The Genetical Theory of Natural Selection by Ronald A. Fisher

Review of the second revised edition

Why is this book important? Because it is still referred to as the basis for the population statistics on which rests the reigning scientific theory of evolution. As recently as 2010 Fisher was Richard Dawkins’ choice for the greatest biologist since Darwin: "He therefore could be said to have provided researchers in biology and medicine with their most important research tools, as well as with the modern version of biology’s central theorem.”

But a quick skim through the contents page raises a disquieting issue. Roughly midway come single-chapter treatments of sexual selection and mimicry. Before those two possibly-token chapters come six chapters on genetic theory, after them come five chapters on eugenics. Given that this book was published in the heyday of eugenics in 1930 the writing of it can be suspected of being intended primarily to provide eugenics with a more solid basis. Of “The theory to be here developed” Fisher writes, “neither its logical cogency, nor its importance to sociological theory, seem to have been ever widely grasped, and apart from a few ephemeral papers of my own, and a brief discussion in Major Darwin’s recent book ‘The Need for Eugenic Reform,’ it might be said to have been totally neglected.” At the end of this review I give some further quotes to this effect.

Given that, I think the reasoning presented in this book deserves a critical examination that, judging from how hard it is to find, I doubt it’s getting. No copy was available on interlibrary loan, and readers advised against purchase of the available reprint of the original edition. I bought a copy of the 1958 revised Dover edition to review. Not that I’m the one to do it, I have no training in or talent for statistics. All I can do is cast a generally skeptical eye on the assumptions made and see if they pass muster.

What I wanted to know is: does this book succeed in making genetic mutation the basis for our primary theory of evolution, as it is said to do? I concluded, no.

For both Charles Darwin and Fisher the mechanism of evolution consisted of a process of selection acting on a continuously-replenished supply of variation. Darwin, from his familiarity with livestock and pigeon breeders, appears to me to have seen variation as a continuous supply of equally viable creatures. With changes to the environment, different variations would become optimal; their higher rates of survival would then lead to those variations being represented more frequently in future generations. Darwin supposed that such a mechanism of adaptation to changing environments could in time incorporate sufficient variation as to amount to a new species. Selection among variations for those coming already more viable in a changed environment he referred to as natural selection.

Darwin’s attempt to extend this theory to account for the origin of all life from a single founder species revealed a fatal flaw in his conception of variation. If all variations needed to define modern species were already implicit in the founder, ready to appear and be selected as new environments appeared, his theory amounted to that of Robert Chambers’ in “Vestiges of the Natural History of Creation,” published in 1844, that specifications of all living creatures had been embedded by God in the original embryo, ready for changed environments to elicit them.

As Darwinism passed it on, the problem of accounting for evolution lay in coming up with a plausible origin for the variation needed for selection to work on. Fisher’s answer began with proposing a new source of variation. “That an independent study of Natural Selection is now possible is principally due to the great advance which our generation has seen in the science of genetics.” His new source of variation was the various kinds of damage that such large molecules as our chromosomes are subject to, including damage resulting from the processes involved in their reproduction.

Having redefined variation he now had to redefine the corresponding process of selection. Its role changes. To be accepted as the primary mechanism of all evolution it now had to turn a source of damage into a mechanism for the creation of new genes, ultimately all those required to turn blueprints for bacteria into blueprints for elephants, say.

I regret having to compose such a long introduction, but it allows me to point out the challenge Fisher faced. He had to come up with a new process that could eliminate all the harm resulting from that damage, and make the most of any benefit it brought.

Taking the possibility of benefit first he, or his predecessors, came up with idea that, given enough damage, simply by logic and the laws of chance some will inevitably be an improvement. Take as an example a blueprint for a two-stroke gasoline engine; damage leading to a shaving of metal from the engine case could make the engine more efficient in use. Eventually, Fisher, supposed, such changes could amount to those required to turn a blueprint for a two stroke engine into that for a four-stroke engine. To these improvements conjured up by logic and the laws of chance was given the name “beneficial mutations.” If such mutations did exist then Fisher supposes the creatures bearing them could be regarded as the kinds of viable alternative variants that Darwin’s form of natural selection could be applied to, leading to the evolution of new species and, if a sufficiently promising stream of beneficial mutations was forthcoming, to the evolution of new orders, even kingdoms. Perhaps for this inclusion of Darwin’s process in it, Fisher gave his form of selection the same name, natural selection, Darwin gave to his.

All that remains now is to eliminate the much greater incidence of harm stemming from random damage. Here, if my analysis is correct, Fisher’s statistics contain a critical flaw. He does supply formulae tracking the slow increase and decrease in fitness contributed by individual beneficial and harmful mutations, that he jiggles to suggest that the contribution of a beneficial mutation will be greater and lead to a net increase of fitness and greater representation of the beneficial gene. “If the mutant gene were opposed, even by a very minute selective disadvantage, the change would be brought to a standstill at a very early stage.” He doesn’t explain why this process would be faster than how a mutant gene being favored would lead to it gaining in frequency. This seems a case of him wishing it so.

But he nowhere presents a formula assessing the contributions of all the consequences of the damage, with variables representing the much greater number of mutations contributing harm. As Fisher admits, among harmful and beneficial mutations, harmful mutations will in every generation be in the great majority. Posting plausible numbers in those variables in such a formula would, I believe, indicate a rapid decline in fitness. And we would be without a genetic theory of evolution.

Let’s consider other aspects of this work. To introduce the concept of beneficial mutations he surmises “In addition to the defective mutations, which by their conspicuousness attract attention, we may reasonably suppose that other less obvious mutations are occurring which, at least in certain surroundings, or in certain combinations, might prove themselves to be beneficial.” He doesn’t explain why beneficial genes will attract less attention; to me that sounds like an excuse for why they had not been observed. And his justification for supposing them to exist is “we may reasonably suppose” so. Are they likely to ever be observed? “it would require an enormous number of experimental animals, and extremely precise methods of experimentation, to demonstrate so small an effect experimentally.” In other words, no. We are to take on trust the genetic basis for evolution as Fisher conceived it.

How efficient is the process of selection? Several times Fisher gives a value of 1%. “…it will be readily understood that if we speak of a selective advantage of one per cent., with the meaning that animals bearing one gene have an expectation of offspring only one per cent. greater than those bearing its allelomorph, the selective advantage in question will be a very minute one.” “If we confine attention to mutations possessing a selective advantage of just 1 per cent…” Despite that small value Fisher claimed it was enough to reverse the preponderance of a “great majority” of harmful mutations into a preponderance of occasional beneficial mutations.

Throughout, a reader might suppose from Fisher’s remarks that an increase in fitness is the invariable consequence of damage to genes. “Against the action of Natural Selection in constantly increasing the fitness of every organization…” “In order to consider in outline the consequences to the organic world of the progressive increase of fitness of each species of organism…..” In the following example (page 39 in my copy) he even likens his mechanism for evolution, which appears to decrease entropy, to the increase in entropy otherwise prevailing throughout the universe. “It will be noticed that the fundamental theorem proved above bears come remarkable resemblances to the second law of thermodynamics. Both are properties of populations, or aggregates, true irrespective of the nature of the units which compose them; both are statistical laws; each requires the constant increase of a measurable quantity, in the one case the entropy of a physical system and in the other the fitness.. . of a biological population.“

Again illustrating his assumption of the success of his theory, he says of a variable he includes in that theorem that he refers to as “proved above,” “Any group of individuals selected as bearers of a particular gene, and consequently the genes themselves, will have rates of increase of fitness which may differ from the average. The excess over the average of any such selected group will be represented by a, and similarly the average of effect upon m of introducing the gene in question will be represented by [alpha].” Any equation including this factor can be only as convincing as this definition.

Why did Fisher assume genetics was bound to be the key to evolution? “It has often been remarked, and truly,” he wrote, “that without mutation evolutionary progress, whatever direction it may take, will ultimately come to a standstill for lack of further possible improvements.” If now his theory fails to confirm that, the value a lifetime since of investment in the modern synthesis is thrown into question.

Concerning Fisher's well-known predilection for eugenics: “Numerous of investigations… have shown… that the birth rate is much higher in the poorer than in the more prosperous classes, and that this difference has been increasing in recent generations… The type of man selected, as an ancestor of future generations, is he whose probability is least of winning admiration, or rewards, for useful services to the society to which he belongs…. The composition of existing populations, graded both in social ability and in effective fertility, presents special, and much graver difficulties, which only a people capable of deliberate and intentional policy could hope to overcome.”

Below, microdata:

Evolution for the Humanities
The Genetical Theory of Natural Selection evolution

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