An Allelocentric Analysis of Hamiltonʹs Rule for Overlapping Generations

Although comprehensive population genetic analyses of Hamiltonʹs rule are available for discrete generations, existing treatments of overlapping generations only cover rare mutations. Here the general case including partial dominance using an allelocentric method is analysed. The assumptions are weak selection, fitness changes in individual lifetimes negligibly small, random mating, outbreeding, and additivity of fitness effects. Costs to helpers and benefits to recipients are defined directly in terms of their life-history effects (on age-specific survivorship and fecundity) weighted by the relevant partial selection pressures. From this it follows that survivorship benefits should be allocated between relatives according to their reproductive values, in agreement with Charlesworth & Charnov (1981, J. theor. Biol.88 , 103-119) and Taylor (1990, Am. Nat.135, 95-106).