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On Fisher's "Nature of Inheritance"

Natural selection is commonly associated with Darwin’s theory of evolution, but it has rarely received the kind of individual attention R.A. Fisher thinks it deserves. The first sentence of the book illustrates this point exactly, “Natural selection is not evolution.” The overall goal of his book, The Genetical Theory of Natural Selection, is to treat natural selection on its own terms, which is not to diminish natural selection’s importance in the theory of evolution. For present purposes, I will restrict the following analysis to arguments presented in Chapter 1, “The Nature of Inheritance.” Chapter 1 tries to abandon blending theory because of peculiarly large mutation rates that it requires, set in its place the mechanism of particulate inheritance (Mendelism) since it requires mutation to a far lesser degree, and begins to formulate a quantitative model or framework that synthesizes the Mendelian theory and the biometrical approach to the study of heredity.

The blending theory concludes that offspring is simply the fusion of the characteristics of two parents. Inheritance of these characteristics will tend to produce uniformity in successive generations. In essence, the blending theory would recognize that every generation will halve heritable variance. Over time, the blending theory will be unable to explain variability except through some mechanism of drastic change. The mechanism of change that the blending theory sees fit to explain heritable variance is mutation. Since there is so much evidence of variance within many species, cases of mutation would have to be much more prevalent than not. Fisher says, “To maintain stationary variance fresh mutations must be available in each generation to supply the half of the variance so lost. If variability persists, as Darwin rightly inferred, causes of new variability must continually be at work. Almost every individual of each generation must be a mutant… and moreover must be a mutant in many different characters.” According to Fisher, the blending theory would have to say that variance is due to the predominance of mutation than on some other mechanism of change.

Darwin had accepted the blending theory since that was the accepted theory of his time; however, some of his work seems to suggest that he was not satisfied with the blending theory as an explanation for heritable variance. In a quotation that Fisher cites, Darwin seems to abandon the blending theory because of its notion of “true fusion” in favor of a “sort of mixture” that incorporates not only heritable characteristics of the offspring’s parents but also the distant ancestors of the offspring. Other reasons for Darwin’s dissatisfaction with the blending theory abounds. First, Darwin did not seem to accept that reversion was an independent principle. On the contrary, Darwin wanted to show how reversion was merely a consequence of inheritance. Second, the variability of domesticated animals presented a problem to Darwin. He did not believe that the food supply could have increased so much to account for the greater variability of anciently domesticated species. Finally, Darwin seems to deny that fluctuating environmental conditions could not account for the causes of variability. Therefore, although Darwin seemed to recognize problems having to do with the blending theory, he did not present a theory to counteract the odd consequences of the blending theory.

A theory that seems to counteract the strange consequences of the blending theory is what Fisher terms particulate inheritance. The theory of particulate inheritance seems to be consistent with Mendel’s theory. One virtue of the theory of particulate inheritance is the ability to reduce the importance of mutations. An indicator of particulate inheritance is “the admitted non-inheritance of scars and mutilations [which] would have prepared him to conceive of the hereditary nature of an organism as something none the less definite because possibly represented inexactly by its visible appearance” (Fisher 1958, p. 7f). Particulate inheritance demonstrates a clear segregation of single and multiple pairs of genes. Fisher explains:

Those organisms (homozygotes) which received like genes, in any pair of corresponding loci, from their two parents, would necessarily hand on genes of this kind to all of their offspring alike; whereas those (heterozygotes) which received from their two parents genes of different kinds, and would be, in respect of the locus in question, crossbred, would have, in respect of any particular offspring, an equal chance of transmitting either kind. The heterozygote when mated to either kind of homozygote would produce both heterozygotes and homozygotes in a ratio which, with increasing numbers of offspring, must tend to equality, while if two heterzygotes were mated, each homozygous form would be expected to appear in a quarter of the offspring, the remaining half being heterozygous. (Fisher 1958, p. 8)

The theory of particulate inheritance and Mendel’s theory, in particular, seems to demonstrate the fact of dominance – why an offspring’s characteristics is not an intermediate of the two parent’s characteristics. Mendel’s work also points toward the fact of linkage, whereby the “pair of genes received from the same parent are more often than not handed on together to the same child.” Thus, the theory of particulate inheritance concludes that the offspring may resemble either one’s parents or some distant relative.

As the above seems to suggest, particulate inheritance theory differs in many respects from the blending theory. First, particulate inheritance has no tendency for the variability to diminish. According to the blending theory, variability would diminish, and the only way to explain variability would revert to a very high mutation rate. If particulate inheritance is correct, then the mutation rate is significantly lower than what the blending theory requires. Second, mutation would be merely a “heritable novelty,” not the mechanism of natural selection as the blending theory seems to suggest. Fisher acknowledges Weismann’s suggestion that the process of mutation acquires a kind of momentum. Thinking of mutation as a kind of momentum is useful for two reasons: (1) enables an assumed minimal mutation in an advantageous direction to be increased by further mutations and (2) explains the continuous decrease of useless organs. Finally, and most importantly, particulate inheritance rejects the notion that mutation governs the direction of evolutionary change.

In chapter 1, Fisher begins to devise a quantitative model or groundwork that synthesizes the Mendelian theory and the biometrical approach to the study of heredity. Space does not allow to give the particular details of the quantitative model Fisher offers in chapter 1. All that I have attempted to do is sketch Fisher’s reasons for the necessity of such a model. Some criticisms of Fisher’s ideas seem to be in order. First, has Fisher completely abandoned the blending theory? Fisher devotes a great deal of space to explaining the reasons why one should abandon the blending theory. Although strict adherence to the principles of blending theory seems problematic, a more lenient adherence to the principles of the blending theory seems to be quite apt. For instance, when Fisher explains the details of particulate inheritance, he still accepts the idea that an offspring may possess the genetic makeup of both parents. The consequences of the blending theory may be wrong, but that does not seem to be enough reason to eliminate all of the principles associated with the blending theory. Second, Fisher tries to demolish whatever is left of the blending theory by accusing it of allowing mutation to govern evolution. Is this accusation warranted? The blending theorist may deem mutations a side-effect of the evolutionary process or a consequence of evolutionary change and need not accept Fisher’s claim that mutation governs evolution. The blending theorist may be able to explain away Fisher’s objections by formulating a careful argument and providing some evidence in favor of this argument. Finally, I find it most disturbing that Fisher’s quantitative method or framework seems to rest on a foundation that begs the question. Fisher says, “The sole surviving theory is that of Natural Selection, and it would appear impossible to avoid the conclusion that if any evolutionary phenomenon appears to be inexplicable on this theory, it must be accepted at present merely as one of the facts which in the current state of knowledge does seem inexplicable” (Fisher 1958, p. 21). He asks us accept this fact and move on. There does not seem to be any reason for accepting something if we have no reason to accept it. Without a reason to accept a claim as true, we should not feel compelled to accept the claim as merely an inexplicable fact.

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