Incorporating individual heterogeneity into mark-recapture models

Mark-recapture analysis is a fundamental tool for understanding populations, since it allows the estimation of demographic parameters, such as survival, movement and reproduction, which can be used to infer population status and predict dynamics. As individuals in wild populations do not all behave in the same way, a challenge is presented in the collection and analysis of these data. Within a natural population, animals may exhibit substantial individual variation which can manifest through these demographic parameters. Inherent individual dierences in movement and behavior can introduce bias into mark-recapture estimates (most notoriously, of population size), and are often of considerable interest in their own right. There has been much focus in mark-recapture research on the development of methods to account for individual heterogeneity, yet easily applied, accurate methods are still lacking. The most natural, but computationally complex, approach for modeling individual heterogeneity assumes a continuous distribution using random eects. This method introduces the complexity of solving for the individual random eects which has been a stumbling block of much work in the mark-recapture eld. The focus of this thesis is the development of methods to better estimate individual heterogeneity in mark-recapture data. In chapter 1 I introduce the concepts arising in this thesis and briey outline techniques for modeling individual heterogeneity. Chapter 2 explores the population consequences of individual heterogeneity in spatial use in the context of a marine protected area. Using population projections, I explore the population consequences of individual heterogeneity in proportion of time spent inside a marine protected area. The projections indicate that individual heterogeneity in spatial use and site delity could have important implications under certain conditions for the dynamics of populations managed using marine protected areas. In several scenarios, high individual heterogeneity resulted in larger population size and positive population trajectories, compared to decline and eventual extinction with low individual heterogeneity in site delity. I then present three novel statistical approaches for handling individual heterogeneity using random effects. The rst, developed in chapter 3, is an approach using Laplace approximation with Gaussian random efects, implemented in the language Automatic Dierentiation Model Builder (ADMB). In chapter 4 I develop a Markov chain Monte Carlo sampling framework with a parametric distribution for the individual heterogeneity. This is extended in chapter 5 to incorporate the non-parametric Dirichlet process prior. The natural subgroups often seen in mark-recapture studies, and the complexity of real mark-recapture data means that parametric and discrete style models can be insucient. Non-parametric models avoid these often restrictive assumptions. The Dirichlet process prior is a flexible extension to a parametric model as it avoids assumptions about the functional form of the distribution, and it extends discrete style models to the infinite limit by avoiding any prespecications about the number of groups. Each of these methods was tested using simulated data. In each case the simulation studies demonstrated accurate estimation of true parameter values with random effects. In the case of the Dirichlet process, the simulation studies were used to explore the ability and limits of the Dirichlet process in identifying multiple behavioural modes. The methods are applied to data for up to 1100 individually identified North Atlantic humpback whales, where an unseen individual may be present but not seen, temporarily absent, or dead. There was some evidence of individual heterogeneity in site fedelity and multimodality in the probability of observation.