The Genetical Evolution of Social Behaviour
Self-sacrifice can evolve — if it saves enough copies of the gene in your relatives.
Natural selection rewards out-reproducing your neighbours — so why do so many animals give up their own chance at offspring to help someone else?
One equation for kindness
A young biologist named William Hamilton answered with a single inequality: r·B > C. An animal should help a relative when the benefit B to that relative, multiplied by how closely related they are (r), outweighs the cost C to itself. The trick is to stop thinking about the animal and start thinking about its genes. You share half your genes with a brother, an eighth with a first cousin — so a gene that makes you help them is, in part, helping copies of itself.
Seen that way, self-sacrifice isn't a flaw in evolution's logic. It's a prediction of it — as long as the help is aimed at kin, and the numbers work out.
The puzzle that worried Darwin
Darwin himself flagged “one special difficulty” he feared might be fatal to his whole theory: the sterile workers of ant and bee colonies. They never reproduce, yet they are beautifully built to serve the hive. How could survival of the fittest produce a creature with no offspring at all? For a century the puzzle sat unsolved.
In 1964, while still a PhD student in London and working largely alone, Hamilton published a dense two-part paper that cracked it. The maths was hard and at first overlooked, but it quietly reorganised all of evolutionary biology. (Years earlier the geneticist J. B. S. Haldane had hinted at the same idea with a famous quip — that he would lay down his life for two brothers or eight cousins — but Hamilton turned the joke into a theory.)
Why it mattered
It explained behaviours that had looked impossible: alarm calls that put the caller in danger, animals that babysit their siblings instead of breeding, the whole architecture of insect societies. More deeply, it handed biology a new lens — the gene's-eye view — in which a body is partly a vehicle for getting genes into the next generation, through any relative who happens to carry them. A decade later that idea reached the public as Richard Dawkins's “selfish gene”.
Counting copies, not bodies
Think of your genes as a message you want to survive. You can carry the message yourself — or you can rescue other people who happen to be carrying the same message. A brother carries half of it; a first cousin, an eighth. Hamilton's rule is just careful accounting: spend effort saving relatives only when the copies you rescue (their benefit, times how much they share with you) outnumber the copies you risk losing (your cost). Save two brothers, or eight cousins, and the books exactly balance.
Before and after
It sits directly downstream of Darwin (1859) and Mendel's genetics, and right alongside the game theory of John Nash — indeed John Maynard Smith, who named “kin selection” the same year, soon fused the two into evolutionary game theory. Hamilton's accounting recast Darwin's struggle for existence as a struggle among genes, and set the agenda for the study of cooperation that runs all the way to today's work on microbes and human society.
A genetical mathematical model is described which allows for interactions between relatives on one another's fitness. Making use of Wright's Coefficient of Relationship as the measure of the proportion of replica genes in a relative, a quantity is found which incorporates the maximizing property of Darwinian fitness, named “inclusive fitness”. Species following the model should tend to evolve behaviour such that each organism appears to be attempting to maximize its inclusive fitness.
Inclusive fitness may be imagined as the personal fitness which an individual actually expresses in its production of adult offspring as it becomes after it has been first stripped and then augmented in a certain way.