  This document is due to appear as a chapter of the forthcoming Handbook of
Approximate Bayesian Computation (ABC) by S. Sisson, L. Fan, and M. Beaumont.
Here we describe some of the circumstances under which statistical ecologists
might benefit from using methods that base statistical inference on a set of
summary statistics, rather than on the full data. We focus particularly on one
such approach, Synthetic Likelihood, and we show how this method represents an
alternative to particle filters, for the purpose of fitting State Space Models
of ecological interest. As an example application, we consider the
prey-predator model of Turchin and Ellner (2000), and we use it to analyse the
observed population dynamics of Fennoscandian voles.
