Heterogeneity in Capture-Recapture: Bayesian Methods to Balance Realism and Model Complexity

Simon Bonner successfully defended his Ph.D. project entitled "Heterogeneity in Capture-Recapture: Bayesian Methods to Balance Realism and Model Complexity" on 21 November 2008.

Capture-recapture experiments are important for monitoring many endangered animal populations, such as salmon threatened by over-harvesting and migratory songbirds impacted by habitat loss. An important consideration in the analysis of capture-recapture data is potential variation in the probabilities of capture and survival. Failure to account for this variation can lead to incorrect inference, but traditional models incorporating heterogeneity may be very complex. This thesis presents three projects employing Bayesian methods to balance realistically modelling heterogeneity in capture-recapture data and increasing model complexity. In the first project, I consider the analysis of data from two-sample experiments used in estimating the number of juvenile salmon leaving their spawning grounds. These migrations may last for several weeks and standard models may require many parameters to account for variations over time. My solution is to model the population size as a smooth function of time by fitting a Bayesian penalised spline. The method is applied to two datasets from the migration of juvenile salmon and provides more precise estimates of the population size that are less affected by outliers in the data.

My second project addresses estimation of the size of an open population when individual capture or survival probabilities are functions of a time-dependent, continuous covariate. The main challenge is that these covariates can only be observed on occasions when an individual is captured. I develop a two-stage Bayesian method that first examines the covariate's effect by analysing the capture of marked individuals, and then applies the results to estimate the total population size. The model is used to study the dynamics of a population of Soay sheep (Ovis aries) whose survival is affected by body mass.

Finally, I develop a method to allow more flexibility in modelling the relationship between a co- variate and individual survival probabilities. Standard methods assume that the relationship is linear on some scale. My model incorporates Bayesian adaptive splines to allow smooth but local fitting of the linear predictor. I apply this model to study the effect of body condition on the survival of reed warblers (Acrocephalus scirpaceus) breeding in Holland.

Keywords: Adaptive spline; Bayesian inference; Capture-recapture; Hierarchical modelling; Penalized spline; Time-dependent covariate

This type of interdisciplinary work is a hallmark of our program in Applied Statistics at Simon Fraser University. For more information, please contact Simon Bonner (sbonner@stat.sfu.ca) or his supervisor Carl Schwarz (cschwarz@stat.sfu.ca), Department of Statistics and Actuarial Science.