In 1974 Richard Lewontin’s book The Genetic Basis of Evolutionary Change pointed out the “Paradox of Variation.” Put simply this paradox is the observation that genetic diversity seems to be limited to a small range and is not responsive to actual population sizes in the way that we originally assumed it would be.

Mutations can be deleterious, advantageous or effectively neutral. It was believed that for most purposes we could ignore the deleterious and advantageous since the first would be quickly purged from the population and the latter would be exceedingly rare. Assuming for a moment that this is true, we will say that mutations occur at some frequency (µ) and that when a mutation occurs its probability of fixing is equal to 1/2N. This gives us the ability to predict the heterozygosity in the population with the formula H =4Nµ /4Nµ +1.

This theoretical understanding was achieved in advance of our ability to accurately measure heterozygosity. The advent of electrophoretic examination of allozymes allowed us to get our first real glimpse of the heterozygosity of different organisms. In 1974 heterozygosity measurements ranged from .056 to .185. This equated to Nµ values between .01483 and .0567. This variation would mean that population sizes range across less than a fourfold difference. Lewontin and others were certain that this could not be the case. So were had we gone wrong? Obviously some part of our understanding of the spectrum and behavior of mutations was incorrect. Continued research broadened the range of observed heterozygosity however the data still did not agree with our theoretical predictions.

One clue to the possible answer is that heterozygosity of mtDNA shows no sensitivity to population size. What is one of the key differences in mtDNA and nuclear DNA? Recombination. So how is a lack of recombination nullifying the influence of population size on heterozygosity? The answer might be hitch-hiking. Hitch-hiking is the phenomenon where the physical proximity of two loci causes the fate of one to be driven by the other.

John Gillespie tackled this idea with his theory of genetic draft. Gillespie’s idea is basically that occasionally a beneficial mutation will occur and all of the alleles that are physically found on the same chromosome (linked) as the one with the advantageous mutation will be selected and driven to fixation with the one advantageous mutation. Remember the standard formula incorporating only genetic drift is H =4Nµ /4Nµ +1. Gillespie expands this model to allow for hitch-hiking or genetic draft. Heterozygosity would now be equal to 4Nu / (1+2NpE{y

^{2}}+4Nu). The middle term 2NpE{y

^{2}} is the new term that we need to understand. The term E{y

^{2}} is the average frequency of the hitch-hiking allele after a selective sweep. To simplify we will assume that the two sites of interest are tightly linked and that this term can be treated as equal to 1. This leaves us with p… this is the rate of substitutions of advantageous mutations. This is also the most contentious part of Gillespie’s theory. For the theory of genetic draft to explain the observed data p must be independent of N. However, intuitively we would expect p to increase as the population increases.

I’m not sure that I really understand all the implications of genetic draft. So I will continue this post once I have finished reading and digesting this stuff.

To be continued

Forget the neutrality assumption - that was wrong direction. Though admittedly this illusion is quite persistent because non-neutral mutations en mass follow Hardy-Weinberg as if they were neutral: http://arxiv.org/abs/1306.4117

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