Overdominance maintaining polymorphism

One of the classic ways to maintain genetic variation with a population is "overdominance," in short, a state where heterozygotes exhibit greater fitness than the homozygote genotypes. Imagine for example a locus, A, with two alleles, A1 & A2. Now, assume the fitness is distributed like so across the genotypes:

A1A1 = 0.75
A1A2 = 1.00
A2A2 = 0.75

In a random mating population the equilibrium genotypes given particular allele frequencies are described by the Hardy-Weinberg Equilibrium like so:

p2 + 2pq + q2

In a diallelic scenario q is by definition 1 - p, resulting in some algebraic simplification (i.e., the above equation is equivalent to p2 + 2p{1 - p} + {1 - p}2). We can imagine that A1 is equivalent to p, while A2 is equivalent to q. From the fitness values above we then know that the fitness of the genotypes are:

p2 = 0.75
2pq = 1.00
q2 = 0.75

Intuitively what would you expect? The frequencies of p & q need to equilibrate so that 2pq, the heterozygote, is maximized! Here is the formalism which describes the frequency of q at equilibirum:

q = (selection against p)/(selection against p + selection against q)

Now, fitness equals 1 minus the selection coefficient, that is, 1 - s. So, from the numbers above:

0.50 = (0.25)/(0.25 + 0.25)

In other words, when homozygotes are less fit than the heterozygote in a diallelic model, and they are of equal fitness, they will be extant within the population at equal frequencies. By the nature of the Hardy-Weinberg Equilibrium the maximum heterozygosity attainable is 0.50 with a diallelic model; and this is exactly what is produced by p & q frequencies of 0.5 within the population . Note that if the selection coefficients "favor" one allele over the the other in a homozygote state the ratio would differ, but if the heterozygote is modally fit then polymporphism will be maintained.

Of course, this is all abstract. I just assigned "fitness" values without elaborating any scenario. Now, consider this from Introduction to Quantitative Genetics:

...Another example is the resistance of wild rates to the anti-coagulant poison warfarin...The gene conferring resistance is dominant, so the heterozygotes and homozygotes are resistant. Homozygotes, however, have a much increased requirement for vitamin K, which is not met by the normal diet. So in areas where the poison is being used, one homozygote is selected against by the poison and the other by the vitamin K deficiency, leading to an equilibrium frequency of the resistance gene, which was about 0.35 in the area studied.

In other words, in regards to resistance to warfarin the mutant allele exhibits physiological dominance. But, in regards to vitamin K deficiency it does not (insofar as one copy of the wild type allele is enough to prevent the nutritional deficit). The combination of these two physiological processes result in a natural advantage for the heterozygote genotype within the population, which preserves genetic variation and extant frequencies of both the mutant resistance allele and the wild type.

I thought this example would be apropos since Larry Moran has a post up on the biochemistry of warfarin. So go check it out! Nothing in biology makes sense except in light of evolution, but evolutionary biology without mechanism is lame....


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Could something like this explain male homosexuality?

QTL hasn't picked up a 'gay gene.' if it is a gene of large effect there should be a smokin' impact to result in a trait which reduces fitness so much. i.e., if you assume homos are q2 you should find some major ass impact on fitness re: 2pq. don't think anyone has (though some claim to find some differences).