Fitting Population Models to Time Series Data

Abstract

Like many scientists, population ecologists exhibit a kind of schizophrenia when it comes to time series. On one hand, the development of mathematical models representing the dynamics of one or more populations has a long and glorious history (e.g., Kingsland 1985). On the other hand, when confronted with actual population time series data, most ecologists fall back on familiar empirical models (e.g., ARMA models) that have little or no connection to the underlying ecological processes. In the few exceptions in which actual population models are used (e.g., Hassell et al. 1976), model fitting tends to be ad hoc. The purpose of this chapter is to outline how formal statistical methods can be used to fit a population model to data and, at the same time, to point out that this approach may be problematic.