Ecological systems in a modeling perspective

Abstract

May (1974,1976) opened the debate on whether biological populations might exhibit nonlinear dynamics and chaos. However, it has in general been difficult to verify nonlinear dynamics in biological populations. There are many reports concerning problems with this issue and some of them can be traced back to Hassell, Lawton, and May (1976) and Morris (1990) Our objective is not a discussion of the presence of nonlinear dynamics in biological populations. Instead, we analyze whether ecological census data can be used for validating nonlinearities at all. We choose our models and our situation so that as much as possible can be done rigorously with by hand computations. We consider a clearly nonlinear chemostat based model that is isolated. Some noise must be considered, and we choose a minimal approach: Only noise originating from the fact that ecological populations remain finite is considered, cf. Bailey (1964). Not only the interacting populations but also collected data sets tend to remain finite. Collection of long data sets might be associated with huge costs in ecology. Examples of exceptionally long and carefully studied ecological time series are those collected by Nicholson (1954) and Utida (1957). These data sets contain a few hundred data points, and we use this as a guideline for when an ecological time series should be considered exceptionally long in this chapter.