Ecological systems in a modeling perspective

TL;DR

This paper investigates whether ecological census data can be used to validate nonlinear dynamics in biological populations, focusing on a nonlinear chemostat model with minimal noise considerations.

Contribution

It provides a rigorous analysis of ecological time series data for detecting nonlinearities, emphasizing hand computations and minimal noise assumptions.

Findings

Ecological time series with a few hundred data points are considered exceptionally long.

The study demonstrates the potential for validating nonlinear models using real ecological data.

Focuses on a specific nonlinear chemostat model with noise from finite populations.

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). In ecology, exceptionally long and famous time series are those collected by Nicholson (1954) and Utida (1957). Our judgement is that ecological time series data containing a few hundred data points is exceptionally long.