DSpace Collection:

Estimating seasonal abundance of a central place forager using counts and telemetry data

2013-04-21T01:06:35Z

Abstract: Obtaining population estimates of species that are not easily observed directly can be problematic. However, central place foragers can often be observed some of the time, e.g. when seals are hauled out. In these instances, population estimates can be derived from counts, combined with information on the proportion of time that animals can be observed. We present a modelling framework to estimate seasonal absolute abundance using counts and information from satellite telemetry data. The method was tested on a harbour seal population in an area of southeast Scotland. Counts were made monthly, between November 2001 and June 2003, when seals were hauled out on land and were corrected for the proportion of time the seals were at sea using satellite telemetry. Harbour seals (n=25) were tagged with satellite relay data loggers between November 2001 and March 2003. To estimate the proportion of time spent hauled out, time at sea on foraging trips was modelled separately from haul-out behaviour close to haul-out sites because of the different factors affecting these processes. A generalised linear mixed model framework was developed to capture the longitudinal nature of the data and the repeated measures across individuals. Despite seasonal variability in the number of seals counted at haul-out sites, the model generated estimates of abundance, with an overall mean of 846 (95% CI: 767 to 979). The methodology shows the value of using count and telemetry data collected concurrently for estimating absolute abundance, information that is essential to assess interactions between predators, fish stocks and fisheries. Description: R.J.S. was supported by a Natural Environment Research Council studentship.

Generating transformation semigroups using endomorphisms of preorders, graphs, and tolerances

2013-04-21T02:38:18Z

Abstract: Let ΩΩ be the semigroup of all mappings of a countably infinite set Ω. If U and V are subsemigroups of ΩΩ, then we write U≈V if there exists a finite subset F of ΩΩ such that the subsemigroup generated by U and F equals that generated by V and F. The relative rank of U in ΩΩ is the least cardinality of a subset A of ΩΩ such that the union of U and A generates ΩΩ. In this paper we study the notions of relative rank and the equivalence ≈ for semigroups of endomorphisms of binary relations on Ω. The semigroups of endomorphisms of preorders, bipartite graphs, and tolerances on Ω are shown to lie in two equivalence classes under ≈. Moreover such semigroups have relative rank 0, 1, 2, or d in ΩΩ where d is the minimum cardinality of a dominating family for NN. We give examples of preorders, bipartite graphs, and tolerances on Ω where the relative ranks of their endomorphism semigroups in ΩΩ are 0, 1, 2, and d. We show that the endomorphism semigroups of graphs, in general, fall into at least four classes under ≈ and that there exist graphs where the relative rank of the endomorphism semigroup is 2ℵ0.

Fitting complex ecological point process models with integrated nested Laplace approximation

2013-02-26T13:01:04Z

Abstract: Summary 1. We highlight an emerging statistical method, integrated nested Laplace approximation (INLA), which is ideally suited for fitting complex models to many of the rich spatial data sets that ecologists wish to analyse. 2. INLA is an approximation method that nevertheless provides very exact estimates. In this article, we describe the INLA methodology highlighting where it offers opportunities for drawing inference from (spatial) ecological data that would previously have been too complex to make practical model fitting feasible. 3. We use INLA to fit a complex joint model to the spatial pattern formed by a plant species, Thymus carnosus, as well as to the health status of each individual. 4. The key ecological result revealed by our spatial analysis of these data, relates to the distance-to-water covariate. We find that T. carnosus plants are generally healthier when they are further away from the water. 5. We suggest that this may be the result of a combination of (1) plants having alternative rooting strategies depending on how close to water they grow and (2) the rooting strategy determining how well the plants were able to tolerate an unusually dry summer. 6. We anticipate INLA becoming widely used within spatial ecological analysis over the next decade and suggest that both ecologists and statisticians will benefit greatly from working collaboratively to further develop and apply these emerging statistical methods.

A family of spatial biodiversity measures based on graphs

2013-04-21T03:04:50Z

Abstract: While much research in ecology has focused on spatially explicit modelling as well as on measures of biodiversity, the concept of spatial (or local) biodiversity has been discussed very little. This paper generalises existing measures of spatial biodiversity and introduces a family of spatial biodiversity measures by flexibly defining the notion of the individuals’ neighbourhood within the framework of graphs associated to a spatial point pattern. We consider two non-independent aspects of spatial biodiversity, scattering, i.e. the spatial arrangement of the individuals in the study area and exposure, the local diversity in an individual’s neighbourhood. A simulation study reveals that measures based on the most commonly used neigh-bourhood defined by the geometric graph do not distinguish well between scattering and exposure. This problem is much less pronounced when other graphs are used. In an analysis of the spatial diversity in a rainforest, the results based on the geometric graph have been shown to spuriously indicate a decrease in spatial biodiversity when no such trend was detected by the other types of neighbourhoods. We also show that the choice neighbourhood markedly impacts on the classification of species according to how strongly and in what way different species spatially structure species diversity. Clearly, in an analysis of spatial or local diversity an appropriate choice of local neighbourhood is crucial in particular in terms of the biological interpretation of the results. Due to its general definition, the approach discussed here offers the necessary flexibility that allows suitable and varying neighbourhood structures to be chosen.

Multispecies functional response of the minke whale Balaenoptera acutorostrata based on small-scale foraging studies

2013-04-21T01:36:26Z

Abstract: Atlantic minke whales are important predators in the Barents Sea ecosystem; capelin Mallotus villosus, krill Thysanoessa sp. and Meganyctephanes norvegica and herring Clupea harengus are their major prey. Their consumption of commercial species may present an economic problem for the local fishery. In order to estimate this consumption and understand the potential consequences for prey dynamics, it is essential to determine the multispecies functional response of the whales. The parameterisation of a functional response requires measurements of consumption rates and prey availability. In this localised study, undigested stomach contents were used to assess the amount of each prey that had been consumed immediately prior to capture. To determine the availability of prey to the whales, standard acoustic surveys were run in the same area within 2 d of the capture of the whales. The spatial distribution of prey was modelled using generalised additive models (GAMs). In order to generate a measure of prey availability and the uncertainty in this value, a simple model was assumed for whale movement, and prey abundance was sampled over space according to a Gaussian kernel. A multispecies functional response (MSFR) model was then fitted to the consumption and prey availability data using Bayesian methods. Simple simulations, based on the fitted MSFR, indicate that minke whales may deplete local capelin aggregations at small spatial scales. This is the first time that a multispecies functional response has been fitted for a cetacean predator, and the methods outlined here may prove useful for modelling marine mammal-fish interactions in other systems.

Estimating demographic parameters for capture-recapture data in the presence of multiple mark types

2013-04-21T01:37:31Z

Abstract: In mark-recapture studies, various techniques can be used to uniquely identify individual animals, such as ringing, tagging or photo-identification using natural markings. In some long-term studies more than one type of marking procedure may be implemented during the study period. In these circumstances, ignoring the different mark types can produce biased survival estimates since the assumption that the different mark types are equally catchable (homogeneous capture probability across mark types) may be incorrect.We implement an integrated approach where we simultaneously analyse data obtained using three different marking techniques, assuming that animals can be cross-classified across the different mark types. We discriminate between competing models using the AIC statistic. This technique also allows us to estimate both relative mark-loss probabilities and relative recapture efficiency rates for the different marking methods.We initially perform a simulation study to explore the different biases that can be introduced if we assume a homogeneous recapture probability over mark type, before applying the method to a real dataset. We make use of data obtained from an intensive long-term observational study of UK female grey seals (Halichoerus grypus) at a single breeding colony, where three different methods are used to identify individuals within a single study: branding, tagging and photo-identification based on seal coat pattern or pelage.

Every group is a maximal subgroup of the free idempotent generated semigroup over a band

2013-02-07T12:34:51Z

Abstract: Given an arbitrary group G we construct a semigroup of idempotents (band) BG with the property that the free idempotent generated semigroup over BG has a maximal subgroup isomorphic to G. If G is finitely presented then BG is finite. This answers several questions from recent papers in the area.

On semigroups which are unions of finitely many copies of the free monogenic semigroup

2013-04-12T16:01:01Z

Abstract: Every semigroup which is a finite disjoint union of copies of the free monogenic semigroup (natural numbers under addition) is finitely presented and residually finite.

Ideals and finiteness conditions for subsemigroups

2013-01-29T17:31:02Z

Abstract: In this paper we consider a number of finiteness conditions for semigroups related to their ideal structure, and ask whether such conditions are preserved by sub- or supersemigroups with finite Rees or Green index. Specific properties under consideration include stability, D=J and minimal conditions on ideals.

The geometric mean of relative abundance indices : a biodiversity measure with a difference

2012-12-19T11:01:02Z

Abstract: The 2010 Biodiversity Target of the Convention on Biological Diversity (CBD), set in 2002, which stated that there should be ‘a significant reduction of the current rate of biodiversity loss' by 2010, highlighted the need for informative and tractable metrics that can be used to evaluate change in biological diversity. While the subsequent Aichi 2020 targets are more wide-ranging, they also seek to reduce the rate of biodiversity loss. The geometric mean of relative abundance indices, G, is increasingly being used to examine trends in biological diversity and to assess whether biodiversity targets are being met. Here, we explore the mathematical and statistical properties of G that make it useful for judging temporal change in biological diversity, and we discuss its advantages and limitations relative to other measures. We demonstrate that the index reflects trends in both abundance and evenness, and that it is not prone to bias when detectability of individuals varies by species. We note that it allows data from different surveys to be combined to generate a composite index. However, the index exhibits high variance and unstable behaviour when rarely-recorded species are included in the analyses. Read More: http://www.esajournals.org/doi/abs/10.1890/ES11-00186.1

Using INLA to fit a complex point process model with temporally varying effects – a case study

2012-12-17T16:01:01Z

Abstract: Integrated nested Laplace approximation (INLA) provides a fast and yet quite exact approach to fitting complex latent Gaussian models which comprise many statistical models in a Bayesian context, including log Gaussian Cox processes. This paper discusses how a joint log Gaussian Cox process model may be fitted to independent replicated point patterns. We illustrate the approach by fitting a model to data on the locations of muskoxen (Ovibos moschatus) herds in Zackenberg valley, Northeast Greenland and by detailing how this model is specified within the R-interface R-INLA. The paper strongly focuses on practical problems involved in the modelling process, including issues of spatial scale, edge effects and prior choices, and finishes with a discussion on models with varying boundary conditions.

A Bayesian approach to fitting Gibbs processes with temporal random effects

2013-04-21T02:02:52Z

Abstract: We consider spatial point pattern data that have been observed repeatedly over a period of time in an inhomogeneous environment. Each spatial point pattern can be regarded as a “snapshot” of the underlying point process at a series of times. Thus, the number of points and corresponding locations of points differ for each snapshot. Each snapshot can be analyzed independently, but in many cases there may be little information in the data relating to model parameters, particularly parameters relating to the interaction between points. Thus, we develop an integrated approach, simultaneously analyzing all snapshots within a single robust and consistent analysis. We assume that sufficient time has passed between observation dates so that the spatial point patterns can be regarded as independent replicates, given spatial covariates. We develop a joint mixed effects Gibbs point process model for the replicates of spatial point patterns by considering environmental covariates in the analysis as fixed effects, to model the heterogeneous environment, with a random effects (or hierarchical) component to account for the different observation days for the intensity function. We demonstrate how the model can be fitted within a Bayesian framework using an auxiliary variable approach to deal with the issue of the random effects component. We apply the methods to a data set of musk oxen herds and demonstrate the increased precision of the parameter estimates when considering all available data within a single integrated analysis.

Quantifying temporal change in biodiversity : challenges and opportunities

2012-12-12T16:14:07Z

Abstract: Growing concern about biodiversity loss underscores the need to quantify and understand temporal change. Here, we review the opportunities presented by biodiversity time series, and address three related issues: (i) recognizing the characteristics of temporal data; (ii) selecting appropriate statistical procedures for analysing temporal data; and (iii) inferring and forecasting biodiversity change. With regard to the first issue, we draw attention to defining characteristics of biodiversity time series—lack of physical boundaries, uni-dimensionality, autocorrelation and directionality—that inform the choice of analytic methods. Second, we explore methods of quantifying change in biodiversity at different timescales, noting that autocorrelation can be viewed as a feature that sheds light on the underlying structure of temporal change. Finally, we address the transition from inferring to forecasting biodiversity change, highlighting potential pitfalls associated with phase-shifts and novel conditions.

The functional response of a generalist predator

2012-12-12T12:34:35Z

Abstract: Background: Predators can have profound impacts on the dynamics of their prey that depend on how predator consumption is affected by prey density (the predator's functional response). Consumption by a generalist predator is expected to depend on the densities of all its major prey species (its multispecies functional response, or MSFR), but most studies of generalists have focussed on their functional response to only one prey species. Methodology and principal findings: Using Bayesian methods, we fit an MSFR to field data from an avian predator (the hen harrier Circus cyaneus) feeding on three different prey species. We use a simple graphical approach to show that ignoring the effects of alternative prey can give a misleading impression of the predator's effect on the prey of interest. For example, in our system, a “predator pit” for one prey species only occurs when the availability of other prey species is low. Conclusions and significance: The Bayesian approach is effective in fitting the MSFR model to field data. It allows flexibility in modelling over-dispersion, incorporates additional biological information into the parameter priors, and generates estimates of uncertainty in the model's predictions. These features of robustness and data efficiency make our approach ideal for the study of long-lived predators, for which data may be sparse and management/conservation priorities pressing.

A non-technical overview of spatially explicit capture-recapture models

2012-12-12T16:13:47Z

Abstract: Most capture-recapture studies are inherently spatial in nature, with capture probabilities depending on the location of traps relative to animals. The spatial component of the studies has until recently, however, not been incorporated in statistical capture-recapture models. This paper reviews capture-recapture models that do include an explicit spatial component. This is done in a non-technical way, omitting much of the algebraic detail and focussing on the model formulation rather than on the estimation methods (which include inverse prediction, maximum likelihood and Bayesian methods). One can view spatially explicit capture-recapture (SECR) models as an endpoint of a series of spatial sampling models, starting with circular plot survey models and moving through conventional distance sampling models, with and without measurement errors, through mark-recapture distance sampling (MRDS) models. This paper attempts a synthesis of these models in what I hope is a style accessible to non-specialists, placing SECR models in the context of other spatial sampling models.

Workshop on new developments in cetacean survey methods

2012-12-12T10:20:18Z

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.

A detailed investigation of the properties of a Vlasov-Maxwell equilibrium for the force-free Harris sheet

2013-04-21T02:38:39Z

Abstract: A detailed discussion is presented of the Vlasov-Maxwell equilibrium for the force-free Harris sheet recently found by Harrison and Neukirch [Phys. Rev. Lett. 102, 135003 (2009)]. The derivation of the distribution function and a discussion of its general properties and their dependence on the distribution function parameters will be given. In particular, the distribution function can be single-peaked or multipeaked in two of the velocity components, with possible implications for stability. The dependence of the shape of the distribution function on the values of its parameters will be investigated and the relation to macroscopic quantities such as the current sheet thickness will be discussed.

Growth of generating sets for direct powers of classical algebraic structures

2013-04-21T02:38:17Z

Abstract: For an algebraic structure A denote by d(A) the smallest size of a generating set for A, and let d(A)=(d(A),d(A2),d(A3),…), where An denotes a direct power of A. In this paper we investigate the asymptotic behaviour of the sequence d(A) when A is one of the classical structures—a group, ring, module, algebra or Lie algebra. We show that if A is finite then d(A) grows either linearly or logarithmically. In the infinite case constant growth becomes another possibility; in particular, if A is an infinite simple structure belonging to one of the above classes then d(A) is eventually constant. Where appropriate we frame our exposition within the general theory of congruence permutable varieties.

A general discrete-time modeling framework for animal movement using multi-state random walks

2013-04-21T03:03:27Z

Abstract: Recent developments in animal tracking technology have permitted the collection of detailed data on the movement paths of individuals from many species. However, analysis methods for these data have not developed at a similar pace, largely due to a lack of suitable candidate models, coupled with the technical difficulties of fitting such models to data. To facilitate a general modeling framework, we propose that complex movement paths can be conceived as a series of movement strategies among which animals transition as they are affected by changes in their internal and external environment. We synthesize previously existing and novel methodologies to develop a general suite of mechanistic models based on biased and correlated random walks that allow different behavioral states for directed (e.g., migration), exploratory (e.g., dispersal), area-restricted (e.g., foraging), and other types of movement. Using this “tool-box” of nested model components, multi-state movement models may be custom-built for a wide variety of species and applications. As a unified state-space modeling framework, it allows the simultaneous investigation of numerous hypotheses about animal movement from imperfectly observed data, including time allocations to different movement behavior states, transitions between states, the use of memory or navigation, and strengths of attraction (or repulsion) to specific locations. The inclusion of covariate information permits further investigation of specific hypotheses related to factors driving different types of movement behavior. Using reversible jump Markov chain Monte Carlo methods to facilitate Bayesian model selection and multi-model inference, we apply the proposed methodology to real data by adapting it to the natural history of the grey seal (Halichoerus grypus) in the North Sea. Although previous grey seal studies tended to focus on correlated movements, we found overwhelming evidence that bias towards haul-out or foraging locations better explained seal movement than simple or correlated random walks. Posterior model probabilities also provided evidence that seals transition among directed, area-restricted, and exploratory movements associated with haul-out, foraging, and other behaviors. With this intuitive framework for modeling and interpreting animal movement, we believe the development and application of bespoke movement models will become more accessible to ecologists and non-statisticians.

Status assessment of the Critically Endangered Azores Bullfinch Pyrrhula murina

2013-04-21T03:06:36Z

Abstract: The Azores Bullfinch is endemic to the island of São Miguel (Azores, Portugal). Its status was uplisted to Critically Endangered in 2005 on the basis of an extremely small and declining population that was considered to be restricted to a very small mountain range (43 km2), in a single location, within which the spread of invasive plants constituted a threat to habitat quality. Nevertheless, information was mostly inferred, or the product of, non-systematic studies. In order to carry out a complete assessment of the conservation status we analysed: (i) population trend, calculated from annual monitoring 1991–2008, (ii) population size, and (iii) range size, obtaining estimates in a single morning study in 2008 involving the simultaneous participation of 48 observers. Contrary to previous inferences, the population is no longer decreasing, although quality of laurel forest habitat continues to decline due to the persistent threat of invasive species. Population size (mean ± SE) was estimated at 1,064 ± 304 individuals using distance sampling methods, although the estimate was very sensitive to the survey method used. Range size estimates (extent of occurrence and area of occupancy) were 144 km2 and 83 km2 respectively. Given the present information, we propose the downlisting of Azores Bullfinch to Endangered on the IUCN Red List.

Geometric grid classes of permutations

2012-12-12T13:10:25Z

Unary FA-presentable semigroups

2013-04-21T03:08:14Z

Abstract: Automatic presentations, also called FA-presentations, were introduced to extend nite model theory to innite structures whilst retaining the solubility of interesting decision problems. A particular focus of research has been the classication of those structures of some species that admit automatic presentations. Whilst some successes have been obtained, this appears to be a dicult problem in general. A restricted problem, also of signicant interest, is to ask this question for unary automatic presentations: auto-matic presentations over a one-letter alphabet. This paper studies unary FA-presentable semigroups. We prove the following: Every unary FA-presentable structure admits an injective unary automatic presentation where the language of representatives consists of every word over a one-letter alphabet. Unary FA-presentable semigroups are locally nite, but non-nitely generated unary FA-presentable semigroups may be innite. Every unary FA-presentable semigroup satises some Burnside identity.We describe the Green's relations in unary FA-presentable semigroups. We investigate the relationship between the class of unary FA-presentable semigroups and various semigroup constructions. A classication is given of the unary FA-presentable completely simple semigroups.

Three-dimensional solutions of the magnetohydrostatic equations : rigidly rotating magnetized coronae in spherical geometry

2013-04-21T02:38:37Z

Abstract: Context. Magnetohydrostatic (MHS) equilibria are often used to model astrophysical plasmas, for example, planetary magnetospheres or coronae of magnetized stars. However, finding realistic three-dimensional solutions to the MHS equations is difficult, with only a few known analytical solutions and even finding numerical solution is far from easy. Aims. We extend the results of a previous paper on three-dimensional solutions of the MHS equations around rigidly rotating massive cylinders to the much more realistic case of rigidly rotating massive spheres. An obvious application is to model the closed field line regions of the coronae of rapidly rotating stars. Methods. We used a number of simplifying assumptions to reduce the MHS equations to a single elliptic partial differential equation for a pseudo-potential U, from which all physical quantities, such as the magnetic field, the plasma pressure, and the density, can be derived by differentiation. The most important assumptions made are stationarity in the co-rotating frame of reference, a particular form for the current density, and neglect of outflows. Results. In this paper we demonstrate that standard methods can be used to find numerical solutions to the fundamental equation of the theory. We present three simple different cases of magnetic field boundary conditions on the surface of the central sphere, corresponding to an aligned dipole field, a non-aligned dipole field, and a displaced dipole field. Our results show that it should be possible in the future to use this method without dramatically increasing the demands on computational resources to improve upon potential field models of rotating magnetospheres and coronae.

Three-dimensional solutions of the magnetohydrostatic equations : rigidly rotating magnetized coronae in cylindrical geometry

2013-04-21T02:38:38Z

Abstract: Context. Solutions of the magnetohydrostatic (MHS) equations are very important for modelling astrophysical plasmas, such as the coronae of magnetized stars. Realistic models should be three-dimensional, i.e., should not have any spatial symmetries, but finding three-dimensional solutions of the MHS equations is a formidable task. Aims. We present a general theoretical framework for calculating three-dimensional MHS solutions outside massive rigidly rotating central bodies, together with example solutions. A possible future application is to model the closed field region of the coronae of fast-rotating stars. Methods. As a first step, we present in this paper the theory and solutions for the case of a massive rigidly rotating magnetized cylinder, but the theory can easily be extended to other geometries, We assume that the solutions are stationary in the co-rotating frame of reference. To simplify the MHS equations, we use a special form for the current density, which leads to a single linear partial differential equation for a pseudo-potential U. The magnetic field can be derived from U by differentiation. The plasma density, pressure, and temperature are also part of the solution. Results. We derive the fundamental equation for the pseudo-potential both in coordinate independent form and in cylindrical coordinates. We present numerical example solutions for the case of cylindrical coordinates.

Universal scaling rules predict evolutionary patterns of myogenesis in species with indeterminate growth

2013-04-21T03:33:28Z

Abstract: Intraspecific phenotypic variation is ubiquitous and often associated with resource exploitation in emerging habitats. For example, reduced body size has evolved repeatedly in Arctic charr (Salvelinus alpinus L.) and threespine stickleback (Gasterosteus aculeatus L.) across post-glacial habitats of the Northern Hemisphere. Exploiting these models, we examined how body size and myogenesis evolve with respect to the 'optimum fibre size hypothesis', which predicts that selection acts to minimize energetic costs associated with ionic homeostasis by optimizing muscle fibre production during development. In eight dwarf Icelandic Arctic charr populations, the ultimate production of fast-twitch muscle fibres (FN(max)) was only 39.5 and 15.5 per cent of that in large-bodied natural and aquaculture populations, respectively. Consequently, average fibre diameter (FD) scaled with a mass exponent of 0.19, paralleling the relaxation of diffusional constraints associated with mass-specific metabolic rate scaling. Similar reductions in FN(max) were observed for stickleback, including a small-bodied Alaskan population derived from a larger-bodied oceanic stock over a decadal timescale. The results suggest that in species showing indeterminate growth, body size evolution is accompanied by strong selection for fibre size optimization, theoretically allowing resources saved from ionic homeostasis to be allocated to other traits affecting fitness, including reproduction. Gene flow between small- and large-bodied populations residing in sympatry may counteract the evolution of this trait.

An update to the methods in Endangered Species Research 2011 paper "Estimating North Pacific right whale Eubalaena japonica density using passive acoustic cue counting"

2012-12-12T10:19:25Z

On the growth of generating sets for direct powers of semigroups

2013-04-21T03:04:51Z

Abstract: For a semigroup S its d-sequence is d(S) = (d1, d2, d3, . . .), where di is the smallest number of elements needed to generate the ith direct power of S. In this paper we present a number of facts concerning the type of growth d(S) can have when S is an infinite semigroup, comparing them with the corresponding known facts for infinite groups, and also for finite groups and semigroups.

A toolbox for fitting complex spatial point process models using integrated nested Laplace approximation (INLA)

2013-03-25T11:01:00Z

Abstract: This paper develops methodology that provides a toolbox for routinely fitting complex models to realistic spatial point pattern data. We consider models that are based on log-Gaussian Cox processes and include local interaction in these by considering constructed covariates. This enables us to use integrated nested Laplace approximation and to considerably speed up the inferential task. In addition, methods for model comparison and model assessment facilitate the modelling process. The performance of the approach is assessed in a simulation study. To demonstrate the versatility of the approach, models are tted to two rather dierent examples, a large rainforest data set with covariates and a point pattern with multiple marks.

The steady-state form of large-amplitude internal solitary waves

2013-04-21T02:03:23Z

Abstract: A new numerical scheme for obtaining the steady-state form of an internal solitary wave of large amplitude is presented. A stratified inviscid two-dimensional fluid under the Boussinesq approximation flowing between horizontal rigid boundaries is considered. The stratification is stable, and buoyancy is continuously differentiable throughout the domain of the flow. Solutions are obtained by tracing the buoyancy frequency along streamlines from the undisturbed far field. From this the vorticity field can be constructed and the streamfunction may then be obtained by inversion of Laplace's operator. The scheme is presented as an iterative solver, where the inversion of Laplace's operator is performed spectrally. The solutions agree well with previous results for stratification in which the buoyancy frequency is a discontinuous function. The new numerical scheme allows significantly larger amplitude waves to be computed than have been presented before and it is shown that waves with Richardson numbers as low as 0.062 can be computed straightforwardly. The method is also extended to deal in a novel way with closed streamlines when they occur in the domain. The new solutions are tested in independent fully nonlinear time-dependent simulations and are verified to be steady. Waves with regions of recirculation are also discussed.

Complex Region Spatial Smoother (CReSS)

2012-12-12T10:18:54Z

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.

The primitive permutation groups of degree less than 4096

2013-04-21T03:04:14Z

Abstract: In this paper we use the Classification of the Finite Simple Groups, the O’Nan– Scott Theorem and Aschbacher’s theorem to classify the primitive permutation groups of degree less than 4096. The results will be added to the primitive groups databases of GAP and Magma. Description: The first author is supported by an EPSRC doctoral training grant. The second and third authors acknowledge the support of EPSRC grant number EP/C523229/1.

Groups with the basis property

2013-04-21T03:04:51Z

Abstract: We study finite groups for which every minimal generating set has the same cardinality. A group has the basis property if it and every subgroup satisfies this condition on minimal generating sets. We classify all finite groups with the basis property.

Comparing pre- and post-construction distributions of long-tailed ducks Clangula hyemalis in and around the Nysted offshore wind farm, Denmark : a quasi-designed experiment accounting for imperfect detection, local surface features and autocorrelation

2012-12-12T10:18:29Z

Abstract: We report a novel technique to model abundance patterns of wintering seaducks in relation to the construction of an offshore wind farm (OWF) based on seven years of aerial survey transect data. Distance sampling was used to estimate seaduck densities adjusted for covariates affecting detection probabilities. A generalized additive model (GAM) generated seaduck densities in sampling units in relation to spatially explicit covariates, using bootstrapping to account for uncertainties in both processes. Generalized estimating equations generated precision measures for the GAM robust to spatial and temporal autocorrelation. Comparison of pre- and post-construction model generated surfaces showed significant reductions in long-tailed duck numbers only within the OWF (despite the fact that the model was uninformed about the OWF location), although the absolute numbers involved were trivial in a flyway population context. This method provides quantification of distributional effects on organisms over a gradient in space and time that offers an alternative to Before-After/Control-Impact designs in environmental impact assessment.

Finite groups are big as semigroups

2013-04-21T03:08:13Z

Abstract: We prove that a finite group G occurs as a maximal proper subsemigroup of an infinite semigroup (in the terminology of Freese, Ježek, and Nation, G is a big semigroup) if and only if |G| ≥ 3. In fact, any finite semigroup whose minimal ideal contains a subgroup with at least three elements is big.

A first survey of the global population size and distribution of the Scottish Crossbill Loxia scotica

2013-04-21T03:07:49Z

Abstract: A survey of Scottish Crossbills Loxia scotica was carried out in 3,506 km2 of conifer woodland in northern Scotland during January to April 2008 to provide the first estimate of the global population size for this endemic bird. Population estimates were also made for Common Crossbills L. curvirostra and Parrot Crossbills L. pytyopsittacus within this range. Crossbills were lured to systematically selected survey points for counting, sexing and recording their calls for later call-type (species) identification from sonograms. Crossbills were located at 451 of the 852 survey points, and adequate tape-recordings made at 387 of these. The Scottish Crossbill had a disjunct distribution, occurring largely within the eastern part of the study area, but also in the northwest. Common Crossbills had a mainly westerly distribution. The population size of postjuvenile Scottish Crossbills was estimated as 13,600 (95%C.I. 8,130–22,700), which will approximate to 6,800 (4,065–11,350) pairs. Common Crossbills were more abundant within this range (27,100, 95% C.I. 14,700–38,400) and Parrot Crossbills rare (about 100). The sex ratio was not significantly different from parity for Scottish Crossbills. The modal number at survey points was two but numbers were larger in January than later in the survey. The numbers and distribution of all crossbill species are likely to vary between years, depending upon the size of the cone crops of the different conifers: all were coning in 2008. Common Crossbill and Parrot Crossbill numbers will also be affected by irruptions from continental Europe. A monitoring scheme is required to detect any population trend, and further work on their habitat requirement (e.g. conifer selection at different seasons) is needed to inform habitat management of native and planted conifer forests to ensure a secure future for this endemic bird.

Estimating bird abundance : making methods work

2013-04-21T02:04:06Z

Abstract: In many bird monitoring Surveys, no attempt is made to estimate bird densities or abundance. instead, counts of one form or another are made, and these are assumed to correlate with bird density. Unless complete Counts Oil Sample plots are feasible, this approach can easily lead to false conclusions, because detectability of birds varies by species, habitat, observer and many other factors. Trends in time of counts often reflect trends in detectability, rather than trends in abundance. Conclusions are further compromised when surveys are conducted at unrepresentative sites. We consider how to avoid these problems. We give a brief description of distance sampling methods, which allow detectability to be estimated. We consider strategies to ease their implementation, to enhance their reliability, to adapt the methods for difficult species, and to deal with circumstances in which representative sampling is problematic. We also consider some of the common problems encountered, and suggest solutions.

Double-observer line transect methods : levels of independence

2013-04-21T01:36:40Z

Abstract: Double-observer line transect methods are becoming increasingly widespread, especially for the estimation of marine mammal abundance from aerial and shipboard surveys when detection of animals on the line is uncertain. The resulting data supplement conventional distance sampling data with two-sample mark–recapture data. Like conventional mark–recapture data, these have inherent problems for estimating abundance in the presence of heterogeneity. Unlike conventional mark–recapture methods, line transect methods use knowledge of the distribution of a covariate, which affects detection probability (namely, distance from the transect line) in inference. This knowledge can be used to diagnose unmodeled heterogeneity in the mark–recapture component of the data. By modeling the covariance in detection probabilities with distance, we show how the estimation problem can be formulated in terms of different levels of independence. At one extreme, full independence is assumed, as in the Petersen estimator (which does not use distance data); at the other extreme, independence only occurs in the limit as detection probability tends to one. Between the two extremes, there is a range of models, including those currently in common use, which have intermediate levels of independence. We show how this framework can be used to provide more reliable analysis of double-observer line transect data. We test the methods by simulation, and by analysis of a dataset for which true abundance is known. We illustrate the approach through analysis of minke whale sightings data from the North Sea and adjacent waters.

Design and analysis of line transect surveys for primates

2013-04-21T02:02:37Z

Abstract: Line transect surveys are widely used for estimating abundance of primate populations. The method relies on a small number of key assumptions, and if these are not met, substantial bias may occur. For a variety of reasons, primate surveys often do not follow what is generally considered to be best practice, either in survey design or in analysis. The design often comprises too few lines (sometimes just one), subjectively placed or placed along trails, so lacks both randomization and adequate replication. Analysis often involves flawed or inefficient models, and often uses biased estimates of the locations of primate groups relative to the line. We outline the standard method, emphasizing the assumptions underlying the approach. We then consider options for when it is difficult or impossible to meet key assumptions. We explore the performance of these options by simulation, focusing particularly on the analysis of primate group sizes, where many of the variations in survey methods have been developed. We also discuss design issues, field methods, analysis, and potential alternative methodologies for when standard line transect sampling cannot deliver reliable abundance estimates. Description: An erratum to this article can be found at http://dx.doi.org/10.1007/s10764-010-9470-y

Line transect sampling of primates : can animal-to-observer distance methods work?

2013-04-21T02:02:36Z

Abstract: Line transect sampling is widely used for estimating abundance of primate populations. Animal-to-observer distances (AODs) are commonly used in analysis, in preference to perpendicular distances from the line. This is in marked contrast with standard practice for other applications of line transect sampling. We formalize the mathematical shortcomings of approaches based on AODs, and show that they are likely to give strongly biased estimates of density. We review papers that claim good performance for the method, and explore this performance through simulations. These confirm strong bias in estimates of density using AODs. We conclude that AOD methods are conceptually flawed, and that they cannot in general provide valid estimates of density. Description: An erratum to this article can be found at http://dx.doi.org/10.1007/s10764-010-9469-4

Estimating the Barents Sea polar bear subpopulation size

2013-04-21T01:36:45Z

Abstract: A large scale survey was conducted in August 2004 to estimate the size of the Barents Sea polar bear subpopulation. We combined helicopter line transect distance sampling surveys in most of the survey area with total counts in small areas not suitable for distance sampling. Due to weather constraints we failed to survey some of the areas originally planned to be covered by distance sampling. For those, abundance was estimated using a ratio estimator, in which the auxiliary variable was the number of satellite telemetry fixes (in previous years). We estimated that the Barents Sea subpopulation had approximately 2650 (95% CI approx 1900 to 3600) bears. Given current intense interest in polar bear management due to the potentially disastrous effects of climate change, it is surprising that many subpopulation sizes are still unknown. We show here that line transect sampling is a promising method for addressing the need for abundance estimates.

The effect of sea-ice loss on beluga whales (Delphinapterus leucas) in West Greenland

2013-04-21T02:36:26Z

Abstract: An aerial survey was conducted to estimate the abundance of belugas (Delphinapterus leucas) on their wintering ground in West Greenland in March–April 2006 and 2008. The survey was conducted as a double platform aerial line transect survey, and sampled approximately 17% of the total survey area of ca. 125 000 km2. The abundance of belugas was 10 595 (95% confidence interval 4904–24 650). The largest abundance was found at the northern part of Store Hellefiske Bank, at the eastern edge of the Baffin Bay pack ice, a pattern similar to that found in eight systematic surveys conducted since 1981. A clear relationship between decreasing sea-ice cover and increasing offshore distance of beluga sightings was established from all previous surveys, suggesting that belugas expand their distribution westward as new areas on the banks of West Greenland open up earlier in spring with reduced sea-ice coverage or early annual ice recession. This is in contrast to the relatively confined distribution of belugas near the coast in limited open areas in the early 1980s, when sea-ice cover was greater. However, the effects of the changes in coastal availability of belugas can also be observed with the correlation between catches from the local Inuit hunt and sea-ice cover, where the catches increased significantly with increasing sea-ice coverage during the period 1954–2006. These results, based on nearly 30 years of dedicated survey effort, are among the first available evidence showing a shift in distribution of an Arctic cetacean in response to changes in sea-ice coverage.

Density estimation implications of increasing ambient noise on beaked whale click detection and classification

2012-12-12T10:17:01Z

Abstract: Acoustic based density estimates are being increasingly used. Usually density estimation methods require one to evaluate the eﬀective survey area of the acoustic sensors, or equivalently estimate the mean detection probability of detecting the animals or cues of interest. This is often done based on an estimated detection function, the probability of detecting an object of interest as a function of covariates, usually distance and additional covariates. If the actual survey data and the data used to estimate a detection function are not collected simultaneously, as in Marques et al. (2009), the estimated detection function might not correspond to the detection process that generated the survey data. This would lead to biaseddensity estimates. Here we evaluate the inﬂuence of ambient noise in the detection and classiﬁcation of beaked whale clicks at the Atlantic Undersea Test and Evaluation Center (AUTEC) hydrophones, to assess if the density estimates reported in Marques et al. (2009) might have been biased. To do so we contaminated a data set with increasing levels of ambient noise, and then estimated the detection function accounting for the noise level as an additional covariate. The results obtained suggest that for the particular results obtained at AUTEC’s deep water hydrophones the inﬂuence of ambient noise on the beaked whale’s click detection probability might have been minor, and hence unlikely to have had an impact on density estimates. However, we do not exclude the possibility that the results could be diﬀerent under other scenarios.

Generating continuous mappings with Lipschitz mappings

2013-04-21T01:03:20Z

Abstract: If X is a metric space, then C-X and L-X denote the semigroups of continuous and Lipschitz mappings, respectively, from X to itself. The relative rank of C-X modulo L-X is the least cardinality of any set U\L-X where U generates C-X. For a large class of separable metric spaces X we prove that the relative rank of C-X modulo L-X is uncountable. When X is the Baire space N-N, this rank is N-1. A large part of the paper emerged from discussions about the necessity of the assumptions imposed on the class of spaces from the aforementioned results.

Generating the full transformation semigroup using order preserving mappings

2013-04-21T01:02:02Z

Abstract: For a linearly ordered set X we consider the relative rank of the semigroup of all order preserving mappings O-X on X modulo the full transformation semigroup Ex. In other words, we ask what is the smallest cardinality of a set A of mappings such that = T-X. When X is countably infinite or well-ordered (of arbitrary cardinality) we show that this number is one, while when X = R (the set of real numbers) it is uncountable.

On defining groups efficiently without using inverses

2013-04-21T00:33:40Z

Abstract: Let G be a group, and let be a finite group presentation for G with \R\ greater than or equal to \A\. Then there exists a, finite semigroup, presentation for G such that \Q\ - \B\ = \R\ - \A\. Moreover, B is either the same generating set or else it contains one additional generator.