Speaking Volumes: R. A. Fisher's The Genetical Theory of Natural Selection

December 12, 1997

I was standing in the Cambridge genetics department office in 1958 when R. A. Fisher's secretary handed him his pre-publication copies of the Dover edition of The Genetical Theory of Natural Selection. "Hmph," said Fisher at his first sight of the pattern on the cover. "It looks like a book by Hogben." Lancelot Hogben, author of Mathematics for the Million and Science for the Citizen, was a scourge of Fisher and his statistical methods.

A few weeks later I asked him: "Why is it that in herd animals where dominant males monopolise the mating, natural selection has not adjusted the sex ratio accordingly?" He replied: "Go and read The Genetical Theory." So I bought a copy, at 15 shillings. Thus began my study of one of the great scientific books of the century.

It has borne the brunt of my studies over the past 40 years, and still there are surprises. I have only recently discovered that Fisher's treatment of natural selection and the sex ratio, which is celebrated as the prime example in evolutionary biology of a game-theoretic argument, can be traced to the first edition of Darwin's The Descent of Man. Fisher had the second edition, from which Darwin had removed the argument, but not before it had been taken up by continental writers, whence it came to Fisher's attention.

The first passage I marked with my undergraduate pen is in the preface: "No practical biologist interested in sexual reproduction would be led to work out the detailed consequences experienced by organisms having three or more sexes; yet what else should he do if he wishes to understand why the sexes are, in fact, always two?" Nowadays, however, I would mark the opening sentence: "Natural selection is not evolution." Next, my pen was at work in chapter 2, "The fundamental theorem of natural selection". "Why?" makes its plaintive appearance in the margin in my youthful hand. What trouble this theorem caused in its first 60 years. Half the world's mathematical geneticists burnt their fingers on it, and only those who expressed a cautious optimism that one day we might understand it have escaped. It seems so simple now that it has been fathomed.

At the end of the chapter I marked, in red, a passage new to the 1958 edition, where Fisher stresses the theme of the book, that it is individual, not group, selection that drives evolution, the theme G. C. Williams, W.D. Hamilton, R. Dawkins and others have turned into the received wisdom of evolutionary biology.

The discussion on natural selection and the sex ratio comes in chapter 6, and my attempts to understand it led to my first paper in mathematical genetics in 1960 when, with W.F. Bodmer, I created the mathematics that Fisher had so inconsiderately left out. Little did we then know that we had been beaten to it by 75 years by C. Dusing of Jena, whose book was in the departmental library all along.

At its original publication J. B. S. Haldane thought The Genetical Theory "brilliant", Sewall Wright thought it "certain to take rank as one of the major contributions to the theory of evolution" and the Russian mathematician A. M. Kolmogorov referred to it as "das wundervolle Buch" for its invention of stochastic diffusion theory. For me, it is the book that for 40 years has proved an inexhaustible store of intellectual riches, linking my world to Darwin and On The Origin of Species through Fisher and Leonard Darwin, Charles's fourth son and Fisher's mentor, to whom the book is dedicated, "In gratitude for the encouragement given to the author during the last 15 years".

A.W.F. Edwards is reader in biometry, University of Cambridge.

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