Gene Expression

Fisher web

Just found this web site that has a good bibliography of R.A. Fisher’s work. Good supplement to the R.A. Fisher digital archive. Why do I obsess with Fisher? First, ANOVA is ubiquitous. Second, stories like this would shock & awe a lot less if people read The Correlation Between Relatives on the Supposition of Mendelian Inheritance (PDF of full paper). Now, the text of the paper can be rather opaque, and the dancing flow of algebraic manipulations and moments magic can elude your grasp, but the gist is simple: the variance components of the offspring of heterozygous parents can be predicted a priori from Mendelian assumptions. And, this variation is not exhausted through admixture because of the discrete character of Mendelian genetics.

Update: I’ve been told that “the variance components of the offspring of heterozygous parents can be predicted a priori from Mendelian assumptions” is well nigh unintelligible. OK, the PDF of the paper is provided above…and it is a rather opaque piece of prose. Fisher tends to leap around a lot more than I think is warranted, but hey, that’s life. Basically what I was trying to get at is that variation on a trait is easily derivable from small discrete differences within the genome. People who are “mixed” in appearance are not analog mixtures, or “blends,” of parental types, they are discrete combinations of parental genotypes. This explains the link where I show two “brown” parents giving rise to a “white” twin, the standing genetic variation is preserved within the parental generation, even if it is expressed in particular specific genotypes. In the next generation it simply reemerges from the parental type in a way that can be understood assuming simple Mendelian genetics.

Mendelian genetics is a trivially easy dodge of the classical problem in Darwinian evolution: how to preserve variation for selection to work upon as a population “mixes” randomly. If offspring are mixes of the “essences” of the parental generation, then over time you will have a blurring and smoothing of the initial population variation. Darwin and others appealed to various factors, some straightforward like demographic or sexual disruption and differentiation, to preserve the range of traits, but Mendelian genetics was an elegant solution to the problem. Traits are simply reduced to the sum of their genetic parts, which themselves are never destroyed except through processes like random genetic drift and selection. Fisher’s paper shows in part how to derive exactly how the variation between relatives can be discerned, and Mendelian assumptions clearly show that parents who are genetically varied will give rise to a host of offspring, many of whom will recapitulate the variation extent within the population.

To make it even more boring, to some extent population genetics can be thought of as drawing balls from an urn.

Comments

  1. #1 Ron
    February 27, 2006

    Hey, thanks, very useful for my classes on geostatistics. Fisher did not take into account spatial autocorrelation, of course, in his development of analysis of variance as it is applied to agronomic experiments, for example. Do you have anything on the implications of auto-correlation for classical Fisherian models? I don’t know if this would be relevant to applications in genetics.

  2. #2 razib
    February 27, 2006

    ron, it seems like the applications would be more relevant in modern day genomics. but i can’t think of anything off the top of my head, anyone else know?