Detecting population regulation via a nonlinear time series model

Jonathan Alsop

Injury Prevention Research Unit, University of Otago, New Zealand

Abstract

Testing for the presence of density dependence in a time series of population counts is problematic. Often linear time series models have been used as bases for testing for population regulation. A non-linear model has been devised which incorporates these simple models, but allows for a 'stronger' form of density dependence. This model can be readily extended to include additional lag terms and extraneous variables. Under certain parameter conditions the model is chaotic. This behaviour is examined via bifurcation diagrams and estimates of the Lyapunov exponent.