People often talk about random genetic drift. Like sexual selection it is the deus ex machina of choice when you are shit out of luck in regards to hypotheses. And yet though it looms large in our minds R.A. Fisher dismissed it as an important evolutionary force. Sewall Wright in his Shifting Balance Model tended to emphasize the interactions of genes more than the random fluctuation of frequency as such. Drift only came into its own with the rise of Neutral Theory and molecular evolution. In any case, I'm going throw out an algebraic relation out there that I think is important to keep in mind when thinking of these issues.
Imagine if you will two alleles, variants, of a gene, p & q. p = 1 - q & q = 1 - p. The sampling variance moving from one generation to the next is defined by:
(p X q) / (2 X effective population), or (pq)/2N
The standard deviation of this value, is [(pq)/2N]0.5, its square root.
The key point is that as the population drops the sampling variance starts to shoot up, that is, drift to and fro from generation to generation. This is the root cause of the "random walk" process of changing frequencies and eventual fixation. Obviously a large population is less effected by this perturbation than a small one.
- Log in to post comments
Yeah, that helps. I intuitively grasped your earlier comments about drift as sampling error, but one can't really grok this without studying the formalisms.
play around with some simultations. there is pop genetic freeware out there.
But, once at equilibrium (yeah, I know, unrealistic assumption) the rate of neutral evolution is independent of pop size, but you already knew that.
Haven't we both been arguing, however, that population size is most important for determining the power of selection? We don't so much get more neutral evolution in a smaller population, just less adaptive evolution. Ie, selection on nearly neutral alleles in non-effective in small populations.
sure, but often in day-to-day discussions we're addressing issues like the extent of transient polymorphism within a population. obviously small populations and populations under selection will have less polymorphism then large neutral populations.
Razib, could you please explain in words how emphasis on the "interaction of genes" can be seen as an alternative to "random genetic drift" ? I've always been suspicious of the latter for reasons that are unrelated to the mathematical aspect of population genetics (of which I currently have little knowledge).
jack,
wright viewed the interactions between loci as contingent and dependent fitness parameters. he conceived of an adaptive landscape with alternative fitness peaks defined by the interaction of genes. so, you could have
peak 1 - allele A1A1 allele B1B1
peak 2 - allele A2A2 allele B2B2
between these two peaks you might have A1A1 B2B2 and A2A2 B1B1, which would be suboptimal in fitness. fisher disagreed insofar as he believed that it was almost certain that either 1 or 2 would be higher, and over the long hall selection would shift those at the lower peak to the higher peak. now, how do populations get to peak 1 or peak 2? well, they, in part, random walk to it via drift which results in the shift in the genetic backgrounds. but drift is just the means toward the ends, which is still constrained by selection on alternative peaks.
please note that many people disagree with the importance of statistical epistasis as relevant for variation. fisher did, and most of his heirs intellectual do. epistasis of this sort would seem to conflict with recombination, since the latter would break apart favorable combinations....