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# W. D. Hamilton

William Donald Hamilton, F.R.S. (1 August 1936 — 7 March 2000) was a British evolutionary biologist, considered one of the greatest evolutionary theorists of the 20th century.[1] From 1984 to his death in 2000, he was the Royal Society Research Professor at Oxford University. Hamilton became famous for his theoretical work expounding a rigorous genetic basis for the existence of kin selection. This insight was a key part of the development of a gene-centric view of evolution, and he can therefore be seen as one of the forerunners of the discipline of sociobiology popularized by Edward Osborne Wilson. Hamilton also published important work on sex ratios and the evolution of sex.

## 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 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 while 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 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 he 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 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 getting only a 2:1 degree.

### Hamilton's rule

Main article: Hamilton's rule

Hamilton having various ideas and problems enrolled on an MSc course in human demographics at the London School of Economics (LSE), under Norman Carrier who secured for him various grants. Later when work became more mathematical and then genetical, he had his supervision transferred to John Hajnal of the LSE and Cedric Smith of University College London (UCL).

Both 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. Thus became Hamilton's rule. Briefly, the rule is that a costly action should be performed if:

$C < R \times B$

Where C is the cost in fitness to the actor, R the genetic relatedness between the actor and the recipient and B is the fitness benefit to the recipient. Fitness costs and benefits are measured in fecundity. His two 1964 papers entitled The Genetical Evolution of Social Behavior are now widely referenced.

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. To date, however, there have been no empirical studies that have calculated values for R, B, and C to determine if Hamilton's rule is ever satisfied in nature; as such, even after more than 40 years, the theory remains unproven, though predictions based upon the theory are largely supported.

A large part of the discussion related to the evolution of eusociality in insects of the order Hymenoptera (ants, bees and wasps) based on their unusual haplodiploid sex-determination system. This system means that females are more closely related to their sisters than to their own (potential) offspring. Thus, Hamilton reasoned, a "costly action" would be better spent in helping to raise their sisters, rather than reproducing themselves.

### Extraordinary sex ratios

Between 1964 and 1978 Hamilton was a 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. Hamilton had been introduced to the idea and formulated its solution in 1960 when he had been assigned to help Fisher's pupil A.W.F. Edwards test the Fisherian sex ratio hypothesis. Hamilton combined his extensive knowledge of natural history with deep insight into the problem, opening up a whole new area of research.

The paper was also 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 peer 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 committed suicide 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 1966 he married Christine Friess and they were to have three daughters, Helen, Ruth and Rowena. 26 years 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

Hamilton was an early proponent of the Red Queen theory of the evolution of sex,[2] first proposed by Leigh Van Valen. This was named for a character in Lewis Carroll's Through the Looking Glass, who is continuously running but never actually travels any distance:

"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!" (Carroll, pp. 46)

This theory hypothesizes that sex evolved because new and unfamiliar combinations of genes could be presented to parasites, preventing the parasite from preying on that organism—species with sex were able to continuously "run away" from their parasites. Likewise, parasites were able to evolve mechanisms to get around the organism's new set of genes, thus perpetuating an endless race.

### 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 HIV

During the 1990s Hamilton became increasingly convinced by the controversial argument that the origin of the HIV virus 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 from a cerebral haemorrhage.

### Postscript

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

His body was interred in Wytham Woods. He however had written an essay on My intended burial and why in which he wrote:[3]

 “ 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.

### Social evolution

The field of social evolution, of which Hamilton's rule has central importance, is broadly defined as being the study of the evolution of social behaviours, i.e. those that impact on the fitness of individuals other than the actor. Social behaviours can be categorized according to the fitness consequences they entail for the actor and recipient. A behaviour that increases the direct fitness of the actor is mutually beneficial if the recipient also benefits, and selfish if the recipient suffers a loss. A behaviour that reduces the fitness of the actor is altruistic if the recipient benefits, and spiteful if the recipient suffers a loss. This classification was first proposed by Hamilton in 1964.

Through his collaboration with Hugh N. Comins and Robert M. May on evolutionarily stable dispersal strategies, Hamilton acquired an Erdős number of 5.

## Awards

• 1978 Foreign Honorary Member of American Academy of Arts and Sciences
• 1980 Fellow of the Royal Society of London
• 1982 Newcomb Cleveland Prize of the American Association for the Advancement of Science
• 1988 Darwin Medal of the Royal Society of London
• 1989 Scientific Medal of the Linnean Society
• 1991 Frink Medal of Zoological Society of London
• 1992/3 Wander Prize of the University of Bern
• 1993 Crafoord Prize of the Royal Swedish Academy of Sciences
• 1993 Kyoto Prize of the Inamori Foundation
• 1995 Frissen Prize of the Fyssen Foundation

## 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. 2007 Nature's oracle: an intellectual biography of evolutionist W. D. Hamilton. Oxford University Press. See http://www.oup.com/uk/catalogue/?ci=9780198607274

## Works

### Collected papers

Hamilton started to publish his collected papers starting in 1996, along the lines of Fisher's collected papers, with short essays giving each paper context. He died after the preparation of the second volume, so the essays for the third volume come from his coauthors.

• Hamilton, W.D. (1996) Narrow Roads of Gene Land vol. 1: Evolution of Social Behaviour Oxford University Press,Oxford. ISBN 0-7167-4530-5
• Hamilton, W.D. (2002) Narrow Roads of Gene Land vol. 2: Evolution of Sex Oxford University Press,Oxford. ISBN 0-19-850336-9
• Hamilton, W.D. (2005) Narrow roads of Gene Land, vol. 3: Last Words (with essays by coauthors, ed. M. Ridley). Oxford University Press, Oxford. ISBN 0-19-856690-5

### Significant papers

• Hamilton, W.D. (1964). The genetical evolution of social behaviour I and II. — Journal of Theoretical Biology 7: 1-16 and 17-52. pubmed I pubmed II
• Hamilton, W.D. (1967). Extraordinary sex ratios. Science 156: 477-488. pubmed JSTOR
• Hamilton, W.D. (1971). Geometry for the selfish herd. Journal of Theoretical Biology. 31: 295-311.
• Hamilton, W.D. (1975). Innate social aptitudes of man: an approach from evolutionary genetics. in R. Fox (ed.), Biosocial Anthropology, Malaby Press, London, 133-53.
• Axelrod, R. and W.D. Hamilton (1981) The evolution of co-operation Science 211: 1390-6 Pubmed, JSTOR

### Other references

• Edwards, A.W.F. (1998), Notes and Comments. Natural selection and sex ratio: Fisher's sources. American Naturalist 151: 564-569
• Fisher, R.A. (1930). The Genetical Theory of Natural Selection. Clarendon Press, Oxford.
• Ford E.B. (1945) New Naturalist 1: Butterflies. Collins: London.
• Maynard Smith, J. and G.R. Price (1973) The logic of animal conflict. Nature 146: 15—18.
• Dawkins, R. (1989), The Selfish Gene, 2nd ed. Oxford University Press.
• Madsen, E.A., Tunney, R., Fieldman, G., Plotkin, H.C., Dunbar, R.I.M., Richardson, J.M., & McFarland, D. (2006) Kinship and altruism: A cross-cultural experimental study. British Journal of Psychology [1]

## Cited references

1. ^ Obituary by Richard Dawkins - The Independent - 10 March 2000
2. ^ The Red Queen Hypothesis at Indiana University. Quote: "W.D. Hamilton and John Jaenike were among the earliest pioneers of the idea."
3. ^ Hamilton, W.D. (2000) My intended burial and why, Ethology Ecology and Evolution 12 111-122 PDF

## Other references

• Obituaries and reminiscences
• Royal Society citation
• Truth and Science: Bill Hamiltonís legacy
• Centro Itinerante de Educação Ambiental e Científica Bill Hamilton (The Bill Hamilton Itinerant Centre for Environmental and Scientific Education) (in Portuguese)
• Non-mathematical excerpts from Hamilton 1964
• "If you have a simple idea, state it simply" a 1996 interview with Hamilton

### Game Theory

• W.D. Hamilton's work in game theory

### AIDS

• Polio vaccines and AIDS
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