Stochastic analogues of deterministic single-species population models

Authored by D J T Sumpter, A Braennstroem

Date Published: 2006

DOI: 10.1016/j.tpb.2006.01.006

Sponsors: No sponsors listed

Platforms: MATLAB

Model Documentation: Other Narrative Mathematical description

Model Code URLs: Model code not found

Abstract

Although single-species deterministic difference equations have long been used in modeling the dynamics of animal populations, little attention has been paid to how stochasticity should be incorporated into these models. By deriving stochastic analogues to difference equations from first principles, we show that the form of these models depends on whether noise in the population process is demographic or environmental. When noise is demographic, we argue that variance around the expectation is proportional to the expectation. When noise is environmental the variance depends in a non-trivial way on how variation enters into model parameters, but we argue that if the environment affects the population multiplicatively then variance is proportional to the square of the expectation. We compare various stochastic analogues of the Ricker map model by fitting them, using maximum likelihood estimation, to data generated from an individual-based model and the weevil data of Utida. Our demographic models are significantly better than our environmental models at fitting noise generated by population processes where noise is mainly demographic. However, the traditionally chosen stochastic analogues to deterministic models-additive normally distributed noise and multiplicative lognormally distributed noisegenerally fit all data sets well. Thus, the form of the variance does play a role in the fitting of models to ecological time series, but may not be important in practice as first supposed. (c) 2006 Elsevier Inc. All rights reserved.

Tags

behavior time-series Dynamics ecology Climate-change Environmental stochasticity Observation error