Kin Selection: Hamilton's Rule and the Evolution of Altruism

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rB/C = 1.33 — altruism favored

With relatedness r = 0.5, benefit B = 8, cost C = 3, Hamilton's rule is satisfied (0.5 × 8 > 3): altruistic behavior is favored by kin selection.

Formula

rB > C (Hamilton's rule for altruism)
ΔW = -C + r × B × N (inclusive fitness change)
r = (probability of IBD allele sharing)

The Paradox of Altruism

Altruism — helping others at a cost to oneself — seems to contradict natural selection. If selfish individuals outcompete altruists, how can genes for self-sacrifice persist? W.D. Hamilton resolved this paradox in 1964 with a simple but profound insight: natural selection acts on genes, not individuals. A gene for altruism can spread if it causes its bearer to help relatives who carry copies of the same gene.

Hamilton's Rule: rB > C

The elegant inequality rB > C captures the entire logic of kin selection. The relatedness coefficient r measures the probability that actor and recipient share a gene by common descent. Full siblings share r = 0.5; half-siblings r = 0.25; cousins r = 0.125. The rule says: sacrifice yourself only if the benefit B to relatives, weighted by their relatedness r, exceeds the cost C to you.

Inclusive Fitness in Action

Kin selection explains a vast array of biological phenomena. Worker bees sacrifice their reproduction to help their mother queen — haplodiploid genetics makes sisters more related (r = 0.75) than mothers to daughters (r = 0.5). Ground squirrels give alarm calls that endanger themselves but warn nearby kin. Even plants distribute resources preferentially to closely related neighbors.

The Reach of Hamilton's Insight

Hamilton's framework extends beyond obvious altruism. Parent-offspring conflict (Trivers 1974) arises because parents and offspring have different optimal investment levels (r = 0.5, not 1.0). Sibling rivalry reflects competition among relatives with r = 0.5. Genomic imprinting — where genes are expressed differently depending on parent of origin — creates an intragenomic battleground over resource allocation. Kin selection theory pervades modern evolutionary biology.

FAQ

What is Hamilton's rule?

Hamilton's rule states that an altruistic behavior will spread if rB > C, where r is the genetic relatedness between actor and recipient, B is the fitness benefit to the recipient, and C is the fitness cost to the actor. The rule shows that genes for altruism can increase in frequency if the behavior helps enough copies of those same genes in relatives.

What is inclusive fitness?

Inclusive fitness is an individual's total fitness: direct fitness (personal reproduction) plus indirect fitness (the additional reproduction of relatives caused by the individual's behavior, weighted by relatedness). This concept, introduced by W.D. Hamilton in 1964, revolutionized biology by explaining apparent altruism as genetic self-interest at the gene level.

Does kin selection explain eusociality?

Kin selection is the leading explanation for eusociality (reproductive division of labor), particularly in haplodiploid insects where sisters share 75% of genes. However, the debate continues — some researchers (notably E.O. Wilson and Martin Nowak) argue that group selection and ecological factors are equally important. Most evolutionary biologists still consider kin selection the primary driver.

Can kin selection lead to spite?

Yes. Hamilton's framework predicts that negative relatedness (r < 0, meaning less related than average) can favor spiteful behavior — harming others at a cost to yourself. This is rare in nature but may occur in structured populations where competitors are less related than random individuals. Some bacterial toxin systems may represent spiteful behavior.

Sources

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