Spatial and spatio-temporal models with applications in vegetation dynamics and wildlife population estimation

Abstract

This thesis applies spatial and spatio-temporal modelling to two broad areas of environmental statistics: wildlife abundance estimation and vegetation dynamics. The first methodology considered is spatial modelling for estimating global characteristics through predicting the value of a response variable at new locations. The approach is based on generalized additive models and illustrated using spatio-temporal fisheries survey data. The method incorporates historical data to overcome shortcomings in the survey design. The GAM-based method substantially improves the precision of estimates over a traditional estimation method and is also useful in explaining complex space-time trends using environmental variables. The second methodology addressed is spatial modelling for the description of the underlying process. Its objectives lie in exploring local properties, such as autocorrelation. Auto-models (Markov Random Fields) are used for modelling discrete data. Autocorrelation is estimated directly from the response, as a fixed effect, through the specification of a conditional probability of each observation, given its neighbouring values. The auto-Poisson model for counts has traditionally been restricted to the modelling of negative autocorrelation. This restriction is overcome by right truncating the Poisson distribution. Further modifications of this model are also investigated. Parameter estimation methods for this truncated auto-Poisson model are then compared via a simulation study. The method with accompanying model selection and validation techniques is illustrated for the auto-Poisson and auto-negative binomial model using seed and mite counts. An example of modelling the presence and absence of deer illustrating the auto-logistic model for binary data is also presented. Finally, methodology for spatio-temporal modelling of the underlying process is considered. The use of transition models for modelling change of semi-natural vegetation in Scotland is investigated. The transition model is extended to incorporate spatial effects and it is shown that estimates of transition probabilities for Markov models can be improved.