UNIFYING GENETIC AND GAME-THEORETIC MODELS OF KIN SELECTION FOR CONTINUOUS TRAITS

A framework is presented for unifying single locus genetic and game th eoretic models of continuous traits under frequency-dependent selectio n when there are interactions among relatives. This framework serves t wo purposes. First, it is used to determine how ''games between relati ves'' must be modeled to be genetically valid. There are two commonly employed phenotypic approaches used, in this setting, and we demonstra te that, although some of their predictions are always genetically val id, others are invalid in general, and this is true for both haploid a sexual and diploid sexual organisms. In particular, we show that both approaches obtain the correct equilibrium and convergence stability co nditions, but neither obtains the correct condition for evolutionary s tability. Unlike earlier results for discrete trait matrix games (Hine s & Maynard Smith, 1979), there is no simple correspondence between ph enotypic and genetic predictions, and we provide two examples to illus trate this point. It is possible however, to obtain these earlier resu lts within the present setting by restricting attention to a particula r class of fitness functions. These results demonstrate; that, even wh en selection is weak, phenotypic models can fail if fitness is frequen cy-dependent. The second purpose is to determine when population mean inclusive fitness effect provides an adaptive topography in games betw een relatives. Our results show that the fitness function must have a special form for this to be true, and this form differs between haploi d and diploid organisms. (C) 1998 Academic Press.