ABSTRACT
Ecology aims to understand the abundance and distribution of organisms. This chapter considers the prey–predator model proposed by Turchin and Ellner, which has been used to describe the population dynamics of Fennoscandian voles. It focuses on a particular family of intractable models: state space models. The chapter describes this class of partially observed models, which are very popular in the ecological literature, and introduces two approaches that can be used to perform statistical inference for such models. The choice of summary statistics is crucial for the performance of approximate Bayesian computation (ABC) methods, hence, the topic has been the subject of much research. ABC methods offer an approach to intractable ecological models that forgo information in exchange for generality and, possibly, robustness. The chapter concludes by making some practical considerations regarding the benefits and drawbacks of using ABC or synthetic likelihood, rather than less approximate methods, when working with state space models.
