Bayesian meta-analysis of demographic parameters in three small, temperate passerines

Accurate estimates of population parameters are vital for estimating extinction risk. Such parameters, however, are typically not available for threatened populations. We used a recently developed software tool based on Markov Chain Monte Carlo methods for carrying out Bayesian inference (the BUGS package) to estimate four demographic parameters; the intrinsic growth rate, the strength of density dependence, and the demographic and environmental variance, in three species of small temperate passerines from two sets of time series data taken from a dipper and a song sparrow population, and from previously obtained frequentist estimates of the same parameters in the great tit. By simultaneously modeling variation in these demographic parameters across species and using the resulting distributions as priors in the estimation for individual species, we improve the estimates for each individual species. This framework also allows us to make probabilistic statements about plausible parameter values for small passerines temperate birds in general which is often critically needed in management of species for which little or no data are available. We also discuss how our work relates to recently developed theory on dynamic stochastic population models, and finally note some important differences between frequentist and Bayesian methods.