Cite this article as: David M. Ramsey, A large population parental care game: Polymorphisms and feedback between patterns of care and the operational sex ratio, Journal of Theoretical Biology, doi:10.1016Biology, doi:10. /j.jtbi.2010 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
A LARGE POPULATION PARENTAL CARE GAME: POLYMORPHISMS AND FEEDBACK BETWEEN PATTERNS OF CARE AND THE OPERATIONAL SEX RATIO DAVID M. RAMSEYAbstract. This article presents a game theoretic model of parental care which models the feedback between patterns of care and the operational sex ratio. It is assumed here that males can be in one of two states: searching for a mate or breeding (including caring for their offspring).Females can be in one of three states: receptive (searching), non-receptive or breeding. However, these sets of states can be adapted to the physiology of a particular species. The length of time an individual remains in the breeding state depends on the level of care an individual gives.When in the searching state, individuals find partners at a rate dependent on the proportion of members of the opposite sex searching. These rates are defined to satisfy the Fisher condition that the total number of offspring of males equals the total number of offspring of females.The operational sex ratio is not defined exogenously, but can be derived from the adult sex ratio and the pattern of parental care. Pure strategy profiles and so called single sex stable polymorphisms, in which behaviour is varied within one sex, are derived analytically. The difference between mixed evolutionarily stable strategies and stable polymorphisms within this framework is highlighted. The effect of various physiological and demographic parameters on patterns of care are considered.