Altruism evolves when inclusive fitness benefit exceeds cost
rb > c
r = coefficient of relatedness | b = benefit to recipient | c = cost to actor
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Generation
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Altruist frequency
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Selfish frequency
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rb − c
Hamilton's Rule (1964): An altruistic allele spreads if rb > c.
r = coefficient of relatedness (sibling=0.5, cousin=0.125).
In kin groups, altruists preferentially help related individuals → the allele indirectly promotes copies of itself. Inclusive fitness = direct fitness + indirect fitness (effects on relatives × r).
Examples: eusociality in Hymenoptera (r=0.75 for sisters), alarm calls in ground squirrels, worker bees sacrificing for queen's offspring.
Selfish strategies invade altruist populations only when rb < c.