The evolution of territory size—some ESS models

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We present two classes of models for the evolution of territory size. Both are frequency dependent (employing the concept of the evolutionary stable strategy or ESS), and are based on finite population sizes and continuous strategy sets. A territorial strategy is defined in the first class by the size of territory an individual defends if it is one of the individuals successful in obtaining a territory in a patch of resources when others are excluded. The ESS for territory size may be spitefully large when the potential fecundity of individuals is low, but as fecundity (or population numbers) increases, the ESS decreases towards the size which maximizes individual reproductive success. When the costs of defending a territory are a function not only of area but also of the number of competitors (excludeds plus holders) against which the area is defended, then the individuals excluded from resources (excludeds) are likely to lower the ESS more markedly than the individuals who have acquired territories (holders). In the second class of models, all individuals gain access to resources, but the amount an individual acquires depends on its defensive effort strategy relative to the defensive effort of other competitors. Here, in contrast, the ESS for defensive effort increases with increasing potential fecundity. When the second class of model is extended to include phenotypic variation in individual success (at a given defensive effort), variance in phenotypic ESSs diminishes as the number of competitors increases.

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    Present address: Department of Zoology, University of Liverpool, Liverpool L69 3BX, England.

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