approach using MCMC provides a flexible and powerful analysis framework.
This model is extended to provide predictions of future population trajectories. Adopting random effects models for the survival and productivity parameters, we implement the MCMC algorithm to obtain a posterior sample of the underlying process means and variances (and population sizes) within the study period. Given this sample, we predict future demographic parameters, which in turn allows us to predict future population sizes and obtain the corresponding posterior distribution. Under the assumption that recent, unfavourable conditions persist in the future, we obtain a posterior probability of 70% that there is a population decline of >25% over a 10-year period.
Lastly, using MRR data we test for spatial, temporal and age-related correlations in guillemot survival among three widely separated Scottish colonies that have varying overlap in nonbreeding distribution. We show that survival is highly correlated over time for colonies/age classes sharing wintering areas, and essentially uncorrelated for those with separate wintering areas. These results strongly suggest that one or more aspects of winter environment are responsible for spatiotemporal variation in survival of British guillemots, and provide insight into the factors driving multi-population dynamics of the species.Tue, 30 Nov 2010 00:00:00 GMThttp://hdl.handle.net/10023/16352010-11-30T00:00:00ZReynolds, Toby J.Integrated data analyses are becoming increasingly popular in studies of wild animal populations where two or more separate sources of data contain information about common parameters. Here we develop an integrated population model using abundance and demographic data from a study of common guillemots (Uria aalge) on the Isle of May, southeast Scotland. A state-space model for the count data is supplemented by three demographic time series (productivity and two mark-recapture-recovery (MRR)), enabling the estimation of prebreeder emigration rate - a parameter for which there is no direct observational data, and which is unidentifiable in the separate analysis of MRR data. A Bayesian approach using MCMC provides a flexible and powerful analysis framework.
This model is extended to provide predictions of future population trajectories. Adopting random effects models for the survival and productivity parameters, we implement the MCMC algorithm to obtain a posterior sample of the underlying process means and variances (and population sizes) within the study period. Given this sample, we predict future demographic parameters, which in turn allows us to predict future population sizes and obtain the corresponding posterior distribution. Under the assumption that recent, unfavourable conditions persist in the future, we obtain a posterior probability of 70% that there is a population decline of >25% over a 10-year period.
Lastly, using MRR data we test for spatial, temporal and age-related correlations in guillemot survival among three widely separated Scottish colonies that have varying overlap in nonbreeding distribution. We show that survival is highly correlated over time for colonies/age classes sharing wintering areas, and essentially uncorrelated for those with separate wintering areas. These results strongly suggest that one or more aspects of winter environment are responsible for spatiotemporal variation in survival of British guillemots, and provide insight into the factors driving multi-population dynamics of the species.Statistical models for the long-term monitoring of songbird populations: a Bayesian analysis of constant effort sites and ring-recovery data
http://hdl.handle.net/10023/885
Abstract: To underpin and improve advice given to government and other interested parties
on the state of Britain’s common songbird populations, new models for
analysing ecological data are developed in this thesis. These models use data
from the British Trust for Ornithology’s Constant Effort Sites (CES) scheme,
an annual bird-ringing programme in which catch effort is standardised. Data
from the CES scheme are routinely used to index abundance and productivity,
and to a lesser extent estimate adult survival rates. However, two features of
the CES data that complicate analysis were previously inadequately addressed,
namely the presence in the catch of “transient” birds not associated with the
local population, and the sporadic failure in the constancy of effort assumption
arising from the absence of within-year catch data. The current methodology
is extended, with efficient Bayesian models developed for each of these demographic
parameters that account for both of these data nuances, and from which
reliable and usefully precise estimates are obtained.
Of increasing interest is the relationship between abundance and the underlying
vital rates, an understanding of which facilitates effective conservation.
CES data are particularly amenable to an integrated approach to population
modelling, providing a combination of demographic information from a single
source. Such an integrated approach is developed here, employing Bayesian
methodology and a simple population model to unite abundance, productivity
and survival within a consistent framework. Independent data from ring-recoveries
provide additional information on adult and juvenile survival rates.
Specific advantages of this new integrated approach are identified, among which
is the ability to determine juvenile survival accurately, disentangle the probabilities
of survival and permanent emigration, and to obtain estimates of total
seasonal productivity.
The methodologies developed in this thesis are applied to CES data from Sedge
Warbler, Acrocephalus schoenobaenus, and Reed Warbler, A. scirpaceus.Fri, 25 Jun 2010 00:00:00 GMThttp://hdl.handle.net/10023/8852010-06-25T00:00:00ZCave, Vanessa M.To underpin and improve advice given to government and other interested parties
on the state of Britain’s common songbird populations, new models for
analysing ecological data are developed in this thesis. These models use data
from the British Trust for Ornithology’s Constant Effort Sites (CES) scheme,
an annual bird-ringing programme in which catch effort is standardised. Data
from the CES scheme are routinely used to index abundance and productivity,
and to a lesser extent estimate adult survival rates. However, two features of
the CES data that complicate analysis were previously inadequately addressed,
namely the presence in the catch of “transient” birds not associated with the
local population, and the sporadic failure in the constancy of effort assumption
arising from the absence of within-year catch data. The current methodology
is extended, with efficient Bayesian models developed for each of these demographic
parameters that account for both of these data nuances, and from which
reliable and usefully precise estimates are obtained.
Of increasing interest is the relationship between abundance and the underlying
vital rates, an understanding of which facilitates effective conservation.
CES data are particularly amenable to an integrated approach to population
modelling, providing a combination of demographic information from a single
source. Such an integrated approach is developed here, employing Bayesian
methodology and a simple population model to unite abundance, productivity
and survival within a consistent framework. Independent data from ring-recoveries
provide additional information on adult and juvenile survival rates.
Specific advantages of this new integrated approach are identified, among which
is the ability to determine juvenile survival accurately, disentangle the probabilities
of survival and permanent emigration, and to obtain estimates of total
seasonal productivity.
The methodologies developed in this thesis are applied to CES data from Sedge
Warbler, Acrocephalus schoenobaenus, and Reed Warbler, A. scirpaceus.Topics in estimation of quantum channels
http://hdl.handle.net/10023/869
Abstract: A quantum channel is a mapping which sends density matrices to density
matrices. The estimation of quantum channels is of great importance to the
field of quantum information. In this thesis two topics related to estimation
of quantum channels are investigated. The first of these is the upper
bound of Sarovar and Milburn (2006) on the Fisher information obtainable
by measuring the output of a channel. Two questions raised by Sarovar and
Milburn about their bound are answered. A Riemannian metric on the space
of quantum states is introduced, related to the construction of the Sarovar
and Milburn bound. Its properties are characterized.
The second topic investigated is the estimation of unitary channels. The
situation is considered in which an experimenter has several non-identical
unitary channels that have the same parameter. It is shown that it is possible
to improve estimation using the channels together, analogous to the case of
identical unitary channels. Also, a new method of phase estimation is given
based on a method sketched by Kitaev (1996). Unlike other phase estimation
procedures which perform similarly, this procedure requires only very basic
experimental resources.Wed, 23 Jun 2010 00:00:00 GMThttp://hdl.handle.net/10023/8692010-06-23T00:00:00ZO'Loan, Caleb J.A quantum channel is a mapping which sends density matrices to density
matrices. The estimation of quantum channels is of great importance to the
field of quantum information. In this thesis two topics related to estimation
of quantum channels are investigated. The first of these is the upper
bound of Sarovar and Milburn (2006) on the Fisher information obtainable
by measuring the output of a channel. Two questions raised by Sarovar and
Milburn about their bound are answered. A Riemannian metric on the space
of quantum states is introduced, related to the construction of the Sarovar
and Milburn bound. Its properties are characterized.
The second topic investigated is the estimation of unitary channels. The
situation is considered in which an experimenter has several non-identical
unitary channels that have the same parameter. It is shown that it is possible
to improve estimation using the channels together, analogous to the case of
identical unitary channels. Also, a new method of phase estimation is given
based on a method sketched by Kitaev (1996). Unlike other phase estimation
procedures which perform similarly, this procedure requires only very basic
experimental resources.Multi-species state-space modelling of the hen harrier (Circus cyaneus) and red grouse (Lagopus lagopus scoticus) in Scotland
http://hdl.handle.net/10023/864
Abstract: State-space modelling is a powerful tool to study ecological systems. The direct inclusion of uncertainty, unification of models and data, and ability to model unobserved, hidden states increases our knowledge about the environment and provides
new ecological insights. I extend the state-space framework to create multi-species
models, showing that the ability to model ecosystem interactions is limited only by data availability. State-space models are fit using both Bayesian and Frequentist methods, making them independent of a statistical school of thought. Bayesian approaches can have the advantage in their ability to account for missing data and fit hierarchical structures
and models with many parameters to limited data; often the case in ecological studies.
I have taken a Bayesian model fitting approach in this thesis.
The predator-prey interactions between the hen harrier (Circus cyaneus) and red grouse (Lagopus lagopus scoticus) are used to demonstrate state-space modelling’s
capabilities. The harrier data are believed to be known without error, while missing
data make the cyclic dynamics of the grouse harder to model. The grouse-harrier interactions are modelled in a multi-species state-space model, rather than including
one species as a covariate in the other’s model. Finally, models are included for the
harriers’ alternate prey.
The single- and multi-species state-space models for the predator-prey interactions
provide insight into the species’ management. The models investigate aspects of the species’ behaviour, from the mechanisms behind grouse cycles to what motivates harrier immigration. The inferences drawn from these models are applicable to management, suggesting actions to halt grouse cycles or mitigate the grouse-harrier conflict. Overall, the multi-species models suggest that two popular ideas for grouse-harrier management, diversionary feeding and habitat manipulation to reduce alternate prey densities, will not have the desired effect, and in the case of reducing prey densities, may even increase the harriers’ impact on grouse chicks.Wed, 23 Jun 2010 00:00:00 GMThttp://hdl.handle.net/10023/8642010-06-23T00:00:00ZNew, Leslie FrancesState-space modelling is a powerful tool to study ecological systems. The direct inclusion of uncertainty, unification of models and data, and ability to model unobserved, hidden states increases our knowledge about the environment and provides
new ecological insights. I extend the state-space framework to create multi-species
models, showing that the ability to model ecosystem interactions is limited only by data availability. State-space models are fit using both Bayesian and Frequentist methods, making them independent of a statistical school of thought. Bayesian approaches can have the advantage in their ability to account for missing data and fit hierarchical structures
and models with many parameters to limited data; often the case in ecological studies.
I have taken a Bayesian model fitting approach in this thesis.
The predator-prey interactions between the hen harrier (Circus cyaneus) and red grouse (Lagopus lagopus scoticus) are used to demonstrate state-space modelling’s
capabilities. The harrier data are believed to be known without error, while missing
data make the cyclic dynamics of the grouse harder to model. The grouse-harrier interactions are modelled in a multi-species state-space model, rather than including
one species as a covariate in the other’s model. Finally, models are included for the
harriers’ alternate prey.
The single- and multi-species state-space models for the predator-prey interactions
provide insight into the species’ management. The models investigate aspects of the species’ behaviour, from the mechanisms behind grouse cycles to what motivates harrier immigration. The inferences drawn from these models are applicable to management, suggesting actions to halt grouse cycles or mitigate the grouse-harrier conflict. Overall, the multi-species models suggest that two popular ideas for grouse-harrier management, diversionary feeding and habitat manipulation to reduce alternate prey densities, will not have the desired effect, and in the case of reducing prey densities, may even increase the harriers’ impact on grouse chicks.Distance software: design and analysis of distance sampling surveys for estimating population size
http://hdl.handle.net/10023/817
Abstract: 1. Distance sampling is a widely used technique for estimating the size or density of biological populations. Many distance sampling designs and most analyses use the software Distance. 2. We briefly review distance sampling and its assumptions, outline the history, structure and capabilities of Distance, and provide hints on its use. 3. Good survey design is a crucial pre-requisite for obtaining reliable results. Distance has a survey design engine, with a built-in geographic information system, that allows properties of different proposed designs to be examined via simulation, and survey plans to be generated. 4. A first step in analysis of distance sampling data is modelling the probability of detection. Distance contains three increasingly sophisticated analysis engines for this: CDS (conventional distance sampling), which models detection probability as a function of distance from the transect and assumes all objects at zero distance are detected; MCDS (multiple covariate distance sampling), which allows covariates in addition to distance; and MRDS (mark-recapture distance sampling), which relaxes the assumption of certain detection at zero distance. 5. All three engines allow estimation of density or abundance, stratified if required, with associated measures of precision calculated either analytically or via the bootstrap. 6. Advanced analysis topics covered include the use of multipliers to allow analysis of indirect surveys (such as dung or nest surveys), the DSM (density surface modelling) analysis engine for spatial and habitat modelling, and information about accessing the analysis engines directly from other software. 7. Synthesis and applications. Distance sampling is a key method for producing abundance and density estimates in challenging field conditions. The theory underlying the methods continues to expand to cope with realistic estimation situations. In step with theoretical developments, state-of-the-art software that implements these methods is described that makes the methods accessible to practicing ecologists.Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10023/8172010-01-01T00:00:00ZThomas, LenBuckland, Stephen TerrenceRexstad, EricLaake, J LStrindberg, SHedley, S LBishop, J R BMarques, Tiago Andre Lamas Oliveira1. Distance sampling is a widely used technique for estimating the size or density of biological populations. Many distance sampling designs and most analyses use the software Distance. 2. We briefly review distance sampling and its assumptions, outline the history, structure and capabilities of Distance, and provide hints on its use. 3. Good survey design is a crucial pre-requisite for obtaining reliable results. Distance has a survey design engine, with a built-in geographic information system, that allows properties of different proposed designs to be examined via simulation, and survey plans to be generated. 4. A first step in analysis of distance sampling data is modelling the probability of detection. Distance contains three increasingly sophisticated analysis engines for this: CDS (conventional distance sampling), which models detection probability as a function of distance from the transect and assumes all objects at zero distance are detected; MCDS (multiple covariate distance sampling), which allows covariates in addition to distance; and MRDS (mark-recapture distance sampling), which relaxes the assumption of certain detection at zero distance. 5. All three engines allow estimation of density or abundance, stratified if required, with associated measures of precision calculated either analytically or via the bootstrap. 6. Advanced analysis topics covered include the use of multipliers to allow analysis of indirect surveys (such as dung or nest surveys), the DSM (density surface modelling) analysis engine for spatial and habitat modelling, and information about accessing the analysis engines directly from other software. 7. Synthesis and applications. Distance sampling is a key method for producing abundance and density estimates in challenging field conditions. The theory underlying the methods continues to expand to cope with realistic estimation situations. In step with theoretical developments, state-of-the-art software that implements these methods is described that makes the methods accessible to practicing ecologists.Embedding population dynamics in mark-recapture models
http://hdl.handle.net/10023/718
Abstract: Mark-recapture methods use repeated captures of individually identifiable animals to provide estimates of properties of populations. Different models allow estimates to be obtained for population size and rates of processes governing population dynamics. State-space models consist of two linked processes evolving simultaneously over time. The state process models the evolution of the true, but unknown, states of the population. The observation process relates observations on the population to these true states.
Mark-recapture models specified within a state-space framework allow population dynamics models to be embedded in inference ensuring that estimated changes in the population are consistent with assumptions regarding the biology of the modelled population. This overcomes a limitation of current mark-recapture methods.
Two alternative approaches are considered. The "conditional" approach conditions on known numbers of animals possessing capture history patterns including capture in the current time period. An animal's capture history determines its state; consequently, capture parameters appear in the state process rather than the observation process. There is no observation error in the model. Uncertainty occurs only through the numbers of animals not captured in the current time period.
An "unconditional" approach is considered in which the capture histories are regarded as observations. Consequently, capture histories do not influence an animal's state and capture probability parameters appear in the observation process. Capture histories are considered a random realization of the stochastic observation process. This is more consistent with traditional mark-recapture methods.
Development and implementation of particle filtering techniques for fitting these models under each approach are discussed. Simulation studies show reasonable performance for the unconditional approach and highlight problems with the conditional approach. Strengths and limitations of each approach are outlined, with reference to Soay sheep data analysis, and suggestions are presented for future analyses.Wed, 24 Jun 2009 00:00:00 GMThttp://hdl.handle.net/10023/7182009-06-24T00:00:00ZBishop, Jonathan R. B.Mark-recapture methods use repeated captures of individually identifiable animals to provide estimates of properties of populations. Different models allow estimates to be obtained for population size and rates of processes governing population dynamics. State-space models consist of two linked processes evolving simultaneously over time. The state process models the evolution of the true, but unknown, states of the population. The observation process relates observations on the population to these true states.
Mark-recapture models specified within a state-space framework allow population dynamics models to be embedded in inference ensuring that estimated changes in the population are consistent with assumptions regarding the biology of the modelled population. This overcomes a limitation of current mark-recapture methods.
Two alternative approaches are considered. The "conditional" approach conditions on known numbers of animals possessing capture history patterns including capture in the current time period. An animal's capture history determines its state; consequently, capture parameters appear in the state process rather than the observation process. There is no observation error in the model. Uncertainty occurs only through the numbers of animals not captured in the current time period.
An "unconditional" approach is considered in which the capture histories are regarded as observations. Consequently, capture histories do not influence an animal's state and capture probability parameters appear in the observation process. Capture histories are considered a random realization of the stochastic observation process. This is more consistent with traditional mark-recapture methods.
Development and implementation of particle filtering techniques for fitting these models under each approach are discussed. Simulation studies show reasonable performance for the unconditional approach and highlight problems with the conditional approach. Strengths and limitations of each approach are outlined, with reference to Soay sheep data analysis, and suggestions are presented for future analyses.The importance of analysis method for breeding bird survey population trend estimates
http://hdl.handle.net/10023/685
Abstract: Population trends from the Breeding Bird Survey are widely used to focus conservation efforts on species thought to be in decline and to test preliminary hypotheses regarding the causes of these declines. A number of statistical methods have been used to estimate population trends, but there is no consensus us to which is the most reliable. We quantified differences in trend estimates or different analysis methods applied to the same subset of Breeding Bird Survey data. We estimated trends for 115 species in British Columbia using three analysis methods: U.S. National Biological Service route regression, Canadian Wildlife Service route regression, and nonparametric rank-trends analysis. Overall, the number of species estimated to be declining was similar among the three methods, but the number of statistically significant declines was not similar (15, 8, and 29 respectively). In addition, many differences existed among methods in the trend estimates assigned to individual species. Comparing the two route regression methods, Canadian Wildlife Service estimates had a greater absolute magnitude on average than those of the U.S. National Biological Service method. U.S. National Biological Service estimates were on average more positive than the Canadian Wildlife Service estimates when the respective agency's data selection criteria were applied separately. These results imply that our ability to detect population declines and to prioritize species of conservation concern depend strongly upon the analysis method used. This highlights the need for further research to determine how best to accurately estimate trends from the data. We suggest a method for evaluating the performance of the analysis methods by using simulated Breeding Bird Survey data.Mon, 01 Jan 1996 00:00:00 GMThttp://hdl.handle.net/10023/6851996-01-01T00:00:00ZThomas, LenMartin, KathyPopulation trends from the Breeding Bird Survey are widely used to focus conservation efforts on species thought to be in decline and to test preliminary hypotheses regarding the causes of these declines. A number of statistical methods have been used to estimate population trends, but there is no consensus us to which is the most reliable. We quantified differences in trend estimates or different analysis methods applied to the same subset of Breeding Bird Survey data. We estimated trends for 115 species in British Columbia using three analysis methods: U.S. National Biological Service route regression, Canadian Wildlife Service route regression, and nonparametric rank-trends analysis. Overall, the number of species estimated to be declining was similar among the three methods, but the number of statistically significant declines was not similar (15, 8, and 29 respectively). In addition, many differences existed among methods in the trend estimates assigned to individual species. Comparing the two route regression methods, Canadian Wildlife Service estimates had a greater absolute magnitude on average than those of the U.S. National Biological Service method. U.S. National Biological Service estimates were on average more positive than the Canadian Wildlife Service estimates when the respective agency's data selection criteria were applied separately. These results imply that our ability to detect population declines and to prioritize species of conservation concern depend strongly upon the analysis method used. This highlights the need for further research to determine how best to accurately estimate trends from the data. We suggest a method for evaluating the performance of the analysis methods by using simulated Breeding Bird Survey data.Retrospective power analysis
http://hdl.handle.net/10023/679
Abstract: Many papers have appeared in the recent biological literature encouraging us to incorporate statistical power analysis into our hypothesis testing protocol (Peterman 1990; Fairweather 1991; Muller & Benignus 1992; Taylor & Gerrodette 1993; Searcy-Bernal 1994; Thomas & Juanes 1996). The importance of doing a power analysis before beginning a study (prospective power analysis) is universally accepted: such analyses help us to decide how many samples are required to have a good chance of getting unambiguous results. In contrast, the role of power analysis after the data are collected and analyzed (retrospective power analysis) is controversial, as is evidenced by the papers of Reed and Blaustein (1995) and Hayes and Steidl (1997). The controversy is over the use of information from the sample data in retrospective power calculations. As I will show, the type of information used has fundamental implications for the value of such analyses. I compare the approaches to calculating retrospective power, noting the strengths and weaknesses of each, and make general recommendations as to how and when retrospective power analyses should be conducted.
Description: The pdf contains the article; the ASCII file contains SAS code to calculate power and confidence limits for simple linear regression, as detailed in the article appendix.Wed, 01 Jan 1997 00:00:00 GMThttp://hdl.handle.net/10023/6791997-01-01T00:00:00ZThomas, LenMany papers have appeared in the recent biological literature encouraging us to incorporate statistical power analysis into our hypothesis testing protocol (Peterman 1990; Fairweather 1991; Muller & Benignus 1992; Taylor & Gerrodette 1993; Searcy-Bernal 1994; Thomas & Juanes 1996). The importance of doing a power analysis before beginning a study (prospective power analysis) is universally accepted: such analyses help us to decide how many samples are required to have a good chance of getting unambiguous results. In contrast, the role of power analysis after the data are collected and analyzed (retrospective power analysis) is controversial, as is evidenced by the papers of Reed and Blaustein (1995) and Hayes and Steidl (1997). The controversy is over the use of information from the sample data in retrospective power calculations. As I will show, the type of information used has fundamental implications for the value of such analyses. I compare the approaches to calculating retrospective power, noting the strengths and weaknesses of each, and make general recommendations as to how and when retrospective power analyses should be conducted.A unified framework for modelling wildlife population dynamics
http://hdl.handle.net/10023/678
Abstract: This paper proposes a unified framework for defining and fitting stochastic, discrete-time, discrete-stage population dynamics models. The biological system is described by a state–space model, where the true but unknown state of the population is modelled by a state process, and this is linked to survey data by an observation process. All sources of uncertainty in the inputs, including uncertainty about model specification, are readily incorporated. The paper shows how the state process can be represented as a generalization of the standard Leslie or Lefkovitch matrix. By dividing the state process into subprocesses, complex models can be constructed from manageable building blocks. The paper illustrates the approach with a model of the British Grey Seal metapopulation, using sequential importance sampling with kernel smoothing to fit the model.
Description: The pdf document contains the full article text; program code (in S-PLUS 6.1) for the example analysis is in the three text files; data is available from the Sea Mammal Research Unit (http://www.smru.st-and.ac.uk)Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/10023/6782005-01-01T00:00:00ZThomas, LenBuckland, Stephen T.Newman, KBHarwood, JohnThis paper proposes a unified framework for defining and fitting stochastic, discrete-time, discrete-stage population dynamics models. The biological system is described by a state–space model, where the true but unknown state of the population is modelled by a state process, and this is linked to survey data by an observation process. All sources of uncertainty in the inputs, including uncertainty about model specification, are readily incorporated. The paper shows how the state process can be represented as a generalization of the standard Leslie or Lefkovitch matrix. By dividing the state process into subprocesses, complex models can be constructed from manageable building blocks. The paper illustrates the approach with a model of the British Grey Seal metapopulation, using sequential importance sampling with kernel smoothing to fit the model.WinBUGS for population ecologists: Bayesian modeling using Markov Chain Monte Carlo methods.
http://hdl.handle.net/10023/677
Abstract: The computer package WinBUGS is introduced. We first give a brief introduction to Bayesian theory and its implementation using Markov chain Monte Carlo (MCMC) algorithms. We then present three case studies showing how WinBUGS can be used when classical theory is difficult to implement. The first example uses data on white storks from Baden Württemberg, Germany, to demonstrate the use of mark-recapture models to estimate survival, and also how to cope with unexplained variance through random effects. Recent advances in methodology and also the WinBUGS software allow us to introduce (i) a flexible way of incorporating covariates using spline smoothing and (ii) a method to deal with missing values in covariates. The second example shows how to estimate population density while accounting for detectability, using distance sampling methods applied to a test dataset collected on a known population of wooden stakes. Finally, the third case study involves the use of state-space models of wildlife population dynamics to make inferences about density dependence in a North American duck species. Reversible Jump MCMC is used to calculate the probability of various candidate models. For all examples, data and WinBUGS code are provided.
Description: This paper was presented at the EURING 2007 Technical Meeting, January 14-21, Dunedin, New Zealand. It has been submitted for publication in the conference proceedings, which will appear as a special issue of Environmental and Ecological Statistics.; The zip file contains accompanying code in WinBUGSTue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10023/6772008-01-01T00:00:00ZGiminez, OBonner, S JKing, Ruth, 1977-Parker, R ABrooks, S PJamieson, L EGrosbois, VMorgan, B J TThomas, LenThe computer package WinBUGS is introduced. We first give a brief introduction to Bayesian theory and its implementation using Markov chain Monte Carlo (MCMC) algorithms. We then present three case studies showing how WinBUGS can be used when classical theory is difficult to implement. The first example uses data on white storks from Baden Württemberg, Germany, to demonstrate the use of mark-recapture models to estimate survival, and also how to cope with unexplained variance through random effects. Recent advances in methodology and also the WinBUGS software allow us to introduce (i) a flexible way of incorporating covariates using spline smoothing and (ii) a method to deal with missing values in covariates. The second example shows how to estimate population density while accounting for detectability, using distance sampling methods applied to a test dataset collected on a known population of wooden stakes. Finally, the third case study involves the use of state-space models of wildlife population dynamics to make inferences about density dependence in a North American duck species. Reversible Jump MCMC is used to calculate the probability of various candidate models. For all examples, data and WinBUGS code are provided.Density estimation and time trend analysis of large herbivores in Nagarhole, India
http://hdl.handle.net/10023/669
Abstract: Density estimates for six large herbivore species were obtained through
analysis of line transect data from Nagarhole National Park, south-western India,
collected between 1989 and 2000. These species were Chital (Axis axis), Sambar
(Cervus unicolor), Gaur (Bos gaurus), Wild Pig (Sus scrofa), Muntjac (Muntiacus
muntjak) and Asian Elephant (Elephas maximus). Multiple Covariate Distance
Sampling (MCDS) models were used to derive these density estimates. The distance
histograms showed a relatively large spike at zero, which can lead to problems when
fitting MCDS models. The effects of this spike were investigated and remedied by
forward truncation. Density estimates from unmodified dataset were 10-15% higher
than estimates from the forward truncated data, with this going up to 37% for
Muntjac. These could possibly be over estimates. Empirical trend models were then
fit to the density estimates. Overall trends were stable, though there were intra-habitat
differences in trends for some species. The trends were similar both in cases where
forward truncation was done as well as in those where they were not.
Description: MRes in Environmental BiologySat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/10023/6692005-01-01T00:00:00ZGangadharan, AdityaDensity estimates for six large herbivore species were obtained through
analysis of line transect data from Nagarhole National Park, south-western India,
collected between 1989 and 2000. These species were Chital (Axis axis), Sambar
(Cervus unicolor), Gaur (Bos gaurus), Wild Pig (Sus scrofa), Muntjac (Muntiacus
muntjak) and Asian Elephant (Elephas maximus). Multiple Covariate Distance
Sampling (MCDS) models were used to derive these density estimates. The distance
histograms showed a relatively large spike at zero, which can lead to problems when
fitting MCDS models. The effects of this spike were investigated and remedied by
forward truncation. Density estimates from unmodified dataset were 10-15% higher
than estimates from the forward truncated data, with this going up to 37% for
Muntjac. These could possibly be over estimates. Empirical trend models were then
fit to the density estimates. Overall trends were stable, though there were intra-habitat
differences in trends for some species. The trends were similar both in cases where
forward truncation was done as well as in those where they were not.Models of random wildlife movement with an application to distance sampling
http://hdl.handle.net/10023/668
Abstract: In this paper we present three models of random wildlife movement: a one dimensional model of wildlife-observer encounters on roads, an analogous two dimensional model, and an further two-dimensional model that borrows from the ideas of statistical mechanics. We then derive unbiased estimates of wildlife density in terms of encounters for each of these models. By extending these results to incorporate uncertain detection, we suggest three novel distance sampling methods and briefly consider possible field applications.Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10023/6682007-01-01T00:00:00ZDiTraglia, Francis J.In this paper we present three models of random wildlife movement: a one dimensional model of wildlife-observer encounters on roads, an analogous two dimensional model, and an further two-dimensional model that borrows from the ideas of statistical mechanics. We then derive unbiased estimates of wildlife density in terms of encounters for each of these models. By extending these results to incorporate uncertain detection, we suggest three novel distance sampling methods and briefly consider possible field applications.Designing a shipboard line transect survey to estimate cetacean abundance off the Azores Archipelago, Portugal
http://hdl.handle.net/10023/667
Abstract: Management schemes dedicated to the conservation of wildlife populations rely on the effective monitoring of population size, and this requires the accurate and precise estimation of abundance. The accuracy and precision of estimates are determined to a large extent by the survey design. Line transect surveys are commonly applied to wildlife population assessments in which the primary purpose of a survey design is to ensure that the critical distance sampling assumptions are met.
Little information is available regarding cetacean abundance in the Archipelago of the Azores (Portugal). This study aims to design a line transect shipboard survey that allows the collection of data required to provide abundance estimates for such species. Several aspects must be taken into consideration when designing a survey to estimate cetacean abundance. This is an iterative process, and there is a constant trade off between the logistic constraints and the desired statistical robustness. Information on this process is provided to aid policy makers and environmental managers, such as the criteria used for the choices made when defining the elements of a survey design.
Three survey effort scenarios are provided to illustrate the range of possibilities between statistical robustness and logistic/ management restrictions. A survey is designed for the more economical scenario (L=5000Km), although the second scenario is the one recommended to be implemented (L=17,600Km) given it provides robust estimates of
abundance (CV<=0.2).
Description: Revised version November 2008. MRes in Marine Mammal ScienceTue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10023/6672008-01-01T00:00:00ZFaustino, Cláudia Estevinho SantosManagement schemes dedicated to the conservation of wildlife populations rely on the effective monitoring of population size, and this requires the accurate and precise estimation of abundance. The accuracy and precision of estimates are determined to a large extent by the survey design. Line transect surveys are commonly applied to wildlife population assessments in which the primary purpose of a survey design is to ensure that the critical distance sampling assumptions are met.
Little information is available regarding cetacean abundance in the Archipelago of the Azores (Portugal). This study aims to design a line transect shipboard survey that allows the collection of data required to provide abundance estimates for such species. Several aspects must be taken into consideration when designing a survey to estimate cetacean abundance. This is an iterative process, and there is a constant trade off between the logistic constraints and the desired statistical robustness. Information on this process is provided to aid policy makers and environmental managers, such as the criteria used for the choices made when defining the elements of a survey design.
Three survey effort scenarios are provided to illustrate the range of possibilities between statistical robustness and logistic/ management restrictions. A survey is designed for the more economical scenario (L=5000Km), although the second scenario is the one recommended to be implemented (L=17,600Km) given it provides robust estimates of
abundance (CV<=0.2).Behavioural changes of a long-ranging diver in response to oceanographic conditions
http://hdl.handle.net/10023/665
Abstract: The development of an animal-borne instrument that can record oceanographic measurements (CTD-SRDL) has enabled the collection of oceanographic data at a scale relevant to the counterpart behavioural data, both in time and 3-dimensional space. This has advanced the potential for studies of the behaviour of deep-diving marine animals and the way in which they respond to their environment, yet the nature of the data delivered by CTD-SRDLs presents substantial analytical challenges and places constraints on its biological interpretation. Behavioural and environmental data, collected using CTD-SRDLs deployed on southern elephant seals (Mirounga leonina) from the South Georgia subpopulation in 2004 and 2005, are analysed for 13 females and 4 males (21,015 dives). Compressed dive profiles are used to classify individual dives into six distinct types based on their 2-dimensional time-depth characteristics using random forest classification. The relationship between dive type and environmental variables, derived from oceanographic data recorded on board the animals, is investigated in the context of regression analysis, employing a multinomial model, as well as independently fitted Generalized Linear Models (GLM) and Generalized Additive Models (GAM) for each dive type. Regression is not found to be an appropriate method for analysing abstracted behavioural dive data, and other methods are suggested. We show that functional specializations can be manifested within a dive type, using square bottom dives (SQ) as an example. The usefulness of dive classification is discussed in the context of behavioural interpretation, and validity of the ecological functions attached to each class. Preliminary analyses are important drivers of further research into improving the interpretability of abstracted behavioural data, and developing efficient, standardized methods for widespread application to this type of data, which is obtained in abundance via satellite telemetry.
Description: BL 5019 Research project. MRes Environmental BiologyMon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10023/6652007-01-01T00:00:00ZPhotopoulos, TheoniThe development of an animal-borne instrument that can record oceanographic measurements (CTD-SRDL) has enabled the collection of oceanographic data at a scale relevant to the counterpart behavioural data, both in time and 3-dimensional space. This has advanced the potential for studies of the behaviour of deep-diving marine animals and the way in which they respond to their environment, yet the nature of the data delivered by CTD-SRDLs presents substantial analytical challenges and places constraints on its biological interpretation. Behavioural and environmental data, collected using CTD-SRDLs deployed on southern elephant seals (Mirounga leonina) from the South Georgia subpopulation in 2004 and 2005, are analysed for 13 females and 4 males (21,015 dives). Compressed dive profiles are used to classify individual dives into six distinct types based on their 2-dimensional time-depth characteristics using random forest classification. The relationship between dive type and environmental variables, derived from oceanographic data recorded on board the animals, is investigated in the context of regression analysis, employing a multinomial model, as well as independently fitted Generalized Linear Models (GLM) and Generalized Additive Models (GAM) for each dive type. Regression is not found to be an appropriate method for analysing abstracted behavioural dive data, and other methods are suggested. We show that functional specializations can be manifested within a dive type, using square bottom dives (SQ) as an example. The usefulness of dive classification is discussed in the context of behavioural interpretation, and validity of the ecological functions attached to each class. Preliminary analyses are important drivers of further research into improving the interpretability of abstracted behavioural data, and developing efficient, standardized methods for widespread application to this type of data, which is obtained in abundance via satellite telemetry.Using generalized estimating equations with regression splines to improve analysis of butterfly transect data
http://hdl.handle.net/10023/488
Abstract: Surveying animal populations is an important aspect of wildlife
management. Distinguishing trend from random fluctuations and
quantifying trend are key goals in any analysis.
The aim of this thesis is to review analyses of Butterfly Monitoring
Survey (BMS) data and to develop new methods which address some
flaws in previous studies. The BMS was established in 1976 at Monks
Wood, Cambridgeshire and sites were added over time throughout
Britain in order to monitor butterfly population trends. Weekly
counts are made over the monitoring season and the main aims are to
produce annual indices and compare these indices over time for any
particular species.
Originally, weekly counts were summed to produce relative indices
and missing counts were estimated using linear interpolation. This
thesis discusses the weaknesses of this basic method
and suggests possible improvements.
In recent years, with advancements in statistical methods and
increased computer power, new methods can be applied to accommodate
the longitudinal and flexible nature of ecological data.
Mixed Models, Generalized Estimating Equations and Generalized
Additive Models are used and the relative merits of each modelling
approach discussed. These methods allow for correlation and
non-linearity in data.
Model selection is an important consideration when modelling and
different tests are introduced and compared.
Once a model is selected, site-level indices are estimated, which
can be collated to produce regional and national indices. Different
methods of estimating precision around indices are also contrasted.
Bootstrapping is found to be a convenient and dependable approach.
Abundance is difficult to disentangle from detectability when only
counts of species are carried out. Methods for dealing with this
problem are suggested.
Once reliable annual abundance estimates are found, they can be
compared over time using a variety of statistical techniques. The
chain-ratio method is applied to a subset of real data.Sun, 01 Jun 2008 00:00:00 GMThttp://hdl.handle.net/10023/4882008-06-01T00:00:00ZBrewer, CiaraSurveying animal populations is an important aspect of wildlife
management. Distinguishing trend from random fluctuations and
quantifying trend are key goals in any analysis.
The aim of this thesis is to review analyses of Butterfly Monitoring
Survey (BMS) data and to develop new methods which address some
flaws in previous studies. The BMS was established in 1976 at Monks
Wood, Cambridgeshire and sites were added over time throughout
Britain in order to monitor butterfly population trends. Weekly
counts are made over the monitoring season and the main aims are to
produce annual indices and compare these indices over time for any
particular species.
Originally, weekly counts were summed to produce relative indices
and missing counts were estimated using linear interpolation. This
thesis discusses the weaknesses of this basic method
and suggests possible improvements.
In recent years, with advancements in statistical methods and
increased computer power, new methods can be applied to accommodate
the longitudinal and flexible nature of ecological data.
Mixed Models, Generalized Estimating Equations and Generalized
Additive Models are used and the relative merits of each modelling
approach discussed. These methods allow for correlation and
non-linearity in data.
Model selection is an important consideration when modelling and
different tests are introduced and compared.
Once a model is selected, site-level indices are estimated, which
can be collated to produce regional and national indices. Different
methods of estimating precision around indices are also contrasted.
Bootstrapping is found to be a convenient and dependable approach.
Abundance is difficult to disentangle from detectability when only
counts of species are carried out. Methods for dealing with this
problem are suggested.
Once reliable annual abundance estimates are found, they can be
compared over time using a variety of statistical techniques. The
chain-ratio method is applied to a subset of real data.Incorporating measurement error and density gradients in distance sampling surveys
http://hdl.handle.net/10023/391
Abstract: Distance sampling is one of the most commonly used methods for estimating density
and abundance. Conventional methods are based on the distances of detected animals
from the center of point transects or the center line of line transects. These distances
are used to model a detection function: the probability of detecting an animal, given
its distance from the line or point. The probability of detecting an animal in the
covered area is given by the mean value of the detection function with respect to
the available distances to be detected. Given this probability, a Horvitz-Thompson-
like estimator of abundance for the covered area follows, hence using a model-based
framework. Inferences for the wider survey region are justified using the survey design.
Conventional distance sampling methods are based on a set of assumptions. In
this thesis I present results that extend distance sampling on two fronts.
Firstly, estimators are derived for situations in which there is measurement error in
the distances. These estimators use information about the measurement error in two
ways: (1) a biased estimator based on the contaminated distances is multiplied by an
appropriate correction factor, which is a function of the errors (PDF approach), and
(2) cast into a likelihood framework that allows parameter estimation in the presence
of measurement error (likelihood approach).
Secondly, methods are developed that relax the conventional assumption that the
distribution of animals is independent of distance from the lines or points (usually
guaranteed by appropriate survey design). In particular, the new methods deal with
the case where animal density gradients are caused by the use of non-random sampler
allocation, for example transects placed along linear features such as roads or streams.
This is dealt with separately for line and point transects, and at a later stage an
approach for combining the two is presented.
A considerable number of simulations and example analysis illustrate the performance of the proposed methods.Thu, 01 Nov 2007 00:00:00 GMThttp://hdl.handle.net/10023/3912007-11-01T00:00:00ZMarques, Tiago Andre Lamas OliveiraDistance sampling is one of the most commonly used methods for estimating density
and abundance. Conventional methods are based on the distances of detected animals
from the center of point transects or the center line of line transects. These distances
are used to model a detection function: the probability of detecting an animal, given
its distance from the line or point. The probability of detecting an animal in the
covered area is given by the mean value of the detection function with respect to
the available distances to be detected. Given this probability, a Horvitz-Thompson-
like estimator of abundance for the covered area follows, hence using a model-based
framework. Inferences for the wider survey region are justified using the survey design.
Conventional distance sampling methods are based on a set of assumptions. In
this thesis I present results that extend distance sampling on two fronts.
Firstly, estimators are derived for situations in which there is measurement error in
the distances. These estimators use information about the measurement error in two
ways: (1) a biased estimator based on the contaminated distances is multiplied by an
appropriate correction factor, which is a function of the errors (PDF approach), and
(2) cast into a likelihood framework that allows parameter estimation in the presence
of measurement error (likelihood approach).
Secondly, methods are developed that relax the conventional assumption that the
distribution of animals is independent of distance from the lines or points (usually
guaranteed by appropriate survey design). In particular, the new methods deal with
the case where animal density gradients are caused by the use of non-random sampler
allocation, for example transects placed along linear features such as roads or streams.
This is dealt with separately for line and point transects, and at a later stage an
approach for combining the two is presented.
A considerable number of simulations and example analysis illustrate the performance of the proposed methods.A Bayesian approach to modelling field data on multi-species predator prey-interactions
http://hdl.handle.net/10023/174
Abstract: Multi-species functional response models are required to model the predation of generalist preda-
tors, which consume more than one prey species. In chapter 2, a new model for the multi-species
functional response is presented. This model can describe generalist predators that exhibit func-
tional responses of Holling type II to some of their prey and of type III to other prey. In chapter
3, I review some of the theoretical distinctions between Bayesian and frequentist statistics and
show how Bayesian statistics are particularly well-suited for the fitting of functional response
models because uncertainty can be represented comprehensively. In chapters 4 and 5, the multi-
species functional response model is fitted to field data on two generalist predators: the hen
harrier Circus cyaneus and the harp seal Phoca groenlandica. I am not aware of any previous
Bayesian model of the multi-species functional response that has been fitted to field data.
The hen harrier's functional response fitted in chapter 4 is strongly sigmoidal to the densities
of red grouse Lagopus lagopus scoticus, but no type III shape was detected in the response to
the two main prey species, field vole Microtus agrestis and meadow pipit Anthus pratensis. The
impact of using Bayesian or frequentist models on the resulting functional response is discussed.
In chapter 5, no functional response could be fitted to the data on harp seal predation. Possible
reasons are discussed, including poor data quality or a lack of relevance of the available data for
informing a behavioural functional response model.
I conclude with a comparison of the role that functional responses play in behavioural, population
and community ecology and emphasise the need for further research into unifying these different
approaches to understanding predation with particular reference to predator movement.
In an appendix, I evaluate the possibility of using a functional response for inferring the abun-
dances of prey species from performance indicators of generalist predators feeding on these prey.
I argue that this approach may be futile in general, because a generalist predator's energy intake
does not depend on the density of any single of its prey, so that the possibly unknown densities
of all prey need to be taken into account.Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/10023/1742006-01-01T00:00:00ZAsseburg, ChristianMulti-species functional response models are required to model the predation of generalist preda-
tors, which consume more than one prey species. In chapter 2, a new model for the multi-species
functional response is presented. This model can describe generalist predators that exhibit func-
tional responses of Holling type II to some of their prey and of type III to other prey. In chapter
3, I review some of the theoretical distinctions between Bayesian and frequentist statistics and
show how Bayesian statistics are particularly well-suited for the fitting of functional response
models because uncertainty can be represented comprehensively. In chapters 4 and 5, the multi-
species functional response model is fitted to field data on two generalist predators: the hen
harrier Circus cyaneus and the harp seal Phoca groenlandica. I am not aware of any previous
Bayesian model of the multi-species functional response that has been fitted to field data.
The hen harrier's functional response fitted in chapter 4 is strongly sigmoidal to the densities
of red grouse Lagopus lagopus scoticus, but no type III shape was detected in the response to
the two main prey species, field vole Microtus agrestis and meadow pipit Anthus pratensis. The
impact of using Bayesian or frequentist models on the resulting functional response is discussed.
In chapter 5, no functional response could be fitted to the data on harp seal predation. Possible
reasons are discussed, including poor data quality or a lack of relevance of the available data for
informing a behavioural functional response model.
I conclude with a comparison of the role that functional responses play in behavioural, population
and community ecology and emphasise the need for further research into unifying these different
approaches to understanding predation with particular reference to predator movement.
In an appendix, I evaluate the possibility of using a functional response for inferring the abun-
dances of prey species from performance indicators of generalist predators feeding on these prey.
I argue that this approach may be futile in general, because a generalist predator's energy intake
does not depend on the density of any single of its prey, so that the possibly unknown densities
of all prey need to be taken into account.Reconstruction of foliations from directional information
http://hdl.handle.net/10023/158
Abstract: In many areas of science, especially geophysics, geography and
meteorology, the data are often directions or axes rather than
scalars or unrestricted vectors. Directional statistics considers
data which are mainly unit vectors lying in two- or
three-dimensional space (R² or R³). One
way in which directional data arise is as normals to foliations. A
(codimension-1) foliation of {R}^{d} is a system
of non-intersecting (d-1)-dimensional surfaces filling out the
whole of {R}^{d}. At each point z of {R}^{d}, any given codimension-1 foliation determines a
unit vector v normal to the surface through z.
The problem considered here is that of reconstructing the foliation
from observations ({z}{i}, {v}{i}), i=1,...,n. One
way of doing this is rather similar to fitting smooth splines to
data. That is, the reconstructed foliation has to be as close to the
data as possible, while the foliation itself is not too rough. A
tradeoff parameter is introduced to control the balance between
smoothness and
closeness. The approach used in this thesis is to take the surfaces to be
surfaces of constant values of a suitable real-valued function h
on {R}^{d}. The problem of reconstructing a foliation is
translated into the language of Schwartz distributions and a deep
result in the theory of distributions is used to give the
appropriate general form of the fitted function h. The model
parameters are estimated by a simplified Newton method. Under appropriate distributional assumptions on v{1},...,v{n}, confidence regions for the true normals
are developed and estimates of concentration are given.Fri, 01 Jun 2007 00:00:00 GMThttp://hdl.handle.net/10023/1582007-06-01T00:00:00ZYeh, Shu-YingIn many areas of science, especially geophysics, geography and
meteorology, the data are often directions or axes rather than
scalars or unrestricted vectors. Directional statistics considers
data which are mainly unit vectors lying in two- or
three-dimensional space (R² or R³). One
way in which directional data arise is as normals to foliations. A
(codimension-1) foliation of {R}^{d} is a system
of non-intersecting (d-1)-dimensional surfaces filling out the
whole of {R}^{d}. At each point z of {R}^{d}, any given codimension-1 foliation determines a
unit vector v normal to the surface through z.
The problem considered here is that of reconstructing the foliation
from observations ({z}{i}, {v}{i}), i=1,...,n. One
way of doing this is rather similar to fitting smooth splines to
data. That is, the reconstructed foliation has to be as close to the
data as possible, while the foliation itself is not too rough. A
tradeoff parameter is introduced to control the balance between
smoothness and
closeness. The approach used in this thesis is to take the surfaces to be
surfaces of constant values of a suitable real-valued function h
on {R}^{d}. The problem of reconstructing a foliation is
translated into the language of Schwartz distributions and a deep
result in the theory of distributions is used to give the
appropriate general form of the fitted function h. The model
parameters are estimated by a simplified Newton method. Under appropriate distributional assumptions on v{1},...,v{n}, confidence regions for the true normals
are developed and estimates of concentration are given.