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# Can't have genetic drift without the other....

Gene ExpressionBy Razib KhanApr 18, 2006 1:55 AM

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Just a quick review about some issues that I assumed implicitly in my post where I took issue with genetic drift as a force for population variation. It isn't like genetic drift can't result in variation...but the researcher seemed to be pointing to founder effect which would homogenize alternative populations and "fix" them into alternative states. For founder effect to really work you need to reduce the effective population size and squeeze genetic polymorphism out of the gene pool. Consider the equation for decline in heterozygosity^1: Ht = (1 - 1/(2N))^tH0 Where H0 is the intial heterozygosity and t is measured in generations. It seems clear that as N approaches infinite there won't be a change, random genetic drift will not sift out the variation from the population because the sampling process is too weak of a force. In contrast, a low N will result in rapid reduction in heterozygosity, ergo, genetic uniformity. Consider: t = 100 generations H0 = 0.5 (half the population is heterozygous) Where N = 20, H20 ~ 0.04, that is, 96% of individuals will now be homozygous. In contrast, where N = 200, H20 ~ 0.39, so only 61% of individuals will be homozygous in the 20^th generation. 20 generations is probably going to be around 400 human years. In any case, you get the general gist, for founder effects to be powerful you need to sample a small number of founders from the original population. This drives the "N" down as the effective population is reduced.^2 The model that the anthropologist proposed assume small founder populations. But, it then assumed that these populations remained genetically distinct. How plausible is this? Not very in my opinion, unless you take into account selection and assortative mating. Long term equilibrium gene frequencies under drift & migration (between populations) is 1/(4Nm + 1), where N is effective population again, and m is the proportion of migrants within a given generation. The key to note is that if you run this equation through any iteration you'll see that only about 1 migrant per generation is needed to maintain equilibrium, and that this equilibrium can be attained very quickly through genetic exchange. Small populations wouldn't need many migrants because they are small. If large populations entered the New World, well, they would exhibit more internal genetic variation and less influence from drift. I suspect you could cobble together a model of drift and subsequent interpopulation barriers...but it doesn't seem to pass the test of parsimony. The only reason I sketch this out minimally is that it might behoove the public to know that a lot of scientists are talking out of their asses when they point to drift. it is basically hand-waving. 1 - Heterozygosity would be the frequency of individuals with alternative alleles at a given locus. For example, someone with a "brown eyed" allele and a "blue eyed" allele on the locus that controls for eye color. 2 - Long term effective population is equivalent to the harmonic mean, so it is closer to the small end of the overall range as a function of time.

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