Composite Likelihood Inference Of Animal Ecological Models Based On Individual Identifications

Animal ecology,closely associated with zoology and ecology,is one of the important contents in modern ecology.The ideas and methods of mathematics and statistics have made enormous contributions to the development and innovation of animal ecology.Animal individual identification is the process of determining whether the animal observed two or more times before and after belongs to the same individual,by examining the unique marker of this animal.The advantages of animal individual identification technology are becoming more and more prominent in the collection of animal ecological data.By building an appropriate mathematical model,a wealth of animal ecological information in the study area,including population size,birth and mortality rates,movement/migration patterns,and social structure,can be extracted from individual identification data.It is well known that the likelihood-based methods such as maximum likelihood estimation and likelihood-ratio test play a crucial role in statistical inference.However,individual identification data often have a complex correlation structure(between different individual animals or between different observation time points),at the same time,suffer from missing values(e.g.,we are unable to observe all individuals in the target animal population).These characteristics of individual identification data make the likelihood function no longer applicable or difficult to compute.Since it was first proposed by Bruce Lindsay in 1988,the composite likelihood has been widely used to the data with high dimensionality and complex dependence structure.The composite likelihood-based methods also provide a new statistical tool for the inference of animal ecological models.In the study of animal ecology,lagged identification rates(LIR)and lagged association rates(LAR)are two key parameters for describing animal movement and social structure.In this thesis,we focus on the models of LIR and LAR,and firstly,we show that both types of models,based on the Markov process,are built by constructing some new random variables;then,we introduce a composite likelihood inference framework for statistical inference of the two types of models and systematically investigate the theoretical properties of the maximum composite likelihood estimators(MCLEs)of model parameters;finally,we propose the information criteria for model selection based on composite likelihood functions,with applications to the models of LIR and LAR.The main contents and contributions of this thesis include the following:Firstly,we introduce a composite likelihood-based inference framework to the animal individual identification data,showing that the modified likelihood methods used for the analysis of animal movement and social structure can be incorporated into this framework,and the parameter estimations of models of LIR and LAR can be obtained by constructing a pairwise product composite likelihood function.Secondly,we investigate the theoretical properties of the MCLEs systematically.In particular,the consistency and asymptotic normality of the MCLEs are established and illustrated through simulated examples.Thirdly,model selection is an important issue in animal ecology.We propose two composite likelihood-based information criteria(CLICa and CLICb).In the analysis of simulated data,we found that the results of model selection based on CLICa and CLICb outperformed those based on Akaike and Bayesian information criteria(AIC and BIC),and quasi-Akaike information criterion(QAIC),which can select the correct models with greater probability.Finally,the proposed composite likelihood-based approach is applied to two real datasets,the female sperm whales off Galapagos and the bottlenose whales in Nova Scotia Gully,to estimate the model parameters for LIR and LAR,and to choose the models by using CLICa and CLICb criteria.In addition,a t-SNE based classification method is applied to classify the two groups of whales.To summarize,in this thesis,we introduce the composite likelihood method into animal ecology based on individual identification data,construct composite likelihood functions for models of LIR and LAR,and perform composite likelihood-based inference for the two types of models.We systematically prove that the MCLEs are consistent and asymptotically normal under the regularity conditions.The information criteria for model selection based on composite likelihood are also introduced.The research work in this thesis provides a new idea for parameter estimation and model selection based on individual identifications with rigorous mathematical justification.In addition to individual identifications data,the proposed methods in this thesis may be also useful for the analysis of other types of animal ecological data with complex dependency structures.