Dynamic kin selection

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Abstract
When an animal performs an action that has consequences both for its own fitness and that of a relative, Hamilton's rule tells us that the action will be favoured by natural selection if br > c, where c is the cost to the animal that performs the action (the `actor'), b is the benefit to its relative (the `recipient'), and r is the relatedness of the two individuals. We consider a period of time ending at T during which the actor makes a series of decisions. We show that the strategy predicted by Hamilton's rule maximizes a particular form of the fitness function defined at T. Furthermore, each decision taken during the interval can be characterized by a form of Hamilton's rule in which b depends not only on the state of the recipient but also on the state of the actor; similarly c depends on the states of both animals. We illustrate this with two schematic examples based on the actor controlling the delivery of food to itself and a relative.

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