Toward evolutionary graphs with two sexes: a kin selection analysis of a sex allocation problem

Evolutionary graphs are used to model the effects of spatial and social structure in social evolutionary problems (e.g. evolutionary games). Recent work has highlighted the fact that evolution on graphs can be understood using kin selection theory. This paper shows how one can use kin selection to study evolutionary graphs inhabited by a diploid sexual organism by means of a simple example. Specifically, we study the well-known sex allocation problem of how best to divide a fixed amount of effort between the production of sons on the one hand and the production of daughters on the other. Like many previous studies, we identify equal investment in sons and daughters as the only phenotype favoured by selection. Our analysis also highlights the advantages and disadvantages of applying kin selection to the study of evolutionary graphs.