Cormack–Jolly–Seber model with environmental covariates: A P‐spline approach

Abstract

In capture-recapture models, survival and capture probabilities can be modelled as functions of time-varying covariates, such as temperature or rainfall. The Cormack-Jolly-Seber (CJS) model allows for flexible modelling of these covariates; however, the functional relationship may not be linear. We extend the CJS model by semi-parametrically modelling capture and survival probabilities using a frequentist approach via P-splines techniques. We investigate the performance of the estimators by conducting simulation studies. We also apply and compare these models with known semi-parametric Bayesian approaches on simulated and real data sets.

Maximum penalized likelihood estimation in semiparametric mark‐recapture‐recovery models

“…(). Our work builds on Viallefont (), Stoklosa and Huggins (, b), extending those authors' P‐spline‐based approaches to the difficult yet important case of individual‐specific and stochastically time‐varying covariates. The proposed semiparametric modeling approach can be applied more widely to alternative capture‐recapture(‐recovery)‐type models, including for example the conditional trinomial approach (Catchpole et al., ), removing the need to model the missing time‐varying individual covariate values; stopover models (Pledger et al., ), removing the conditioning on initial capture; and closed populations, assuming no births, deaths or migrations, so that for these models the capture probabilities are often assumed to be a function of covariates.…”

“…Note that a similar setting was considered, in a Bayesian framework, by Gimenez et al. () and in a frequentist framework by Stoklosa and Huggins (). We consider ring‐recovery data on grey herons ( Ardea cinerea ).…”

“…We first discuss an application that corresponds to the simpler case involving only environmental covariates (see Section 2.3). Note that a similar setting was considered, in a Bayesian framework, by Gimenez et al (2006) and in a frequentist framework by Stoklosa and Huggins (2012a). We consider ring-recovery data on grey herons (Ardea cinerea).…”

“…() and Gimenez and Barbraud (), fit the semiparametric models in a Bayesian framework. Frequentist semiparametric analyses of mark‐recapture‐recovery data are presented by Fewster and Patenaude (), Viallefont (), and Stoklosa and Huggins (, b). However, all these analyses focus on specific types of covariates, and none of the existing frequentist approaches addresses the important case of individual‐specific covariates that evolve stochastically over time (but note that Viallefont, , considers an individual‐specific covariate that is a deterministic function of time, namely age).…”

“…Existing approaches include the use of a conditional ("trinomial") approach, deriving a likelihood conditional on only the observed covariate values (Catchpole et al, 2008), a multiple imputation approach (Worthington et al, 2015), a Bayesian data augmentation approach (Bonner and Schwarz, 2006;King et al, 2008King et al, , 2009) and a numerical integration approach leading to an approximate likelihood that can be evaluated efficiently using the hidden Markov model machinery (Langrock and King, 2013).Here, we aim to build on the existing literature by providing a frequentist inferential framework for semiparametric mark-recapture-recovery models that allows for the consideration of all the different types of covariates-environmental, time-constant individual, and time-varying individual covariates-using a unified machinery. In contrast, previous semiparametric approaches focused exclusively on environmental covariates (Gimenez et al, 2006;Stoklosa and Huggins, 2012a), individualspecific but time-constant or deterministic covariates (Viallefont, 2010;Stoklosa and Huggins, 2012b), or the (most challenging) case of individual-specific and stochastically time-varying continuous covariates. The latter has been considered in Bonner et al (2009) using Bayesian inference for adaptive spline models within a reversible jump Markov chain Monte Carlo framework.…”