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Bifurcation analysis of individual-based models in population dynamics

Siekmann, I (2015) Bifurcation analysis of individual-based models in population dynamics. Ecological Complexity, 21. pp. 177-184. ISSN 1476-945X

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Abstract

Individual-based models (IBMs) enable us to investigate the effects of inter-individual differences within a population much more easily than traditional modelling approaches based on differential equations. However, the greater flexibility of IBMs makes it difficult to systematically analyse the parameter dependency of the model behaviour so that an IBM may be hard to interpret. In this article, bifurcation analysis techniques for investigating models based on ordinary differential equations (ODE) are transferred to IBMs. For this purpose, we infer stationary solutions of the IBM from the asymptotic dynamics. The stability of these stationary solutions can then be studied depending on model parameters. As shown previously for ODE models (Siekmann et al., 2010; Siekmann, 2013), stationary solutions
SiS
can be used as bifurcation parameters which allows us to predict survival or extinction of populations by simple algebraic relationships. This is demonstrated with the example of a simple two-strain infection IBM. Moreover, analysing model behaviour based on stationary solutions provides a unified representation of different models that allows us to rigorously compare IBMs with other modelling frameworks like, for example, ODE models. A comparison of the IBM to a population-based ODE model of a two-strain infection leads to similar predictions although both models were built with very different modelling approaches.

Item Type: Article
Uncontrolled Keywords: 0501 Ecological Applications, 0602 Ecology
Subjects: Q Science > QA Mathematics
Divisions: Applied Mathematics
Publisher: Elsevier
Related URLs:
Date Deposited: 21 Sep 2017 09:33
Last Modified: 21 Sep 2017 09:34
DOI or Identification number: 10.1016/j.ecocom.2014.06.002
URI: http://researchonline.ljmu.ac.uk/id/eprint/7137

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