1.5 Inclusive fitness and kin selection

If genes are what spread, then helping a relative — who carries copies of your genes — can be a way of propagating those genes indirectly. This insight, due to W. D. Hamilton, solved one of biology's deepest puzzles: the existence of self-sacrifice.

Inclusive fitness

Inclusive fitness is an organism's total genetic contribution to the next generation: its own offspring (direct fitness) plus its effect on the reproduction of relatives, weighted by relatedness (indirect fitness). Natural selection maximizes inclusive fitness, not mere personal survival.

Hamilton's rule

The condition for an altruistic act to be favored is captured in one inequality, Hamilton's rule: an act spreads when $rB > C$, where $r$ is the coefficient of relatedness between actor and recipient, $B$ is the reproductive benefit to the recipient, and $C$ is the cost to the actor. The closer the relative and the larger the benefit relative to cost, the more selection favors helping.

Coefficients of relatedness

For sexually reproducing organisms, $r = 1/2$ for parent and child or for full siblings, $r = 1/4$ for grandparent and grandchild or for aunt and niece, and $r = 1/8$ for first cousins. J. B. S. Haldane joked that he would lay down his life for two brothers or eight cousins — a precise application of the math.

A grounding example

Belding's ground squirrels give alarm calls when a predator approaches, drawing dangerous attention to the caller. The behavior looks suicidal until you notice who calls: females, who stay near their birthplace surrounded by relatives, call far more than dispersing males. The alarm protects kin who share the caller's genes — exactly what Hamilton's rule predicts.