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Theoretical Ecology

, Volume 2, Issue 3, pp 149–160 | Cite as

Simple testing procedures for the Holling type II model

  • Sorana FrodaEmail author
  • Ashkan Zahedi
Original paper

Abstract

In this paper, we consider predator–prey data that can be viewed as solutions to a planar system of ordinary differential equations (ODE) observed with random error. The ODE system admits a limit cycle, while the random error is supposed to act additively in the log-scale. One of the oldest such systems is Holling’s type II model. In spite of its simplicity, it is still very popular in data analyses, although more sophisticated models have been introduced in the literature. We propose a simple way of deciding whether a set of predator–prey pairs is indicative or not of a departure from this basic model by exploiting the geometric properties of the solution in the phase plane. To illustrate our method, we use simulated and real data.

Keywords

Holling type II model Observational error Predator–prey system of differential equations Phase plane Isocline Linear regression slope Two-sample tests Nonparametric trend test 

Notes

Acknowledgements

This research received financial support from the Natural Sciences and Engineering Research Council (Canada). We are indebted to C. Jost for providing various data sets; to R. Ferland, C. Gravel, and F. Larribe for advice and support; and to an anonymous referee for careful reading and very useful suggestions. The first author is thankful to F. Rousset and I. Olivieri and her team at the Institut des sciences de l’évolution de Montpellier for their hospitality and very stimulating research exchanges.

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Département de MathématiquesUniversité du Québec à MontréalMontréalCanada

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