A dynamic game-theoretic model of parental care

We present a model in which members of a mated pair decide whether to care for their offspring or desert them. There is a breeding season of finite length during which it is possible to produce and raise several batches of offspring. On deserting its offspring, an individual can search for a new mate. The probability of finding a mate depends on the number of individuals of each sex that are searching, which in turn depends upon the previous care and desertion decisions of all population members. We find the evolutionarily stable pattern of care over the breeding season. The feedback between behaviour and mating opportunity can result in a pattern of stable oscillations between different forms of care over the breeding season. Oscillations can also arise because the best thing for an individual to do at a particular time in the season depends on future behaviour of all population members. In the baseline model, a pair splits up after a breeding attempt, even if they both care for the offspring. In a version of the model in which a pair stays together if they both care, the feedback between behaviour and mating opportunity can lead to more than one evolutionarily stable form of care.