Inclusive fitness in finite populations–effects of heterogeneity and synergy

I review recent results concerning the relationship between the inclusive fitness (IF) effect and standard measures of allele fitness in a finite-population, with attention to the effect of heterogeneity in population structure and nonadditive fitness effects. In both cases, existing theoretical work is somewhat technical and I try to provide a more transparent account. In a heterogeneous population it is known that inclusive fitness will generally fail to incorporate the effects of selection on the distribution of alleles among states unless a reproductive-value weighting is used. But even given that, recent work shows that under certain updating rules, the IF effect can fail to be equivalent to standard measures such as fixation probability. In terms of synergistic fitness effects, I review the result that in the finite population model, the IF effect can be calculated using only "additive" relatedness coefficients so that computational difficulties found in the infinite-population model do not arise. In my own work, there is an interaction here in that my 2012 work on synergy with Maciejewski made an assumption about inclusive fitness that my 2014 work on heterogeneity with Tarnita showed to be wrong. I include (Appendix C) a corrected argument for the 2012 result.