PIMS PDF Colloquium: Counting Sheep -- Bayesian Methods to Account for Time-Dependent Covariates in Open-Population Capture

Capture-recapture methods are widely used to monitor endangered wildlife populations. A requirement of simple capture-recapture models is that all individuals alive on one sampling occasion have the same
probability of capture. While this assumption may be reasonable in
small, isolated populations, there are many variables that might
influence an individual's catchability and estimates of survival rates
or the abundance will be biased if these differences are
ignored. However, covariates of the capture probability which vary
both between individuals and over time, like body mass, present a
challenge in the analysis of capture-recapture data because 1) their
values can only be measured for the individuals captured on each
sampling occasion and 2) the unknown values are not missing at random
and cannot be ignored. I will present Bayesian methods to incorporate
the effects of such covariates in the Cormack-Jolly-Seber and
Jolly-Seber models -- the two most common models for open-population
capture-recapture data.

My talk will begin with an introduction to Bayesian statistics,
capture-recapture methods, and the problems associated with
time-dependent covariates. I will then describe my method for
including such covariates in the Cormack-Jolly-Seber model to estimate
survival rates and how this method can be extended to the Jolly-Seber
model to obtain estimates of abundance. I will illustrate my methods
by application to data from the study of Soay sheep on the Isle of
Hirta, Scotland, and conclude by discussing applications to more
complicated models and comparisons with other approaches.