Simon J. Bonner

WinBUGS for population ecologists: Bayesian modeling using Markov Chain Monte Carlo methods.

The computer package WinBUGS is introduced. We first give a brief introduction to Bayesian theory and its implementation using Markov chain Monte Carlo (MCMC) algorithms. We then present three case studies showing how WinBUGS can be used when classical theory is difficult to implement. The first example uses data on white storks from Baden Wurttemberg, Germany, to demonstrate the use of mark-recapture models to estimate survival, and also how to cope with unexplained variance through random effects. Recent advances in methodology and also the WinBUGS software allow us to introduce (i) a flexible way of incorporating covariates using spline smoothing and (ii) a method to deal with missing values in covariates. The second example shows how to estimate population density while accounting for detectability, using distance sampling methods applied to a test dataset collected on a known population of wooden stakes. Finally, the third case study involves the use of state-space models of wildlife population dynamics to make inferences about density dependence in a North American duck species. Reversible Jump MCMC is used to calculate the probability of various candidate models. For all examples, data and WinBUGS code are provided.

Continuous Covariates in Mark-Recapture-Recovery Analysis: A Comparison of Methods

Time varying, individual covariates are problematic in experiments with marked animals because the covariate can typically only be observed when each animal is captured. We examine three methods to incorporate time varying, individual covariates of the survival probabilities into the analysis of data from mark-recapture-recovery experiments: deterministic imputation, a Bayesian imputation approach based on modeling the joint distribution of the covariate and the capture history, and a conditional approach considering only the events for which the associated covariate data are completely observed (the trinomial model). After describing the three methods, we compare results from their application to the analysis of the effect of body mass on the survival of Soay sheep (Ovis aries) on the Isle of Hirta, Scotland. Simulations based on these results are then used to make further comparisons. We conclude that both the trinomial model and Bayesian imputation method perform best in different situations. If the capture and recovery probabilities are all high, then the trinomial model produces precise, unbiased estimators that do not depend on any assumptions regarding the distribution of the covariate. In contrast, the Bayesian imputation method performs substantially better when capture and recovery probabilities are low, provided that the specified model of the covariate is a good approximation to the true data-generating mechanism.

Individual quality and personality: bolder males are less fecund in the hermit crab Pagurus bernhardus

One explanation for animal personality is that different behavioural types derive from different life-history strategies. Highly productive individuals, with high growth rates and high fecundity, are assumed to live life at a fast pace showing high levels of boldness and risk taking, compared with less productive individuals. Here, we investigate among-individual differences in mean boldness (the inverse of the latency to recover from a startling stimulus) and in the consistency of boldness, in male hermit crabs in relation to two aspects of life-history investment. We assessed aerobic scope by measuring the concentration of the respiratory pigment haemocyanin, and we assessed fecundity by measuring spermatophore size. First, we found that individuals investing in large spermatophores also had high concentrations of haemocyanin. Using doubly hierarchical-generalized linear models to analyse longitudinal data on startle responses, we show that hermit crabs vary both in their mean response durations and in the consistency of their behaviour. Individual consistency was unrelated to haemocyanin concentration or spermatophore size, but mean startle response duration increased with spermatophore size. Thus, counter to expectations, it was the most risk-averse individuals, rather than the boldest and most risk prone, that were the most productive. We suggest that similar patterns should be present in other species, if the most productive individuals avoid risky behaviour.

Back to work: correlates of employment among persons receiving highly active antiretroviral therapy.

Abstract The aim of this study was to quantify the level of employment at one-year and to determine potential predictors of future employment among HIV-positive persons on highly active antiretroviral therapy (HAART) in the province of British Columbia. Of the 392 individuals that were initially unemployed at baseline 63 (16.1%) found a job over the subsequent year. Factors associated with becoming employed included a baseline income over

High Prevalence of Smoking Among Urban-Dwelling Canadian Men Who Have Sex with Men

10 000, having long-term disability or unemployment insurance as an income source, having higher CD4 cell counts, and better physical, social, and role functioning. Factors negatively associated with finding employment included having provincial assistance as an income source and having ever been an injection drug user (IDU). In multivariate analyses, not using provincial assistance as a source of income (Odds Ratio [OR] = 7.39; 95% CI: 3.26–16.7; p < 0.001) and higher MOS-SF role functioning (OR = 1.12 per 10 point increment; 95% CI: 1.03–1.21; p = 0.005) were independent predictors of becoming employed. In conclusion, our study demonstrates that while significant advances have been made in the reduction of HIV-related mortality, the majority of HIV-infected individuals on adequate treatment are still unable to be gainfully employed.

Mark-Recapture with Multiple, Non-Invasive Marks

A small but consistent literature from the United States suggests increased risk for smoking among lesbians and men who have sex with men (MSM). Few studies have investigated smoking among MSM in other countries where different social norms and restrictions on smoking in public apply. We measured smoking behaviours in a convenience sample of urban-dwelling young Canadian MSM (median age 28 years). We compared the prevalence of smoking among MSM with that among other men in British Columbia (BC) using National Population Health Survey data to compute an age-adjusted standardized prevalence ratio (SPR). Independent predictors of smoking among MSM were identified using adjusted odds ratios (OR) with 95% confidence intervals (CI). Smoking during the previous year was reported by twice as many MSM (54.5% of 354) as other men in BC (25.9%) (SPR = 1.94, 95% CI 1.48–2.59), with largest differentials observed among men under 25 years of age. In multivariable analyses, smoking among MSM was significantly associated with younger age (OR 0.94, CI 0.88–1.00 per year), greater number of depressive symptoms (OR 1.12, CI 1.06–1.19 per symptom) and Canadian Aboriginal ethnicity (OR 2.64, CI 1.05–6.60). In summary, MSM in our study were twice as likely to smoke as other men in BC; the greatest differences were observed among the youngest men. The design of effective prevention and cessation programs for MSM will require identification of the age-dependent determinants of smoking initiation, persistence, and attempts to quit.

Accounting for behavioural response to capture when estimating population size from hair snare studies with missing data

SUMMARY Non-invasive marks, including pigmentation patterns, acquired scars, and genetic markers, are often used to identify individuals in mark-recapture experiments. If animals in a population can be identified from multiple, non-invasive marks then some individuals may be counted twice in the observed data. Analyzing the observed histories without accounting for these errors will provide incorrect inference about the population dynamics. Previous approaches to this problem include modeling data from only one mark and combining estimators obtained from each mark separately assuming that they are independent. Motivated by the analysis of data from the ECOCEAN online whale shark (Rhincodon typus) catalog, we describe a Bayesian method to analyze data from multiple, non-invasive marks that is based on the latent-multinomial model of Link et al. (2010, Biometrics 66, 178-185). Further to this, we describe a simplification of the Markov chain Monte Carlo algorithm of Link et al. (2010, Biometrics 66, 178-185) that leads to more efficient computation. We present results from the analysis of the ECOCEAN whale shark data and from simulation studies comparing our method with the previous approaches.

Smoothing population size estimates for time-stratified mark-recapture experiments using Bayesian P-splines.

Summary Hair snares have become an established method for obtaining mark-recapture data for population size estimation of Ursids and have recently been used to study other species including other carnivores, small mammals and ungulates. However, bias due to a behavioural response to capture in the presence of missing data has only recently been recognized and no statistical methodology exists to accommodate it. In a hair snare mark-recapture experiment, data can be missing if animals encounter a hair snare without leaving a hair sample, poor-quality samples are not genotyped, a fraction of all samples collected are genotyped due to cost considerations (subsampling) and/or not all genotyped hair samples provide an individual identification. These are all common features of hair snare mark-recapture experiments. Here, we present methodology that accounts for a behavioural response to capture in the presence of missing data from (i) subsampling and (ii) failure of hair samples to produce an individual identification. Four subprocesses are modelled–animal capture, hair deposition, researcher subsampling and DNA amplification with key parameters estimated from functions of the number of hair samples left by individuals at traps. We assess the properties of this methodology (bias and interval coverage) via simulation and then apply this methodology to a previously published data set. Our methodology removes bias and provides nominal interval coverage of population size for the simulation scenarios considered. In the example data set, we find that removing 75% of the hair samples leads to a 40% lower estimate of population size. Our methodology corrects about half of this bias and we identify a second source of bias that has not previously been reported associated with differential trap visitation rates among individuals within trapping occasions. Our methodology will allow researchers to reliably estimate the size of a closed population in the presence of a behavioural response to capture and missing data for a subset of missing data scenarios. It also provides a framework for understanding this generally unrecognized problem and for further extension to handle other missing data scenarios.

Time-Varying Covariates and Semi-Parametric Regression in Capture–Recapture: An Adaptive Spline Approach

Petersen-type mark-recapture experiments are often used to estimate the number of fish or other animals in a population moving along a set migration route. A first sample of individuals is captured at one location, marked, and returned to the population. A second sample is then captured farther along the route, and inferences are derived from the numbers of marked and unmarked fish found in this second sample. Data from such experiments are often stratified by time (day or week) to allow for possible changes in the capture probabilities, and previous methods of analysis fail to take advantage of the temporal relationships in the stratified data. We present a Bayesian, semiparametric method that explicitly models the expected number of fish in each stratum as a smooth function of time. Results from the analysis of historical data from the migration of young Atlantic salmon (Salmo salar) along the Conne River, Newfoundland, and from a simulation study indicate that the new method provides more precise estimates of the population size and more accurate estimates of uncertainty than the currently available methods.

MC(MC)MC: exploring Monte Carlo integration within MCMC for mark–recapture models with individual covariates

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.