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Hamilton's Rule

Predict when an allele for a costly social behaviour spreads by relocating the accounting from organism to gene: it is favoured whenever rB > C — the relatedness-weighted benefit to relatives exceeds the cost to the actor.

Core Idea

Hamilton's rule (1964) is the condition under which an allele encoding a costly social behaviour is favoured by selection: an altruistic act imposing fitness cost C on the actor and delivering benefit B to a recipient spreads when rB > C, where r is the coefficient of relatedness — the excess probability that the recipient carries the same allele by descent. It resolves the paradox of altruism by shifting the unit of accounting from organism to allele: the organism is altruistic, but the allele, in the gene's-eye accounting, is selfish.

Scope of Application

Hamilton's rule lives across the social-evolution subfields of evolutionary biology, ranging over every sexually reproducing system where relatedness can be defined.

  • Behavioural ecology — cooperation, alarm calls, food-sharing, allocare, helping-at-the-nest, with relatedness-targeted helping the testable signature.
  • Evolution of eusociality — worker sterility in ants, bees, wasps; the haplodiploid r = 0.75 sister asymmetry is Hamilton's headline application.
  • Conflict theory — parent-offspring conflict, sibling rivalry, intragenomic conflict, each the same inequality with different r.
  • Microbial social evolution — secreted public goods and cheating, with r from clonal patch structure approaching one.
  • Non-kin cooperation theory — reciprocity and enforcement framed as departures requiring non-r mechanisms.

Clarity

Hamilton's rule resolves the sharpest standing paradox in Darwinian theory — how selection could favour a behaviour that lowers the actor's own reproduction — through a change in the unit of accounting: the allele gains net copies whenever rB exceeds C. It converts "the evolution of altruism" from a verbal puzzle into a quantitative inequality whose three terms can be measured in the field, and it organises the whole space of social behaviour, with r made a measurable quantity rather than an intuition.

Manages Complexity

Deciding whether a social-behaviour allele will spread is, literally, a forbidding population-genetic bookkeeping problem. Hamilton's rule collapses it onto three measurable scalars and one inequality — r, B, C, with rB > C the spread condition — so the analyst predicts cooperation's fate by estimating three quantities rather than re-deriving allele dynamics. It further organises social behaviour into a four-cell table (altruism, mutualism, selfishness, spite), and makes special cases single substitutions: haplodiploidy reads off worker-sterility accessibility; cooperation at r ≈ 0 flags a non-kin mechanism.

Abstract Reasoning

The rule licenses a diagnostic move (reading targeted helping as a signature of relatedness, and cooperation among near-strangers as a pointer to a non-kin mechanism), an interventionist move (raising r or shifting B and C to move the outcome, as in kin-removal experiments), a boundary-drawing move (separating kin-selected from non-kin regimes, and the haplodiploid sterility regime), and predictive/order-of-events moves (forecasting which systems evolve cooperation and building parent-offspring conflict into the r arithmetic).

Knowledge Transfer

Within evolutionary biology Hamilton's rule transfers as mechanism across every sexually reproducing system with definable relatedness, because the cargo is one inequality grounded in allele-frequency accounting; the three scalars, four-cell table, and near-stranger diagnostic carry without translation across behavioural ecology, eusociality, conflict theory, and microbial cooperation — different content domains of one substrate. Beyond replicators-under-selection the named rule does not travel: cultural or computational analogies strain the genetics, since there is no allele or identity-by-descent. What genuinely recurs is the deeper move — multilevel accounting of a replicator's success weighted by copy-probability — captured by the parent Price-equation decomposition, of which Hamilton's rule is one special case.

Relationships to Other Abstractions

Local relationship map for Hamilton's RuleParents appear above the current abstraction, mutual partners to the right, and children below. Node labels state whether each abstraction is prime or domain-specific; colors identify relation types.Hamilton's RuleDOMAINPrime abstraction: Threshold — is part ofThresholdPRIMEDomain-specific abstraction: Inclusive Fitness — presupposesInclusiveFitnessDOMAINDomain-specific abstraction: Kin selection — is part ofKin selectionDOMAIN

Current abstraction Hamilton's Rule Domain-specific

Parents (2) — more general patterns this builds on

  • Hamilton's Rule presupposes Inclusive Fitness Domain-specific

    Hamilton’s rule presupposes the inclusive-fitness quantity whose marginal change its inequality tests.

  • Hamilton's Rule is part of Threshold Prime

    Hamilton’s rule contains a threshold boundary at rB equals C between favored and disfavored alleles.

Children (1) — more specific cases that build on this

  • Kin selection Domain-specific is part of Hamilton's Rule

    Kin selection contains Hamilton’s rule as its operational spread criterion.

Hierarchy paths (2) — routes to 2 parentless roots

Neighborhood in Abstraction Space

Hamilton's Rule sits in a crowded region of the domain-specific corpus (18th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.

Family — Population Genetics & Kin Selection (10 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-07-12