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More from less, increased variance from bottlenecks

Gene ExpressionBy Razib KhanMay 7, 2007 10:58 PM

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I have stated before that additive genetic variance is the relevant component of variance when modeling the response to selection in relation to a quantitative trait. In other words: Response = (additive genetic variance)/(total phenotypic variance) X Selection Consider height, which is about 80% heritable in the narrow sense in modern developed nations. What do I mean 80% heritable in the narrow sense? I mean that 4/5 of the variation in height, which is distributed in a normal fashion, is controlled by additive variation in the genotype. In other words, if I substitute allele 2 for allele 1 it is going to have an effect of deviation z upon the phenotype. What are the other components of variation? Obviously environmental variation. In regards to height we're probably talking about nutrition, but since in modern societies we have something of a nutritionally saturated environment this doesn't really vary too much (if you eat more food you just get fatter, not taller, beyond a certain point). There are also other possibilities, such as dominance effects (non-additivity within a locus), epistasis (non-independence between loci) and gene-environment interaction (non-linear dynamics, e.g., norm of reaction). In any case, with respect to height you can see that the breeder's equation, R =

h^2

S, will result in some dividends, as most of the variation is heritable in the narrow sense. As you reduce the heritable variation, you reduce the ability of selection to make an impact upon a quantitative trait. So, one assumes that a population bottleneck will result in a reduced ability of a population to respond to selection because of the implied reduction in genetic variation as a whole. Bottlenecks tend to result in founder effects because of the increased power of sampling variance. Like a low resolution photocopy a founder population invariably exhibits a loss of genetic information as rare allelic variants go extinct, while the proportional relationship between more common variants tends to be shifted. But biology is the science of exceptions: in some cases populations which go through bottlenecks may actually be more responsive to selection upon quantitative traits because of increased additive genetic variation. How does this happen? Well, imagine that dominance or epistatic variation is converted to additive variation! Here's a toy illustration: You have a locus with two alleles, 1 & 2. The three genotypes map onto phenotypic values like so: 11 = a (positive deviation from the mean when substituted) 12 = d (this measures the extent of dominance) 22 = -a (negative deviation from the mean when substituted) The additive & dominance genetic variations can be modeled by the expression: additive variance = 2pq(a + d(q - p))^2 dominance variance = (2pqd)^2 (the formalism should be reasonably familiar) Assume complete dominance, so d = a. Also, for simplicity, a = 1. This means that: additive variance = 8pq^3 (substitute & do the algebra) Take original allele proportions to be p = 0.75 & q = 0.25, and plug & chug: additive variance = 8(0.75)(0.25)^3 = 0.094 Assume that the population passes through a bottleneck which deviates the allele frequencies through sampling error to p = 0.70 and q = 0.30, and plug & chug: additive variance = 8(0.7)(0.3)^3 = 0.1512 Bingo! Additive genetic variance is now greater than before. There are more complex models which take epistatic genetic variance and convert it to additive genetic variance. It is important to recall that much of quantitative genetical theory, and R.A. Fisher's original work, tends to assume an average genetic background. The dynamics of populations though often result in a shift of that background, and in regards to quantitative genetics the act of selection itself tends to shift the allele frequencies in a manner which gives rise to new combinations and radically different genetic architectures many deviations away from the original phenotypic mean. Averages by their nature tell us what we can expect, but it is always important to note that quite often in evolution it is the dispersions away from expectation which hold the keys to the kingdom. Note: Based on the treatment in Evolutionary Genetics: Concepts and Case Studies. Related:Breeding the breeder's equation.

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