I have mentioned a few times that I am re-reading The Genetical Theory of Natural Selection by R.A. Fisher. I read it a few years back when I didn't know anything about evolutionary theory, so I believe this run through will be more frutiful. For those of you who don't know, R.A. Fisher was possibly the most important evolutionary biologist, and probably most important statistician, of the 20th century. Along with Sewall Wright and J.B.S. Haldane he created the field of theoretical population genetics which the Neo-Darwinian Synthesis takes as an a priori starting point. I know that in the current craze over evolutionary developmental biology, "evo-devo," and the importance given over to the modulation of gene expression, some are indicating that the old paradigms are being overthrown. I don't believe this is true, and in fact, like James F. Crow I believe that new empirical techniques from genomics will revive the importance of theoretical insights which for many decades remained untestable. The importance of The Genetical Theory of Natural Selection is manifold, but I will emphasize two. First, on the microscale it was the sum of Fisher's early thinking which would serve as a reference from which Sewall Wright and J.B.S. Haldane could begin their arguments during the early controversies in their field, and so helped shaped the subsequent consensus. Secondly, I believe The Genetical Theory was the first formal step in scaffolding evolutionary biology into a more precise scientific straight-jacket so that the long retreat from "Just So" could commence. Though The Genetical Theory is a somewhat mathematical treatment of natural selection, I don't think people should be frightened over the formalism, in general it goes little beyond calculus (there are some allusions to differential equations), and most of the mathematics is reduced to rather spare algebraic relations at the end of it all. One need not follow the details of the "proof" to imbibe the gestalt insights of the Fundamental Theorem of Natural Selection. The 1999 Variorum Edition which I have weighs in at less than 320 pages, the vast preponderance of which is non-mathematical. The joys of The Genetical Theory are different from the rich prose of The Origin of Species, but they are not to be sneezed at. Though Fisher draws you, at least in the initial chapters, into the domains of abstraction, this is not pure theory, walk outside and see nature in all its glory and the subject of Fisher's work shouts at you still. Chapter 1, The Nature of Inheritance, is somewhat dated insofar as it addresses the controversy between Mendelian and biometrical schools of biology in the early 20th century. Much of the background is covered in my post Every ratio 3:1. The short of it is that Fisher shows that the blending theory of inheritance results in absurd implications, while Mendelian discrete transmission fits the empirical data without fail. To us today this seems obvious, but does it? Every few years the meme that blondes are going extinct seems to erupt into the public space, and most liberal minded folk seem to assume that a racially admixed feature will result in cafe au lait homogeneity.
Though modernity gives lip service to Mendelianism, innate blending theory remains ascendent in the mind's eye!
Blending theory is basically an analog conception of inheritance, while Mendelianism is discrete or digital. The great weakness of blending theory, which Darwin acknowledged, and was not soluble except via rather unparsimonious or unempirical avenues, was that it exhausted variation rather quickly. When two parents "mixed" the offspring would be a synthesis of their natures, and so a population which starts out with variation will be "blended" together into a uniform whole. More precisely, Fisher shows that the rate of the decrease of variance will be 1/2 per generation, that is, 1/2 of the variation will be diminished. An added detail is that the rate has an extra parameter, r, which is basically one of assortative mating, so that the exhaustion of variation would be 1/2(1 - r). In cases where parents matched up perfectly by trait and the trait is perfectly heritable variation would not be exhausted, while in random mating situations variation would be diminished rather quickly. Taking Fisher's rough rule of thumb that 1/2 of variation is exhausted per generation, 1/2^n where n = generations, shows that the variation extant at time t must be of rather recent origin. This implies mutational rates must be inordinately high, and in fact, the variation between siblings that we see that is of genetical origin must also be mutationally derived. Fisher goes to great lengths to show that the mutational rates implied by blending theory are not plausible. He shows that plants who breeding in a "selfing" fashion do not seem to replenish variation to the extent that blending theory implies. In fact, selfing plants are some of the most powerful illustrations of Mendelianism. Consider a plant which selfs that is heterozygous for a trait. If it self-crosses, its offspring will be of the ratio 1:2:1, homozygous:heterozygous:homozygous, by simple Punnett Squares. If those plants themselves self, all the offspring of the homozygotes will result in homozygotes, while the heterozygotes will again result in a 1:2:1 ratio. So in selfing lineages with simple Mendelian rates not only does variation not replenish via high mutation rates, it diminishes in a fashion perfectly predicted by Mendelian inheritance. Another reality is that today we also know the rates of mutations on DNA bases, and for humans they seem to be on the order of 10^-8-10^-9, in other words, Fisher was right! And yet nevertheless as I have stated above, the public discourse tacitly assumes blending inheritance! Why? Because of the importance of polygenic traits that is what we see in expectation in our own lives in families. The problem is that we neglect the variance around this expectation which emerges out of differential sampling from segregating sites in parents. In other words, siblings may recieve different "50%" portions of their parental inheritance. Variation, diversity, is not destroyed in Mendelian inheritance, if it is recessive it may simply turn "latent" in heterozygotes, only to emerge in later generations. Because discrete Mendelian inheritance implies relatively perfect copying (let us ignore drift & mutation) of genomic diversity across generations,
when you add more genomic diversity into the system variance will increase
. In other words, admixture results in the inverse of the cafe au lait universe as novel and new combinations may now arise because of the convergence of new alleles. The future will be more diverse, not less.