External Seminar: Ruth King (University of Edinburgh)

[Statistics & Probability Seminar]

Incorporating memory into capture-recapture models via first-order Markov models

In this talk we focus on incorporating memory into ecological models in a biologically realistic manner. In particular we consider capture-recapture studies, where observers going into the field at a series of capture events. At the initial capture event all observed individuals are uniquely marked, recorded and released back into the population. At each subsequent capture event previously unmarked individuals are marked and all observed individuals are recorded before being released. This leads to data of the form of the capture history of each individual observed, recording whether or not they are observed at each capture event.

We will initially describe how standard capture-recapture models can be expressed as a hidden Markov-type model. We describe the advantages of specifying the models in this framework, including efficient model-fitting techniques and incorporating additional processes. In particular, we focus on open multi-state capture-recapture data, where individuals are recorded in a given discrete time-varying “state” when they are observed. For example, state may refer to “breeding/not breeding” or “hungry/not hungry”. For mathematical convenience it is often assumed that transitions between states can be modelled as first-order Markovian (and hence “memoryless”). However, this is often biologically unrealistic. We will consider the incorporation of memory in a parsimonious manner via the specification of a semi-Markovian transition model and describe how the models can be efficiently fitted using a first-order Markov approximation. We apply the approach to house finch data where state corresponds to “infected” or “not infected” with conjunctivitis.