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Sensitivity analysis of continuous-time models for ecological and evolutionary theories

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An Erratum to this article was published on 30 October 2015

Abstract

Sensitivity analyses are of paramount importance in ecological and evolutionary theories, but their application to continuous time models has been virtually ignored from these fields. We present a simple and general method that makes this analysis possible for any model specified by a system of ordinary differential equations, using the direct method from mathematical theory. The resulting analysis may be used to study the effect of parameter perturbation on the whole trajectories of the state variables as well as for deriving the sensitivity of composite metrics such as the population growth rate. We also present methods for analyzing the sensitivity of discrete events within a continuous-time framework, such as the age at maturation, where timing may be affected by the perturbation. These methods are applied to a model for the energetics of individual growth, reproduction, and mortality. The method is versatile and can be applied to study transient as well as asymptotic dynamics, and its application may benefit many fields of ecology and evolution.

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Acknowledgments

We are grateful to Andre de Roos and Hal Caswell for thorough comments on the manuscript, and to Ottar Bjornstad and Jeremy Fox for useful discussions. This work was supported by Ed McCauley’s NSERC Accelerator Award and Operating Grant, Canada Research Chair, and grants from the Water Research Institute. Romain Richard received additional support from a Pacific Institute for the Mathematical Sciences IGTC fellowship in mathematical biology.

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Author notes

  1. Romain Richard

    Present address: Institut de Recherche sur la Biologie de l’Insecte, IRBI UMR CNRS 7261, Université de Tours, 37200, Tours, France

Authors and Affiliations

  1. Department of Biological Sciences, University of Calgary, Calgary, Alberta, T2N 1N4, Canada

    Romain Richard & Edward McCauley

  2. Institut de Recherche sur la Biologie de l’Insecte, IRBI UMR CNRS 7261Université de Tours, 37200, Tours, France

    Jérôme Casas

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Correspondence to Romain Richard.

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Richard, R., Casas, J. & McCauley, E. Sensitivity analysis of continuous-time models for ecological and evolutionary theories. Theor Ecol 8, 481–490 (2015). https://doi.org/10.1007/s12080-015-0265-9

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