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Professor William Hamilton, who has died aged 63, was the most influential evolutionary biologist of his generation.
Bill Hamilton's paper on "the genetical evolution of social behaviour" (1964) became the most cited paper in all science. He was responsible almost single-handedly for a revolution in the study of animal behaviour. He remained in frontline research until his death, caused by an infection caught while on a research expedition in the Congo.
The full story of how Hamilton came to write his classic paper only emerged in his autobiographical sketches published in 1995. As a shy and lonely graduate student dividing his time between the London School of Economics and University College London, Hamilton was ignored at one institution and mistrusted at the other.
He later wrote of his time at University College: "I never had a desk there nor was ever invited to give any presentation to explain my work or my occasional presence to others. Most of the time I was extremely lonely. Sometimes I came to dislike my bed-sitting room so much that I would go to Waterloo Station, where I continued reading or trying to write out a [mathematical] model sitting on the benches among waiting passengers in the main hall."
The question that obsessed Hamilton, if none of his peers, was how altruism could evolve as an instinct. The prevailing mood in evolutionary biology saw animal behaviour as always devoted to the "good of the species".
Hamilton, who was influenced by the writings of the great Cambridge statistician and biologist, Sir Ronald Fisher, thought this made no sense, because an animal's closest competitor was often a member of its own species, so evolution should produce selfish, not altruistic individuals. Yet it plainly did not. As Darwin had been worried to observe, the extreme co-operation seen in the social insects - termites, bees and ants - seemed hard to explain.
The answer that Hamilton came up with was that animals might be selected to have altruistic instincts towards relatives, whose genes they share, because that would cause the spread of those instincts. So altruism will evolve in rabbit warrens if on average the rabbits are sufficiently closely related.
This was expressed in what is now known as Hamilton's rule, encapsulated in the formula k>1/r. In other words altruism is favoured when k is greater than 1 divided by r - where r is the relatedness between individuals and k is the ratio of gain to loss of the behaviour.
He illustrated his theory, which became known as kin selection or inclusive fitness, with a study of the social Hymenoptera - ants, bees and wasps - whose unusual genetics put them in the strange position of being more closely related to their sisters than their daughters and who have delegated reproduction to each colony's queen.
Hamilton's paper was rejected out of hand by Nature magazine. The mathematics was dense and the prose denser. It was eventually published in two parts in 1964 in the comparatively obscure Journal of Theoretical Biology. It was the first clear statement of what has since become known variously as the "gene's eye view" of evolution, the "selfish gene" school, or "sociobiology" - the theory that sees individuals as vehicles for competing genes.
Edward O. Wilson, who was later to launch a fierce controversy that splits academia to this day with his book Sociobiology (1975), remembers reading the Hamilton paper on a train from Boston to Florida and spending two days trying to spot what was wrong with its reasoning. By the time the train reached Miami he had given up the struggle and become a convert to Hamilton's theory.
William Donald Hamilton was born on August 1 1936 and went to Tonbridge School. He devoted his spare time to collecting insects in the countryside. He read Zoology at Cambridge, then after National Service and his lonely spell doing the work on altruism in London, made the first of many expeditions to Brazil to teach and to study bees and wasps. There he fell in love with the rich insect fauna.
On his return he got a job as a lecturer at Imperial College and published a series of important papers on genes and behaviour, including one on "extraordinary sex ratios". This foreshadowed a now fashionable theory known as intragenomic conflict, which is used to explain many details of the newly emerging human genome.
He also befriended a self-taught American, George Price, an ardent atheist who became an equally ardent biblical scholar. In between, Price managed to do brilliant work to improve and expand the mathematics of Hamilton's theory, while railing against its implications.
They collaborated on a pair of important papers. When Price eventually committed suicide with nail scissors in an abandoned building near Euston Square at Christmas 1974 having given all his money to the homeless, the police contacted Hamilton, whose name they found among his few effects.
In 1977 Hamilton moved to the University of Michigan, where he experienced at first hand the controversy stirred among radical students by opponents to the sociobiological theories he had spawned, enduring protests and sit-ins. In Michigan he published two immensely influential theories. One, with the political scientist Robert Axelrod, was on how co-operative strategies succeed in the prisoner's dilemma game - this became known as the "tit-for-tat" debate. The other was on the evolution of sexual reproduction as a means of combating parasites - known as the Red Queen theory. In 1984 he returned to take up a Royal Society Research Professorship at Oxford, where was based until his death.
Hamilton was a distinctive figure with his heavy shock of white hair, stooped figure, low monotone voice and unworldly air. This did not make him an inspiring lecturer, but he was fortunate that his ideas were taken up by more lively teachers, notably John Maynard Smith, Richard Dawkins, Edward Wilson and Robert Trivers, all of whom dated their conversion to gene-centred thinking to their first encounters with Hamilton's work. Gene-centred thinking has come to dominate the study of both evolution and behaviour in animals, though it is repeatedly repelled with force when it tries to invade the territory of psychology and sociology.
Hamilton himself disliked the late 20th century's obsessive preference for nurture explanations over nature explanations, and was an enthusiast for evolutionary psychology, though his own work remained focused largely on the animal kingdom. Not for him the well trodden path through administration into professorships and knighthoods. He remained an active researcher, never happier than when collecting a little-known burying beetle or fig wasp deep in the rain forest. He was oblivious of risk. His last expedition, to the war-torn Congo, was to test the theory that the origin of the human Aids epidemic lay with the polio vaccine.
The lonely student eventually gained great renown, though it never changed him. He was awarded numerous prizes by academies all over the world, including the Darwin Medal of the Royal Society and the Crafoord Prize from the Swedish Academy of Sciences.
He married, in 1967, Christine Friess. They had three daughters.