Analyzing complex capture-recapture data in the presence of individual and temporal covariates and model uncertainty

Context-dependent fitness costs of reproduction despite stable body mass costs in an Arctic herbivore

The cost of reproduction on demographic rates is often assumed to operate through changing body condition. Several studies have found that reproduction depresses body mass more if the current conditions are severe, such as high population densities or adverse weather, than under benign environmental conditions. However, few studies have investigated the association between the fitness components and body mass costs of reproduction. Using 25 years of individual-based capture-recapture data from Svalbard reindeer Rangifer tarandus platyrhynchus, we built a novel Bayesian state-space model that jointly estimated interannual change in mass, annual reproductive success and survival, while accounting for incomplete observations. The model allowed us to partition the differential effects of intrinsic and extrinsic factors on both non-reproductive mass change and the body mass cost of reproduction, and to quantify their consequences on demographic rates. Contrary to our expectation, the body mass cost of reproduction (mean = -5.8 kg) varied little between years (CV = 0.08), whereas the between-year variation in body mass changes, that were independent of the previous year's reproductive state, varied substantially (CV = 0.4) in relation to autumn temperature and the amount of rain-on-snow in winter. This body mass loss led to a cost of reproduction on the next reproduction, which was amplified by the same environmental covariates, from a 10% reduction in reproductive success in benign years, to a 50% reduction in harsh years. The reproductive mass loss also resulted in a small reduction in survival. Our results show how demographic costs of reproduction, driven by interannual fluctuations in individual body condition, result from the balance between body mass costs of reproduction and body mass changes that are independent of previous reproductive state. We illustrate how a strong context-dependent fitness cost of reproduction can occur, despite a relatively fixed body mass cost of reproduction. This suggests that female reindeer display a very conservative energy allocation strategy, either aborting their reproductive attempt at an early stage or weaning at a relatively constant cost. Such a strategy might be common in species living in a highly stochastic and food limited environment.

Incorporating capture heterogeneity in the estimation of autoregressive coefficients of animal population dynamics using capture-recapture data

Population dynamic models combine density dependence and environmental effects. Ignoring sampling uncertainty might lead to biased estimation of the strength of density dependence. This is typically addressed using state-space model approaches, which integrate sampling error and population process estimates. Such models seldom include an explicit link between the sampling procedures and the true abundance, which is common in capture-recapture settings. However, many of the models proposed to estimate abundance in the presence of capture heterogeneity lead to incomplete likelihood functions and cannot be straightforwardly included in state-space models. We assessed the importance of estimating sampling error explicitly by taking an intermediate approach between ignoring uncertainty in abundance estimates and fully specified state-space models for density-dependence estimation based on autoregressive processes. First, we estimated individual capture probabilities based on a heterogeneity model for a closed population, using a conditional multinomial likelihood, followed by a Horvitz-Thompson estimate for abundance. Second, we estimated coefficients of autoregressive models for the log abundance. Inference was performed using the methodology of integrated nested Laplace approximation (INLA). We performed an extensive simulation study to compare our approach with estimates disregarding capture history information, and using R-package VGAM, for different parameter specifications. The methods were then applied to a real data set of gray-sided voles Myodes rufocanus from Northern Norway. We found that density-dependence estimation was improved when explicitly modeling sampling error in scenarios with low process variances, in which differences in coverage reached up to 8% in estimating the coefficients of the autoregressive processes. In this case, the bias also increased assuming a Poisson distribution in the observational model. For high process variances, the differences between methods were small and it appeared less important to model heterogeneity.

Modeling individual specific fish length from capture-recapture data using the von Bertalanffy growth curve

We use Bayesian methods to explore fitting the von Bertalanffy length model to tag-recapture data. We consider two popular parameterizations of the von Bertalanffy model. The first models the data relative to age at first capture; the second models in terms of length at first capture. Using data from a rainbow trout Oncorhynchus mykiss study we explore the relationship between the assumptions and resulting inference using posterior predictive checking, cross validation and a simulation study. We find that untestable hierarchical assumptions placed on the nuisance parameters in each model can influence the resulting inference about parameters of interest. Researchers should carefully consider these assumptions when modeling growth from tag-recapture data.

Digging through model complexity: using hierarchical models to uncover evolutionary processes in the wild

The growing interest for studying questions in the wild requires acknowledging that eco-evolutionary processes are complex, hierarchically structured and often partially observed or with measurement error. These issues have long been ignored in evolutionary biology, which might have led to flawed inference when addressing evolutionary questions. Hierarchical modelling (HM) has been proposed as a generic statistical framework to deal with complexity in ecological data and account for uncertainty. However, to date, HM has seldom been used to investigate evolutionary mechanisms possibly underlying observed patterns. Here, we contend the HM approach offers a relevant approach for the study of eco-evolutionary processes in the wild by confronting formal theories to empirical data through proper statistical inference. Studying eco-evolutionary processes requires considering the complete and often complex life histories of organisms. We show how this can be achieved by combining sequentially all life-history components and all available sources of information through HM. We demonstrate how eco-evolutionary processes may be poorly inferred or even missed without using the full potential of HM. As a case study, we use the Atlantic salmon and data on wild marked juveniles. We assess a reaction norm for migration and two potential trade-offs for survival. Overall, HM has a great potential to address evolutionary questions and investigate important processes that could not previously be assessed in laboratory or short time-scale studies.

A review of Bayesian state-space modelling of capture-recapture-recovery data

Traditionally, state-space models are fitted to data where there is uncertainty in the observation or measurement of the system. State-space models are partitioned into an underlying system process describing the transitions of the true states of the system over time and the observation process linking the observations of the system to the true states. Open population capture-recapture-recovery data can be modelled in this framework by regarding the system process as the state of each individual observed within the study in terms of being alive or dead, and the observation process the recapture and/or recovery process. The traditional observation error of a state-space model is incorporated via the recapture/recovery probabilities being less than unity. The models can be fitted using a Bayesian data augmentation approach and in standard BUGS packages. Applying this state-space framework to such data permits additional complexities including individual heterogeneity to be fitted to the data at very little additional programming effort. We consider the efficiency of the state-space model fitting approach by considering a random effects model for capture-recapture data relating to dippers and compare different Bayesian model-fitting algorithms within WinBUGS.

Investigating evolutionary trade-offs in wild populations of atlantic salmon (salmo salar): incorporating detection probabilities and individual heterogeneity

Evolutionary trade-offs among demographic parameters are important determinants of life-history evolution. Investigating such trade-offs under natural conditions has been limited by inappropriate analytical methods that fail to address the bias in demographic estimates that can result when issues of detection (uncertain detection of individual) are ignored. We propose a new statistical approach to quantify evolutionary trade-offs in wild populations. Our method is based on a state-space modeling framework that focuses on both the demographic process of interest as well as the observation process. As a case study, we used individual mark-recapture data for stream-dwelling Atlantic salmon juveniles in the Scorff River (Southern Brittany, France). In freshwater, juveniles face two life-history choices: migration to the ocean and sexual maturation (for males). Trade-offs may appear with these life-history choices and survival, because all are energy dependent. We found a cost of reproduction on survival for fish staying in freshwater and a survival advantage associated with the "decision" to migrate. Our modeling framework opens up promising prospects for the study of evolutionary trade-offs when some life-history traits are not, or only partially, observable.