Individual Papers

8:55-9:20 AM Open capture-recapture models with heterogeneity: III. The robust design. - Shirley Pledger, Kenneth H. Pollock, & James L. Norris Finite mixture methods may be used in capture-recapture studies to allow for heterogeneity of survival. Following the methods of Norris and Pollock (1996), Pledger (2000) and Pledger and Schwarz (2002), animals are assumed to belong to one of finitely many groups, each of which has its own survival rates and capture rates. The group to which a specific animal belongs is not known, so its survival and capture probabilities are random vectors from a finite mixture. The promising results from the papers above have led to a series of three proposed papers by Pledger, Pollock and Norris. The first, "Open Capture-Recapture Models with Heterogeneity: I. Cormack-Jolly-Seber Model" is almost ready for submission to Biometrics.It deals with analyses which condition on first capture, allowing the modelling of heterogeneous capture and survival probabilities. The second, "Open Capture-Recapture Models with Heterogeneity: II. Jolly-Seber Model" deals with abundance estimates and their sensitivity to the presence of heterogeneity. The paper is partly written, with the computer programs functioning. This will be submitted to Biometrics in 2003. This third in the series, "Open Capture-Recapture Models with Heterogeneity: III. The robust design", will summarise and tie together the series of three papers, and give details and examples of these methods with the robust design sampling scheme. This paper complements and completes the development of likelihood-based models in Kendall, Pollock and Brownie (1995). 9:20-9:45 AM Multiple Species Capture-Recapture and Removal Models - Kenneth H. Pollock, James L. Norris, & Shirley Pledger A large body of literature exists for estimating species richness. These models allow for uncertain detection of each species (Boulinier et al. 1998a). Statistical methods adapted from capture-recapture and removal sampling, originally used to estimate individual species abundance can be applied here. (See for example, Burnham and Overton 1979; Nichols and Conroy 1996; Boulinier et al. 1998a). These methods have begun gradually to be used in the ecological literature, but progress has been slow, considering that the methodology has been around since 1979. In this paper, we shall begin with a detailed description of the estimation of species richness in the literature and then develop general removal and capture-recapture sampling models where multiple species are removed or marked and recaptured and the objective is to estimate species richness and the species abundance curve. 9:45-10:10 AM Time Varying, Continuous Covariates in the Cormack-Jolly-Seber Model - Simon Bonner & Carl Schwarz One area of research into capture-recapture methodology has focused on techniques to study the impact of different covariates on the population parameters. Straightforward methods have been developed for cases where the covariates are either discrete, constant over time, or apply to the population as a whole, but the problem has not been solved for the case of continuous, time dependent covariates unique to each individual (e.g. body mass). Because it is impossible to measure such variables on occasions where an individual was not captured, estimation can be considered a missing data problem. In this project, a model was constructed using a diffusion process to describe changes in the covariate. Logistic functions were used to link the covariate to capture and survival rates and incorporate the data into the Cormack-Jolly-Seber model. Two methods of parameter estimation were developed based on techniques commonly used to handle missing data: namely the EM-algorithm and Gibb's sampling. These methods were both applied to simulated and real data sets, and comparison of the results is provided. In short, though both methods gave similar results the Gibb's sampling technique was much easier to implement, more efficient to compute, and yielded estimates of the standard errors more readily than the EM-algorithm. 10:10-10:30 AM - break 10:30-10:55 AM Application of Bayesian Statistical Inference to Capture-Recapture Data, using WinBUGS - Howard Stauffer I will describe Bayesian statistical analysis modeling solutions for capture-recapture data. The solutions are based upon Monte Carlo Markov Chain (MCMC) iteration methods available with the Bayesian software WinBUGS. This analysis approach offers an alternative to the maximum likelihood estimation approach available with the frequentist capture-recapture software MARK. The capture-recapture analysis is illustrated with data from a hen clam pollution experiment and compared with results from previous analysis by Anderson, Burnham, and White, using MARK. For non-informative priors, the Bayesian and frequentist statistical results are comparable. For informative priors, however, results may differ. Bayesian inference offers a sequential approach to analysis, based upon multiple datasets obtained from population monitoring, providing periodic reassessments of parameters along with estimates of risk. Such reassessments are useful for adaptive management decision-making. Bayesian models can also be compared, analogous to frequentist models, using information-theoretic methods based upon AIC and DIC weights, for their relative competitiveness at fitting population sample data, and model averaging techniques can be applied to provide robust estimates of parameters. 10:55-11:20 AM Evaluation of ultrastructure and random effects band recovery models for estimating relationships between survival and harvest rates in exploited populations - Dave Otis & Gary White The functional relationship between vital rates and harvest rates of exploited populations is a fundamental interest of population biologists. Despite the development by many authors of a collection of density- dependent population models and functional representations of the relationship between annual survival and harvest rates, statistical analysis techniques for empirical investigation of these phenomena are extremely limited. In the case of band recovery data from harvested species, standard practice has been to incorporate ultrastructure functions of the form Si = S0 ( 1 - b*Ki) or Si = S0 ( 1 - Ki)b into band recovery models and use the estimated parameter b as a index for the relative evidence for additive or compensatory harvest mortality. Satisfactory performance of this approach has been inconsistent, and limited Monte Carlo simulations of the statistical performance of the estimator have revealed some problematic distributional and bias properties. Furthermore, the sensitivity of the estimator for detecting annual survival rate and harvest rate relationships is unknown. An alternative approach to the use of fixed effect ultrastructure models is possible if we consider annual harvest rates and survival rates as random effects. We envision an underlying process covariation between these 2 rates, which represents the parameter of interest, that is randomly perturbed by a collection of additional biotic and abiotic factors. The perturbation could be temporal, as in the case of released banded cohorts from single population for a series of years. Alternatively, if banding is done in multiple populations, we might consider survival and harvest as fixed effects in a given population, and assume random spatial perturbation in the parameters. We construct underlying models that incorporate specified additive, linear compensatory, and nonlinear compensatory functional relationships between harvest and natural mortality in a seasonally exploited population, and use Monte Carlo simulation to generate annual samples of band recovery data. These datasets are then analyzed using fixed effect ultrastructure models and random effects models. Parameter estimation is accomplished by using customized SAS code in PROC NLMIXED. Summary statistics of performance the alternative techniques are presented and compared, design considerations are discussed, and recommendations are made for further development. 11:20-11:45 AM Integrated analysis of wildlife population dynamics - B. Morgan, P. Besbeas, L. Thomas, S. Buckland, J. Harwood, C. Duck, & P. Pomeroy We describe two related methods for the combined analysis of mark-recapture and census data, using data for British grey seals as our motivating example. The first method is based on maximum likelihood: the likelihood for the mark-recapture data is combined with a likelihood from Kalman filter theory applied to a state-space model for the census data. We show that this approach can allow estimation of state parameters (such as fecundity) that would not be estimable using either dataset separately. The Kalman filter works well for normal linear models, but more complex models require more complex analysis methods. As an example, we demonstrate the use of a Bayesian nonlinear particle filter called sequential importance sampling (SIS) to fit nonlinear models including density dependence and movement between breeding colonies. In principle, these approaches could be extended to provide an integrated analysis of many diverse types of data.