Population Genetics & Kin Selection

Abstractions about the mathematical machinery of evolutionary genetics — allele-frequency equilibria (Hardy-Weinberg, Haldane's sieve), the relatedness-weighted accounting of social and sexual selection (Hamilton's rule, inclusive fitness, kin selection, Fisher's principle), and exact identities partitioning selection (Price equation, Fisher's fundamental theorem).

10 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• Fisher's Fundamental Theorem of Natural Selection — Pin the instantaneous speed at which selection improves a population's mean fitness to a single estimable quantity — the additive genetic variance in fitness — and nothing more.
• Fisher's Principle (Sex-Ratio Equilibrium) — Explains the near-1:1 sex ratio of most species not as a group optimum but as the frequency-dependent equilibrium where, whenever one sex is rarer, parents biasing offspring toward it gain more grandchildren until the rarity is erased.
• Haldane's Rule — Predict which sex of a species hybrid breaks down first: when one F1 sex is absent, sterile, or inviable, it is almost always the heterogametic one (XY or ZW), because its single sex chromosome cannot mask accumulated incompatibilities.
• Haldane's Sieve — Explain why new beneficial mutations that are dominant fix far more often than recessive ones — because while rare an allele sits almost only in heterozygotes, so selection sees a dominant from its first copy but is blind to a masked recessive, which usually drifts to loss before homozygotes form.
• 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.
• Hardy-Weinberg Principle — Fix the exactly computable genotype baseline (p², 2pq, q²) a diploid population would reach under no evolutionary forces, so that any observed deviation becomes diagnostic evidence of which force — selection, drift, inbreeding, or technical error — is acting.
• Inclusive Fitness — Redefine the quantity natural selection maximizes as an organism's own reproduction plus its effect on relatives' reproduction, each relative weighted by the coefficient of relatedness r, so a costly helping behaviour is favoured whenever rB exceeds C.
• Kin selection — A costly gene can still spread when it makes its carrier help relatives who likely share that gene, as long as the relatedness-weighted benefit to them (rB) outweighs the cost to the actor (C).
• Price Equation
• Wallace Effect — The evolutionary process (reinforcement) by which natural selection actively strengthens prezygotic reproductive isolation at secondary contact, favouring any heritable trait that reduces cross-population mating whenever the hybrids between the diverging populations are less fit.