Definition
Hamilton's Rule is the mathematical condition under which natural selection favors the evolution of altruistic behavior. Named for the biologist W. D. Hamilton, who formalized it in 1964, the rule states that an altruistic act will be favored by selection when rB > C — where r is the genetic relatedness between the actor and the beneficiary, B is the reproductive benefit to the beneficiary, and C is the reproductive cost to the actor.
The rule dissolves one of the most puzzling problems in evolutionary biology: how can natural selection, which operates by differential survival and reproduction, ever produce behavior that reduces an individual's own reproductive success? The answer is that the unit of selection is the gene, not the individual. Genes that promote altruism toward relatives can spread if those relatives carry the same genes by common descent. A bee that sacrifices itself to defend the hive may not reproduce, but its genes persist in the many relatives it protected. As J. B. S. Haldane is said to have quipped, he would give his life for two brothers or eight cousins — because at 50% and 12.5% relatedness respectively, those sacrifices would exactly preserve his genetic contribution to the next generation.
This framework — called kin selection — does not require that organisms consciously calculate relatedness or fitness. It requires only that mechanisms for recognizing and preferentially helping relatives evolve, and that the rB > C inequality holds often enough for those mechanisms to be favored. In nature, kin recognition operates through spatial proximity (relatives tend to be nearby), familiar olfactory or acoustic signatures, and physical resemblance.
Why it matters
How it works
The inequality rB > C
Each variable in Hamilton's Rule carries specific meaning. C (cost) is the reduction in the actor's expected reproductive success from performing the altruistic act. B (benefit) is the increase in the beneficiary's expected reproductive success. r (relatedness) is the probability that a gene in the actor is also present in the beneficiary because they share a common ancestor — the coefficient of genetic relatedness.
For full siblings in a diploid species, r = 0.5. For half-siblings, r = 0.25. For first cousins, r = 0.125. For identical twins, r = 1.0. The rule predicts that altruism toward identical twins can be favored even when costs greatly exceed benefits, while altruism toward distant cousins requires a large benefit-to-cost ratio to be evolutionarily stable.
The rule can be derived rigorously from population genetics as a condition on whether an allele that promotes altruistic behavior will increase in frequency. It is not a hypothesis about mechanisms but a theorem about the conditions under which altruism-promoting genes can spread — whatever the proximate mechanism.
Inclusive fitness
Hamilton's Rule is the central equation of inclusive fitness theory. Inclusive fitness is the concept that an organism's evolutionary "success" should be measured not only by its own reproductive output but also by its contribution to the reproduction of relatives, weighted by their degree of relatedness. An organism maximizes its inclusive fitness by behaving in ways that promote the propagation of its own genes, whether those genes reside in its own body or in the bodies of its relatives.
This reframing resolves the apparent paradox of sterile worker castes in eusocial insects. Worker bees do not reproduce, yet they engage in behaviors that maximize their inclusive fitness by raising the queen's offspring — their sisters — with extraordinary efficiency. Inclusive fitness can be higher for a worker bee than it would be if the same bee tried to reproduce independently, given the structural advantages of a collaborative colony with a fertile queen.
Where it goes next
Hamilton's Rule opened a research program that has transformed evolutionary biology. It underpins the modern understanding of eusociality, parent-offspring conflict, sex ratio theory, and genomic imprinting. Extensions of the theory address cooperation among non-kin — explaining how cooperation can evolve even between unrelated individuals through reciprocal altruism and other mechanisms that Hamilton's original framework set in sharp relief by contrast.
For social scientists and philosophers, the rule offers a biological grounding for some aspects of human social behavior while also highlighting the limits of evolutionary explanation: humans routinely cooperate with strangers, build institutions, and override kin preferences in ways that far exceed what Hamilton's Rule predicts for a typical mammal. Understanding where the rule applies and where human social evolution has departed from it is one of the central questions of evolutionary social science.