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FURTHER DIFFICULTIES IN THE ANALYSIS OF FUNCTIONAL-RESPONSE EXPERIMENTS AND A RESOLUTION

Published online by Cambridge University Press:  31 May 2012

F.M. Williams  and
Steven A. Juliano
F.M. Williams
Affiliation:
Department of Biology, The Pennsylvania State University, University Park, Pennsylvania 16802
Steven A. Juliano
Affiliation:
Department of Biology, The Pennsylvania State University, University Park, Pennsylvania 16802
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Abstract

The Holling disc equation (Type-II functional response) for predation, which is mathematically equivalent to the Michaelis–Menten enzyme-kinetics and to the Monod microbial-growth equations, has been used in several linear transformations for parameter estimation. The most commonly used is the Lineweaver–Burk double reciprocal. We compare 4 linearizations of the disc equation and a direct nonlinear fit to stimulated predation data. We conclude that (1) the best parameter estimates are obtained by the direct nonlinear method and (2) the Lineweaver–Burk is the worst of the (all unsatisfactory) linearizations. We propose a new nonparametric technique to use when nonlinear methods cannot be used.

Résumé

L'équation “disc” de Holling (réponse fonctionnelle de type II) pour la prédation laquelle équivaut mathématiquement aux équations de Michaelis–Menten pour la cinétique des enzymes, et de Monod pour la croissance mirobienne, est ordinairement soumise à diverses transformations linéaires pour l'estimation des paramètres. La plus communément utilisée est la réciproque double de Lineweaver–Burk. On compare ici 4 formes linéarisées de l'équation de Holling avec un ajustement non linéaire direct à des données de prédation simulées. On conclut que (1) les meilleurs estimés des paramètres sont obtenus avec la méthode non linéaire directe, et (2) la linéarisation de Lineweaver–Burk est la pire méthode (toutes étant insatisfaisantes). On propose une nouvelle technique non-paramétrique lorsque les méthodes non linéaires ne peuvent être utilisées.

Type
Articles
Information
The Canadian Entomologist , Volume 117 , Issue 5 , May 1985 , pp. 631 - 640
Copyright
Copyright © Entomological Society of Canada 1985

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