At a Royal Society conference some time after his 80th birthday John Maynard Smith rose to rebuke a speaker who had alleged that “neo-Darwinian orthodoxy” said something or other. “It doesn’t, and I know this because I am the voice of neo-Darwinian orthodoxy,” he claimed — and it was perfectly true. He deserved his position as the grand old man of evolutionary biology, not just because of the important work he had done in his prime, but because he never for a moment lost his love of, nor his interest in, it. At scientific conferences Maynard Smith spent as little time as possible over the formalities, and as much time as possible interrogating younger scientists in the bar about the details of their work and their theories. He had a hand in the discovery or shaping of some of the most influential theories of late-20th-century biology.

Maynard Smith was also one of the last of the naturally communist members of the British upper classes: educated at Eton and Trinity College, Cambridge, where he took a degree in engineering, he was a disciple of the formidable communist J. B. S. Haldane and did not finally break with the party until after the Soviet invasion of Hungary in 1956. As a young man he had dreamt of being an aviator, but he was almost blind without his glasses. Instead he worked as an aircraft engineer after graduating in 1922, until he left the RAF in 1947 to become a biologist.

His interest in evolution and biology had first been awakened by Olaf Stapledon’s extraordinary work, Last and First Men, which he read in Minehead public library as a child: curiously, this was the same copy of the book as turned the young Arthur C. Clarke’s imagination in the direction of science fiction when he borrowed it from the library.

In 1947 he finally switched from engineering to biology. His attitude to biology remained, in some respects, that of an outsider, though he rapidly became the beloved disciple of Haldane. Nearly 40 years after Haldane’s death, he wept when excavating the letter that Haldane had written to say that he was dying, and his fund of anecdotes about the great man remained apparently inexhaustible.

At the start of his life as a biologist he was interested in applying engineering analysis to apparently biological problems: his first published paper dealt with the evolutions of flight. Because he understood flight deeply as an engineer, he was able to point out that primitive animals were shaped to be naturally stable in flight, like a paper dart, while more advanced ones, such as birds, are unstable like the modern stealth fighter, and so need constant adjustment even to glide. These unstable shapes are much more manoeuvrable than simple gliders, but they require more sophisticated brains to control. Thus, he argued, we can watch the evolution of more complex nervous systems, even though they leave no fossils, by looking at the complexities of the bodies they control.

He was one of the very first people to demonstrate that sex might be bad for the parents’ health when he was able to prolong the life of fruit flies by destroying their ovaries. It was in the 1960s, though, that he made his biggest contributions to the complex of modern ideas that Richard Dawkins would popularise and synthesise in The Selfish Gene in the next decade.

One of Haldane’s obiter dicta, delivered in Bloomsbury pubs in the Fifties, was that a man would lay down his life for two brothers, four nephews or eight cousins. This was the insight at the heart of the theory of kin selection, but Haldane never carried it further, or developed it mathematically. That was done quite independently by W. D. Hamilton, a student at University College London in Maynard Smith’s time there, but not one who could interest anyone in his ideas. In later life Maynard Smith would often lament his failure to spot Hamilton and nurture the man he once called “the only bloody genius we’ve got”. Hamilton’s extension of kin selection into a general mechanism explaining the spread of altruistic and spiteful behaviour among related populations is one of the insights at the heart of modern sociobiology.

But in 1963 Maynard Smith was one of the referees for the long paper that Hamilton sent to the Journal of Theoretical Biology setting out his mathematical treatment of the problem. Before that paper could be published, Maynard Smith had coined the phrase “kin selection” and used it in a letter to Nature. Hamilton’s deep faith in his own powers was not widely shared at that stage of his career, and he never entirely forgave Maynard Smith for what he considered a betrayal. Maynard Smith, for his part, was deeply and frequently contrite over the affair. He lost no opportunity to give credit to Hamilton for independent discovery of the idea, and for his mathematical formalism, but continued to maintain that the basic insight was Haldane’s, and free to anyone who had heard him.

In 1964 Maynard Smith moved to Brighton, to establish a biology department at the University of Sussex, where he was Dean of the School of Biological Sciences until 1985. Here he was hugely successful, and rapidly built the department into a leading centre of biological research. In parallel with this, he worked closely with the strange and eventually suicidal American George Price to discover how behaviour patterns might emerge during the life of a species by applying game theory to evolutionary biology. With his characteristic gift for giving catchy names to ideas whose profundity and importance was not immediately obvious, Maynard Smith came up with the idea of the “evolutionarily stable strategy”, a pattern of behaviour which, once established in a population, cannot be driven out by any other, since animals that pursue a different strategy will suffer in their interactions with the majority. It was this achievement that eventually won him the Crafoord Prize, biology’s equivalent of the Nobel Prize, in 1999.

His gift for reconciling the sums and the stories of biology by providing mathematically rigorous accounts of obviously important processes was also brought out in his work on sex. “The cost of meiosis”, another of his phrases, concentrated attention on the question of why so few complex animals clone, when it seems clearly to the advantage of their genes to do so, since cloning ensures that all genes are passed on to the next generation, while sexual reproduction throws half of them away.

In the 1980s, catastrophe struck his department at Brighton. Though he worked with few graduate students, preferring to think on his own, Maynard Smith was an excellent teacher, and a farsighted planner of this department’s future. But he was hopeless at academic politics and never attended committee meetings in London if he could avoid it. So when Margaret Thatcher’s funding cuts hit higher education, Sussex was almost completely undefended, and his department was decimated. He himself continued to think and work productively throughout the 1990s, describing new problems with undiminished astringent clarity and jest. In 2001 he was awarded the Kyoto Prize, Japan’s most eminent private award for lifetime achievement.

He married Sheila, another biologist, in 1942 and stayed famously married and devoted to her for the next 50 years. The couple had three children.

John Maynard Smith, FRS, biologist, was born on January 6, 1920. He died on April 19, 2004, aged 84.