A general ploidy model for the evolution of helping in viscous populations

There is growing interest in understanding how kin selection drives the evolution of social behaviours in viscous populations. A key result, that has inspired much work on this topic, is the exact cancellation of the genetic relatedness and kin competition effects of dispersal in the simplest models of population viscosity, such that a reduction in the rate of dispersal neither promotes nor inhibits the evolution of helping behaviour. This theoretical result has been demonstrated for populations characterised by haploid, diploid and haplodiploid modes of inheritance. Here we develop a model of general ploidy that recovers these three scenarios as special cases and allows examination of scenarios that have not been considered previously. Specifically, we: clarify the importance of the implicit assumption of monandry in previous models; show that the cancellation result obtains in some models of ploidy but not in others; and reveal that the cancellation result obtains for different reasons in different models of ploidy. The cancellation result therefore hinges upon a population's genetic system as well as its demography.