Stochastic modelling of ecological processes using hybrid Gibbs samplers

Stochastic process models are useful in describing a broad range of individual-based phenomena and are increasingly being applied in ecology. However, the estimation of parameters in such models is an important issue which has typically received much less attention than the exploration of model behaviour. The difficulties of parameter estimation are compounded by the fact that in most situations the available data are incomplete in some sense. Here, we demonstrate how methods of Markov chain Monte Carlo (McMC) Gibbs sampling can be combined within reversible-jump Metropolis–Hastings McMC frameworks to produce a hybrid sampler which can be used to obtain estimates of parameters and missing data for a broad class of stochastic process rate models. We apply these methods to two stochastic models arising from the ecology of grazed ecosystems in order to display the benefits of the hybrid sampler and the usefulness of a stochastic modelling approach to experiments where limited data exist.