On the design of closed recapture experiments

We propose a method to plan the number of occasions of recapture experiments for population size estimation. We do so by fixing the smallest number of capture occasions so that the expected length of the profile confidence interval is less than or equal to a fixed threshold. In some cases, we solve the optimization problem in closed form. For more complex models we use numerical optimization. We detail models assuming homogeneous, time‐varying, subject‐specific capture probabilities, behavioral response to capture, and combining behavioral response with subject‐specific effects. The principle we propose can be extended to plan any other model specification. We formally show the validity of the approach by proving distributional convergence. We illustrate with simulations and challenging examples in epidemiology and ecology. We report that in many cases adding as few as two sampling occasions may substantially reduce the length of confidence intervals.     

The recapture of British salmon in Irish waters

In the years 1972 to 1974, inclusive, a total of 50 salmon originally tagged as smolts in British rivers were recaptured in Irish waters. Although it is not possible to give precise reasons for these changes, some factors can be largely eliminated. The results do, however, indicate that salmon and grilse derived from British rivers occur in Irish inshore waters to a greater extent than was generally accepted.     

Model selection for integrated recovery/recapture data

Catchpole et al. (1998, Biometrics 54, 33-46) provide a novel scheme for integrating both recovery and recapture data analyses and derive sufficient statistics that facilitate likelihood computations. In this article, we demonstrate how their efficient likelihood expression can facilitate Bayesian analyses of these kinds of data and extend their methodology to provide a formal framework for model determination. We consider in detail the issue of model selection with respect to a set of recapture/recovery histories of shags (Phalacrocorax aristotelis) and determine, from the enormous range of biologically plausible models available, which best describe the data. By using reversible jump Markov chain Monte Carlo methodology, we demonstrate how this enormous model space can be efficiently and effectively explored without having to resort to performing an infeasibly large number of pairwise comparisons or some ad hoc stepwise procedure. We find that the model used by Catchpole et al. (1998) has essentially zero posterior probability and that, of the 477,144 possible models considered, over 60% of the posterior mass is placed on three neighboring models with biologically interesting interpretations.     

Open population maximum likelihood spatial capture‐recapture

Open population capture‐recapture models are widely used to estimate population demographics and abundance over time. Bayesian methods exist to incorporate open population modeling with spatial capture‐recapture (SCR), allowing for estimation of the effective area sampled and population density. Here, open population SCR is formulated as a hidden Markov model (HMM), allowing inference by maximum likelihood for both Cormack‐Jolly‐Seber and Jolly‐Seber models, with and without activity center movement. The method is applied to a 12‐year survey of male jaguars (Panthera onca) in the Cockscomb Basin Wildlife Sanctuary, Belize, to estimate survival probability and population abundance over time. For this application, inference is shown to be biased when assuming activity centers are fixed over time, while including a model for activity center movement provides negligible bias and nominal confidence interval coverage, as demonstrated by a simulation study. The HMM approach is compared with Bayesian data augmentation and closed population models for this application. The method is substantially more computationally efficient than the Bayesian approach and provides a lower root‐mean‐square error in predicting population density compared to closed population models.     

A capture–recapture model of amphidromous fish dispersal

Adult movement scale was quantified for two tropical Caribbean diadromous fishes, bigmouth sleeper Gobiomorus dormitor and mountain mullet Agonostomus monticola, using passive integrated transponders (PITs) and radio‐telemetry. Large numbers of fishes were tagged in Río Mameyes, Puerto Rico, U.S.A., with PITs and monitored at three fixed locations over a 2·5 year period to estimate transition probabilities between upper and lower elevations and survival probabilities with a multistate Cormack–Jolly–Seber model. A sub‐set of fishes were tagged with radio‐transmitters and tracked at weekly intervals to estimate fine‐scale dispersal. Changes in spatial and temporal distributions of tagged fishes indicated that neither G. dormitor nor A. monticola moved into the lowest, estuarine reaches of Río Mameyes during two consecutive reproductive periods, thus demonstrating that both species follow an amphidromous, rather than catadromous, migratory strategy. Further, both species were relatively sedentary, with restricted linear ranges. While substantial dispersal of these species occurs at the larval stage during recruitment to fresh water, the results indicate minimal dispersal in spawning adults. Successful conservation of diadromous fauna on tropical islands requires management at both broad basin and localized spatial scales.     

Detection of activity cycles of tsetse from capture–recapture data

ABSTRACT.

• 1 Activity cycles of female tsetse (Glossina palpalis palpalis Robineau-Desvoidy) in the field are contrasted with those of males, using mark-release-recapture data from continuous biconical trap samples over a period of 80 days in two villages in Ivory Coast.
• 2 Variability in recapture rates was examined using the techniques of autocorrelation and spectral analysis. In order to do this a two-dimensional diffusion model incorporating both mortality and emigration was first fitted to corrected recapture rate data to produce a trend line, deviations from which were subjected to the analysis.
• 3 The autocorrelations for the data for males suggest considerable variability in activity, presumably associated with feeding, around a mean period of about 4 days in one village and seven in the other.
• 4 Data for females show a strong regular periodicity of about 9–10 days, reflecting the pregnancy cycle, and shorter, more variable periodicities probably corresponding to feeding.

     

Bayesian model selection for spatial capture–recapture models

A vast amount of ecological knowledge generated over the past two decades has hinged upon the ability of model selection methods to discriminate among various ecological hypotheses. The last decade has seen the rise of Bayesian hierarchical models in ecology. Consequently, commonly used tools, such as the AIC, become largely inapplicable and there appears to be no consensus about a particular model selection tool that can be universally applied. We focus on a specific class of competing Bayesian spatial capture–recapture (SCR) models and apply and evaluate some of the recommended Bayesian model selection tools: (1) Bayes Factor—using (a) Gelfand‐Dey and (b) harmonic mean methods, (2) Deviance Information Criterion (DIC), (3) Watanabe‐Akaike's Information Criterion (WAIC) and (4) posterior predictive loss criterion. In all, we evaluate 25 variants of model selection tools in our study. We evaluate these model selection tools from the standpoint of selecting the “true” model and parameter estimation. In all, we generate 120 simulated data sets using the true model and assess the frequency with which the true model is selected and how well the tool estimates N (population size), a parameter of much importance to ecologists. We find that when information content is low in the data, no particular model selection tool can be recommended to help realize, simultaneously, both the goals of model selection and parameter estimation. But, in general (when we consider both the objectives together), we recommend the use of our application of the Bayes Factor (Gelfand‐Dey with MAP approximation) for Bayesian SCR models. Our study highlights the point that although new model selection tools are emerging (e.g., WAIC) in the applied statistics literature, those tools based on sound theory even under approximation may still perform much better.     

The effects of marking and capture on recapture frequencies of butterflies

Summary As a preliminary to a population study using markrelease-recapture techniques, specimens of the Satyrid buttfly Melanargia galathea (L.) were subjected to a number of marking and capture techniques. Although the adults are thought to display both aposematic and cryptic coloration, the use of marks of different sizes and colours had no significant effect on recapture frequencies. However, repeated disturbance due to capture was found to significantly reduce recapture frequency. The influence of the different techniques on recapture frequencies could not be detected reliably by excessively low recapture rates, or by comparisons to Poisson distributions. It is suggested that these comparisons are of limited value as measures of the suitability of a marking or handling scheme. Subsequent work showed that capture affected recapture rates of several other species. Moreover, these effects could not be readily predicted from knowledge of the biology of these species. The implications of these findings are discussed.