UNSPECIFIED (1997) Oscillations and chaos behind predator-prey invasion: Mathematical artifact or ecological reality? PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON SERIES B-BIOLOGICAL SCIENCES, 352 (1349). pp. 21-38. ISSN 0962-8436

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Abstract

A constant dilemma in theoretical ecology is knowing whether model predictions correspond to real phenomena or whether they are artifacts of the modelling framework. The frequent absence of detailed ecological data against which models can be tested gives this issue particular importance. We address this question in the specific case of invasion in a predator-prey system with oscillatory population kinetics, in which both species exhibit local random movement. Given only these two basic qualitative features, we consider whether we can deduce any properties of the behaviour following invasion. To do this we study four different types of mathematical model, which have no formal relationship, but which all reflect our two qualitative ingredients. The models are: reaction-diffusion equations, coupled map lattices, deterministic cellular automata, and integrodifference equations. We present results of numerical simulations of the invasion of prey by predators for each model, and show that although there are certain differences, the main qualitative features of the behaviour behind invasion are the same for all the models. Specifically, there are either irregular spatiotemporal oscillations behind the invasion, or regular spatiotemporal oscillations with the form of a periodic travelling 'wake', depending on parameter values. The observation of this behaviour in all types of model strongly suggests that it is a direct consequence of our basic qualitative assumptions, and as such is an ecologically reality which will always occur behind invasion in actual oscillatory predator-prey systems.

Item Type:	Journal Article
Subjects:	Q Science > QH Natural history > QH301 Biology
Journal or Publication Title:	PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON SERIES B-BIOLOGICAL SCIENCES
Publisher:	ROYAL SOC LONDON
ISSN:	0962-8436
Date:	29 January 1997
Volume:	352
Number:	1349
Number of Pages:	18
Page Range:	pp. 21-38
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/18006

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