Embedding Population Dynamics in Mark-Recapture Models.

Speaker: Jon Bishop (CREEM)

Abstract

Formulating mark-recapture models as state-space models allows an embedded population dynamics model to be specified. This aims to ensure that estimated changes in the population are consistent with what is assumed to be known about the population biology of the species being modelled.When formulating these state-space models in order to model capture histories we can adopt one of two approaches. Firstly, we consider a ‘conditional’ approach in which the state of an individual animal is determined not only by characteristics such as age and gender but also by its capture history. Therefore, parameters relating to the probability of capture will appear in the vector of state parameters. Secondly, we consider an ‘unconditional’ approach in which the capture histories are regarded as observations. Consequently, the capture histories do not influence the state of an animal. Therefore, the parameters relating to capture probability appear in the vector of observation parameters.The conditional approach is so named because for a specific time period, we condition on the known numbers of animals possessing capture histories which include capture in that time period. Under this approach there is no observation error in the model and stochasticity enters only through the uncertainty in the numbers of animals in state elements corresponding to capture histories that do not include capture in that time period. Under the unconditional approach, capture is treated as a stochastic observation process, and the capture histories are considered to be a single random realization of this process. This latter approach is more consistent with traditional mark- recapture methods.We describe how suitable state-space models can be specified, under both conditional and unconditional approaches, in order to simulate state vectors that satisfy the constraints imposed by the observed data and our knowledge of the biology of the population under study. We also discuss the implementation of particle filtering techniques for fitting these models under each approach.