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.