The parental investment conflict in continuous time: St. Peterʹs fish as an example

The parental investment conflict considers the question of how much each sex should invest in each brood, thereby characterizing different animal species. Each species usually adopts a certain parental care pattern: female-care only, male-care only, biparental care, or even no parental care at all. The differences in care patterns are usually explained by the different costs and benefits arising from caring for the offspring in each animal species. This paper proposes a game-theoretical model to the parental investment conflict based on the parental behavior of St. Peterʹs fish. St. Peterʹs fish exhibit different parental care patterns, allowing the examination of the factors which determine the particular behavior in each mating. We present a continuous time, two-stage, asymmetric game, with two types of players: male and female. According to the modelʹs results, three parental care patterns: male-only care, female-only care and biparental care, are possible evolutionarily stable strategies. The evolutionarily stable parental care pattern in a certain mating depends on a parentʹs increase in mortality due to parental care, and on its advantage from biparental care. These results may explain the different parental care patterns observed in a variety of animal species, including those found in the St. Peterʹs fish.