William Donald Hamilton FRS (1 August 1936 – 7 March 2000) was a British evolutionary biologist, recognised as one of the most significant evolutionary theorists of the 20th century. Hamilton became known for his theoretical work expounding a rigorous genetic basis for the existence of altruism, an insight that was a key part of the development of the gene-centered view of evolution. He is considered one of the forerunners of sociobiology. Hamilton published important work on sex ratios and the evolution of sex. From 1984 to his death in 2000, he was a Royal Society Research Professor at Oxford University.

Richard Dawkins has written that Hamilton was "the greatest Darwinian of my lifetime".

Hamilton was born in 1936 in Cairo, Egypt, the second of seven children. His parents were from New Zealand; his father A.M. Hamilton was an engineer, and his mother Bettina Matraves Hamilton (nee Collier) was a physician. Two sisters qualified in medicine: Mary Bliss, who developed the alternating pressure mattress for the prevention of bedsores, and Janet who became a general practitioner. Another sister Margaret became a pasture scientist and brother an engineer.

The Hamilton family settled in Kent. During the Second World War, Hamilton was evacuated to Edinburgh. He became interested in natural history at an early age and spent his spare time collecting butterflies and other insects. In 1946, he discovered E.B. Ford's New Naturalist book Butterflies, which introduced him to the principles of evolution by natural selection, genetics, and population genetics.

He was educated at Tonbridge School, where he was in Smythe House. As a 12-year-old, he was seriously injured while playing with explosives that his father had, which were left over from making hand grenades for the Home Guard during World War II. Hamilton had to have a thoracotomy and parts of fingers on his right hand amputated in King's College Hospital to save his life. He was left with scarring and needed six months to recover.

Before going to the University of Cambridge, he travelled in France and completed two years of national service. As an undergraduate at St. John's College in Biology, he was uninspired by the "many biologists [who] hardly seemed to believe in evolution".

Hamilton enrolled in an MSc course in demography at the London School of Economics (LSE), under Norman Carrier, who helped secure grants for his studies. Later, when his work became more mathematical and genetical, he had his supervision transferred to John Hajnal of the LSE and Cedric Smith of University College London (UCL).

Both Ronald Fisher and J. B. S. Haldane had seen a problem in how organisms could increase the fitness of their own genes by aiding their close relatives, but not recognised its significance or properly formulated it. Hamilton worked through several examples, and eventually realised that the number that kept falling out of his calculations was Sewall Wright's coefficient of relationship. This became Hamilton's rule: in each behaviour-evoking situation, the individual assesses his neighbour's fitness against his own according to the coefficients of relationship appropriate to the situation. Algebraically, the rule posits that a costly action should be performed if: