The influence of multiple inseminations and multiple foundresses on social evolution

The breeding biology of a population determines the way in which individuals are distributed within and between progeny groups and, thus, affects the genetic variation within and between these groups. The breeding biology of any organism can be characterized by the distribution of the numbers of mates of females, the apportionment of paternity among males, the distribution of the numbers of females reproducing in common nests, and the apportionment of total fecundity within a nest among founding females. In addition, the possibility of genetic correlations among mates or among founding females is an important consideration and will be addressed in a later paper. The influence of the breeding biology on social evolution was evaluated by deriving the necessary conditions for the spread of genes for social behaviors and the rate of spread of these genes for populations with different breeding biologies. The first step in this derivation is to demonstrate that selection for genes determining social behavior can be represented as the covariance between gene frequency and relative fitness. Secondly, it is shown that this covariance can be formally partitioned into within and between group components. Thirdly, each covariance component is shown to be equivalent to the product of a genetic variance and a coefficient of linear regression of relative fitness on gene frequency. Lastly, specific models for the genotype fitnesses and breeding biologies are assumed and the necessary conditions for the increase in the frequency of altruistic alleles are obtained. The theory illustrates that variation in the numbers of mates per female has less of an effect on the evolution of social behaviors than does variation in the numbers of reproductive females per nest. In addition, it points out that the harmonic mean number of mates per female or of females per nest is a more useful summary statistic for characterizing populations with respect to the expected degree of evolved sociality than is the arithmetic mean.