Application of integrated Bayesian modeling and Markov chain Monte Carlo methods to the conservation of a harvested species

Abstract

When endeavoring to make informed decisions, conservation biologists must frequently contend with disparate sources of data and competing hypotheses about the likely impacts of proposed decisions on the resource status. Frequently, statistical analyses, modeling (e.g., for population projection) and optimization or simulation are conducted as separate exercises. For example, a population model might be constructed, whose parameters are then estimated from data (e.g., ringing studies, population surveys). This model might then be used to predict future population states, from current population estimates, under a particular management regime. Finally, the parameterized model might also be used to evaluate alternative candidate management decisions, via simulation, optimization, or both. This approach, while effective, does not take full advantage of the integration of data and model components for prediction and updating; we propose a hierarchical Bayesian context for this integration. In the case of American black ducks (Anas rubripes), managers are simultaneously faced with trying to extract a sustainable harvest from the species, while maintaining individual stocks above acceptable thresholds. The problem is complicated by spatial heterogeneity in the growth rates and carrying capacity of black ducks stocks, movement between stocks, regional differences in the intensity of harvest pressure, and heterogeneity in the degree of competition from a close congener, mallards (Anas platyrynchos) among stocks. We have constructed a population life cycle model that takes these components into account and simultaneously performs parameter estimation and population prediction in a Bayesian framework. Ringing data are used to develop posterior predictive distributions for harvest mortality rates, given as input decisions about harvest regulations. Population surveys of black ducks and mallards are used to obtain stock-specific estimates of population size for both species, for inputs into the population life-cycle model. These estimates are combined with the posterior distributions for harvest mortality, to obtain posterior predictive distributions of future population status for candidate sets of regional harvest regulations, under alternative biological hypotheses for black duck population dynamics. These distributions might then be used for both the exploration of optimal harvest policies and for sequential updating of model posteriors, via comparison of predictive distributions to future survey estimates of stock-specific abundance. Our approach illustrates advantages of MCMC for integrating disparate data sources into a common predictive framework, for use in conservation decision making.