Permissible Spite: Kin Selection, Demography, and the Inverse Hamiltonian Equation

Olga Semenova 

This article revisits Hamilton’s rule by proposing an inverted formulation to evaluate the evolutionary permissibility of spiteful behavior within kin-based populations. We formalize a reverse Hamiltonian equation and apply replicator dynamics to investigate the demographic and genetic conditions under which within group aggression may become evolutionarily stable. The model shows that in low-fertility populations, even close kin may be treated as expendable, while high fertility expands the range of altruistic stability. These findings highlight a previously overlooked symmetry between altruism and aggression and reveal how reproductive demography critically influences the logic of inclusive fitness. The proposed framework provides new analytical tools for understanding kin-directed conflict and the shifting boundaries of social norms under demographic constraints.