I know I’ve posted on this topic before, but I thought I’d revisit it again. You do know that sometimes population bottlenecks can actually result in more variation being freed up for selection? This may strike you as a bit strange; after all, the power of selection to effect phenotypic change is proportional to genetic variance, specifically, additive genetic variance. Population bottlenecks imply a reduction in effective population size, the increase of sample variance across generations, that is, random genetic drift. As population size drops the stochastic change in gene frequencies becames proportionately much greater and alleles rapidly go extinct, or fix, within populations (average time until fixations in generations is proportional to 4N_{e}, where N_{e} is effective population size). The homogenizing effect of this dynamic is similar to what might occur with inbreeding, where effective population size is reduced through population substructure, and individuals within the demes quickly become closely related over a few generations. Obviously you know that inbreeding leads to a loss of variation. So how exactly can we extract more additive genetic variance from this? In short, but converting other types of variance….
My exposition here is borrowed from Evolutionary Genetics: Case Studies and Concepts (an excellent book which has been much blog fodder over the past few years). We start with the idea of statistical epistasis; gene by gene interaction which varies the trait value. Additive genetic variance is pretty simple, you take a locus (gene) and substitue alleles (variants of genes) and see the effect it is has on the trait. Obviously you have variation on other genes, but for additive genetic variance you just assume the average of the genetic background; in other words, ceteris paribus is the order of the day. When it comes to epistasis this sort of averaging of the background won’t do because it’s the combinations across the genes which are relevant; think of epistatic effects as non-linear and additive ones as linear.
The example from Evolutionary Genetics uses additive-by-additive epistasis across two loci; the elements of the matrix are show the outcomes of genotype combinations.
A_{1}A_{1} | A_{1}A_{2} | A_{2}A_{2} | |
B_{1}B_{1} | 1 | 0 | -1 |
B_{1}B_{2} | 0 | 0 | 0 |
B_{2}B_{2} | -1 | 0 | 1 |
As you can see, the effect of the genotypes of A invert contingent upon the background of B. Now imagine that you start with a large panmictic population where A & B are at intermediate frequencies. Obviously there’s only a weak correlaton of phenotype with genotype for change on A in this case; no additive genetic variance. But if stochastic pressures result in a deviaton from a balance between the allelic variants of B, then A will contribute to additive genetic variance.
Here’s a figure which illustrates what I’m talking about….
R. A. Fisher famously believed that evolution via natural selection operated through mass action upon large panmictic populations. He might have been right, but in all cases? I’m not so sure anymore….
Related: The Shifting Balance.