### Abstract

I consider how adaptive changes in behaviour with population size affect the stability of the population dynamics. In any given year the behavioural rule of a member of a single-species population is determined by the value of a certain trait. I allow for the possibility that this trait value can change from year to year. The number of descendants left in one year's time by an individual depends on its trait value, the values of other population members and the population size. The population dynamics is modelled as the change in population size from one year to the next. I focus on a population that is at a fixed point of the dynamics and in which members adopt the evolutionarily stable trait value for that equilibrium size. I compare the stability of the population dynamics under the following two assumptions about the dependence of trait values on population size: (i) trait values do not change from that at the equilibrium size, and (ii) trait values change so as to be evolutionarily stable for the current size. In a range of examples, I show that adaptive behaviour tends to destabilise population dynamics in the sense that stability under assumption (ii) implies stability under assumption (i). In other words, the region of parameter space for which there is instability under an adaptive response contains the region of instability under no response. Various equivalent general criteria for this to hold are given.

Translated title of the contribution | The Effect of Adaptive Behaviour on the Stability of Population Dynamics |
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Original language | English |

Pages (from-to) | 25 - 36 |

Journal | Annales Zoologici Fennici |

Volume | 38 (1) |

Publication status | Published - 2001 |

### Bibliographical note

Publisher: Finnish Zoological Botanical Publisihing BoardOther identifier: IDS number 423PC

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## Cite this

McNamara, JM. (2001). The Effect of Adaptive Behaviour on the Stability of Population Dynamics.

*Annales Zoologici Fennici*,*38 (1)*, 25 - 36.