Sumpter, D.J.T. and Broomhead, D.S.
(2001)
*Relating Individual Behaviour to Population Dynamics.*
Proceedings of the Royal Society B: Biological Sciences, 268 (1470).
pp. 925-932.
ISSN 0962-8452

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## Abstract

How do the behavioural interactions between individuals in an ecological system produce the global population dynamics of that system? We present a stochastic individual-based model of the reproductive cycle of the mite Varroa jacobsoni, a parasite of honeybees. The model has the interesting property in that its population level behaviour is approximated extremely accurately by the exponential logistic equation or Ricker map. We demonstrated how this approximation is obtained mathematically and how the parameters of the exponential logistic equation can be written in terms of the parameters of the individual-based model. Our procedure demonstrates, in at least one case, how study of animal ecology at an individual level can be used to derive global models which predict population change over time.

Item Type: | Article |
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Uncontrolled Keywords: | Population Dynamics Varroa Jacobsoni Individual-Based Modelling Logistic Equation |

Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 39 Difference and functional equations MSC 2010, the AMS's Mathematics Subject Classification > 92 Biology and other natural sciences |

Depositing User: | Professor David Broomhead |

Date Deposited: | 24 May 2006 |

Last Modified: | 20 Oct 2017 14:12 |

URI: | http://eprints.maths.manchester.ac.uk/id/eprint/296 |

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