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# W. D. Hamilton

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Professor William Donald "Bill" Hamilton, F.R.S. (1 August 19367 March 2000) was a British evolutionary biologist. Hamilton became famous for his theoretical work expounding a rigorous genetic basis for the existence of kin selection. This insight formed part of the Williams Revolution and he can therefore be seen as one of the forerunners of the discipline of sociobiology founded by Edward Osborne Wilson. Hamilton also published important work on sex ratios and the evolution of sex.

 Contents

## Biography

### Early life

Hamilton was born in 1936 in Cairo, Egypt, the second eldest of six children. His father, A. M. Hamilton was a New Zealand-born engineer, and his mother, B. M. Hamilton was a medical doctor.

The Hamilton family moved to Kent when Bill was young and during the Second World War he was evacuated to Edinburgh. He had an interest in natural history from an early age and would spend 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 the School House. As a 12-year old he was seriously injured whilst playing with explosives his father had left over from when he made hand grenades for the Home Guard during the Second World War, an accident that probably would have killed him had his mother not been medically qualified. A A thoracotomy in King’s College Hospital saved his life, but the explosion left him with amputated fingers on his right hand and scarring on his body — he took six months to recover.

Hamilton stayed on an extra term at Tonbridge in order to complete the Cambridge entrance examinations , and then travelled in France. He then completed two years of national service. As an undergraduate at St. John's College, he was uninspired by the fact that there "many biologists hardly seemed to believe in evolution". Nevertheless, he came across Ronald Fisher's book The Genetical Theory of Natural Selection; Fisher lacked standing at Cambridge as was viewed only as a statistician. Hamilton wrote on a postcard to his sister Mary on the day he found the book excited by its darker chapters on eugenics. In earlier chapters, Fisher provided a mathematical basis for the genetics of evolution. Working through the stodgy prose, Hamilton later blamed Fisher's book for only getting 2:1 degree.

### Hamilton's rule

He did his doctorate jointly enrolled into University College London and the London School of Economics on the principle that would later become known as Hamilton's rule of inclusive fitness. His two 1964 papers on this subject are now universally referenced. Briefly, the rule is that a costly action should be performed if;

$C < R \times B$

Where C is the cost to the actor, R the genetic relatedness between the actor and the recipient and B is the benefit to the recipient. Costs and benefits are measured in fecundity.

The proof and discussion of its consequences however involved heavy mathematics, and was passed over by two reviewers. The third, John Maynard Smith did not completely understand it either, but recognised its significance; this passing over would later lead to friction between Hamilton and Maynard Smith, Hamilton feeling that Maynard Smith had held his work back to claim credit for the idea himself. The paper was printed in the relatively obscure Journal of Theoretical Biology, and when first published was largely ignored. The significance of it gradually increased, to the point where they are routinely cited in biology books.

A large part of the discussion related to the evolution of eusociality in insects of the orders Homoptera (aphids), Isoptera (termites) and Hymenoptera (bees and wasps) based on their unusual haplodiploid sex-determination system, that meant that "super sisters" were more related to their sisters than to their own offspring and so ought to help their mother produce more sisters rather than breed themselves. However, there are later issues with this application that make it less clear-cut, such as the mothers mating with multiple males reduces relatedness between sisters.

### Extraordinary sex ratios

Between 1964 and 1978 he was lecturer at Imperial College London. Whilst there he published a paper in Science on "extraordinary sex ratios". Fisher (1930) had proposed a model as to why "ordinary" sex ratios were nearly always 1:1 (but see Edwards 1998), and likewise extraordinary sex ratios, particularly in wasps, needed explanations. This opened up a whole new area of research.

The paper was notable for introducing the concept of the "unbeatable strategy", which John Maynard Smith and George R. Price were to develop into the evolutionarily stable strategy (ESS), a concept in game theory not limited to evolutionary biology. Price had originally come to Hamilton after deriving the Price equation, and thus rederiving Hamilton's rule. Maynard Smith later reviewed one of Price's papers, and drew inspiration from it. The paper was not published but Maynard Smith offered to make Price a co-author of his ESS paper, which helped to improve relations between the men. Price took his own life in poverty in 1975, and Hamilton and Maynard Smith were among the few present at the funeral.

Hamilton was regarded as a poor lecturer. This shortcoming would not affect the popularity of his work, however, as it was popularised by Richard Dawkins in Dawkins' 1976 book The Selfish Gene.

In 1976 he married Christine Friess and they were to have three daughters, Helen, Ruth and Rowena. Later they amicably separated.

Hamilton was a visiting professor at Harvard University and later spent nine months with the Royal Society's and the Royal Geographic Society's Xavantina-Cachimbo Expedition as a visiting professor at the University of São Paulo.

From 1978 Hamilton was Professor of Evolutionary Biology at the University of Michigan. Simultaneously, he was elected a Foreign Honorary Member of American Academy of Arts and Sciences. His arrival sparked protests and sit-ins from students who did not like his association with sociobiology. There he worked with the economist Robert Axelrod on the prisoner's dilemma.

### Chasing the Red Queen

He also published the Red Queen theory of the evolution of sex. This was named for a character in Lewis Carroll's Through the Looking Glass.

"Well, in our country," said Alice, still panting a little, "you'd generally get to somewhere else -- if you ran very fast for a long time, as we've been doing."
"A slow sort of country!" said the Queen. "Now, here, you see, it takes all the running you can do, to keep in the same place. If you want to get somewhere else, you must run at least twice as fast as that!" text

Hamilton hypothesised that sex had evolved because new combinations of genes could be presented to parasites - organisms with sex were able to continuously run away from their parasites.

### Back in Britain

In 1980 he was elected a Fellow of the Royal Society, and in 1984 he was invited by Richard Southwood to be the Royal Society Research Professor at New College, Oxford, Department of Zoology, where he remained until his death.

From 1994 Hamilton found companionship with Maria Luisa Bozzi, an Italian science journalist and author.

### On the Origin of AIDS

During the 1990s Hamilton became increasingly convinced by the controversial argument that the origin of the AIDS epidemic lay in oral polio vaccines (the OPV AIDS hypothesis) in Africa during the 1950s. Letters by Hamilton to Science were rejected by the journal, amid accusations that the medical establishment were ranging against the OPV hypothesis.

To find indirect evidence of the OPV hypothesis by assessing natural levels of SIV in primates, he and two others ventured on a field trip to the war-torn Democratic Republic of the Congo, where he contracted malaria. He was rushed home and spent six weeks in hospital before dying.

### Postscript

A secular memorial service (he was an atheist) was held at the Chapel of New College, Oxford on Saturday 1st July 2000, organised by Richard Dawkins.

His body was interred in Wytham Woods, according to his request:

"- I will leave a sum in my last will for my body to be carried to Brazil and to these forests. It will be laid out in a manner secure against the possums and the vultures just as we make our chickens secure; and this great Coprophanaeus beetle will bury me. They will enter, will bury, will live on my flesh; and in the shape of their children and mine, I will escape death. No worm for me nor sordid fly, I will buzz in the dusk like a huge bumble bee. I will be many, buzz even as a swarm of motorbikes, be borne, body by flying body out into the Brazilian wilderness beneath the stars, lofted under those beautiful and un-fused elytra which we will all hold over our backs. So finally I too will shine like a violet ground beetle under a stone."

The second volume of his collected papers was published in 2002.

## Conclusion

Hamilton is remembered as one of the greatest evolutionary theorists of the twentieth century. The other contender for the title is Ronald Fisher, and Hamilton would humbly defer to him. The concepts mentioned above are only the most important of his contributions, and many more may come to light.

## Biographies

• Alan Grafen has written a biographical memoir for the Royal Society. See http://users.ox.ac.uk/~grafen/cv/WDH_memoir.pdf
• A book is also in press: Segerstråle, U. 2005 Nature's oracle: an intellectual biography of evolutionist W. D. Hamilton. Oxford University Press.

## Works

### Collected Papers

• Hamilton, W.D. (1996) Narrow Roads in Gene Land vol. 1 Oxford University Press,Oxford. ISBN 0716745305
• Hamilton, W.D. (2002) Narrow Roads in Gene Land vol. 2 Oxford University Press,Oxford. ISBN 0198503369