Time-varying covariates and semi-parametric regression in capture-recapture: an adaptive spline approach

Abstract

Advances in capture–recapture methodology have allowed the inclusion of continuous, time-dependent individual-covariates as predictors of survival and capture probabilities. The problem posed by these covariates is that they are only observed for an individual when that individual is captured. One solution is to assume a model of the covariate which defines the distribution of unobserved values, conditional on the observed values, and apply Bayesian methods to compute parameter estimates and to test the covariate’s effect. Previous applications of this approach have modeled the survival probability as a linear function of the covariate on some scale (e.g. identity or logistic). In some applications a linear function may not adequately describe the true relationship. Here we incorporate semi-parametric regression to allow for more flexibility in the relationship between the covariate and the survival probabilities of the Cormack– Jolly–Seber model. A fully Bayesian, adaptive algorithm is used to model the relationship with splines, in which the complexity of the relationship is governed by the number and location of the knots in the spline. A reversible jump Markov chain Monte Carlo algorithm is implemented to explore splines with different knot configurations, and model averaging is used to compute the final estimates of the survival probabilities. The method is applied to a simulated data set and to data collected through the Dutch Constant Effort Sites ringing project to study the survival of reed warblers (Acrocephalus scirpaceus) as a function of condition.