Evolution of eusociality in diploid species

Haplodiploid species are naturally biased by their genetic structure toward the evolution of sterile worker castes, as shown by W. D. Hamilton (1964. J. Theoret. Biol., 7, 1–16, 17–52). Diploid species do not have this intrinsic genetic bias toward eusociality. Nonetheless, true sociality has evolved in the diploid ancestors of the modern termites, and varying degrees of quasisociality are not uncommon in diploid species, including mammals. A genetic bias toward investment in relatives rather than offspring can arise in a diploid species as a result of inbreeding. The consequences of several regular incestuous breeding systems are analyzed in detail. It is shown that, under certain conditions, there is a natural bias toward an alternation of inbred and outbred generations. As this alternation proceeds, the genetic bias toward eusociality rapidly approaches an asymptotic value of 4(1 + 2f₀)/3(1 + 3f₀), where f₀ is the average coefficient of relationship for the outbreeding pairs. For f₀ close to zero, the genetic bias toward eusociality is close to 1.33, which is even larger than the genetic bias of 1.25 in haplodiploid species. Under other conditions there may be repeated incestuous matings between successive outbreeding generations. In this case the bias toward eusociality can be as large as 2.