I had what I seemed to me like an interesting thought when I read this, and I wanted to explore it further. But I have been very busy these days, and I just don't have the spare cycles, so I'm just going to throw it out there. My biggest question is: "What am I missing?" R. A. Fisher didn't think that epistasis was an important evolutionary force. I can't believe he would miss this, so the only alternative is that he considered it...

From the link:

Finally, that we failed to find a significant grandfather effect in our monogamous society in which we restricted our data to those men who married only once in their lifetimes (and hence could only gain fitness by grandfathering after the menopause of their wife) strongly suggests that the evolution of prolonged life in men cannot be explained by the selective benefits of grandfathering.

My thought, as I expressed in the comments of that post, was that average fitness is not particularly meaningful, since a relatively small number of males at the top of the social pyramid probably had a disproportionate evolutionary impact - what really counts is the grandfather effect among them. I can easily imagine a scenario where grandfathers decrease fertility of ordinary families (another mouth to feed...), but increase it among the rich. The long-term fitness impact of grandfathers could well be positive, even though the average impact is negative, since the rich have the biggest long-term evolutionary impact.

I can tell this same story on the gene level. Imagine a population which is 99% "aabb" and 1% "aabB", each of which have equal fitness. Now, imagine that there's a mutation "A" that reduces fitness by 10% in "bb" individuals, but raises fitness by 10% in "bB" individuals. Let's say by chance we get a "aAbB" individual before the "A" allele dies out. That "aAbB" individual will have the same fitness as a normal "aabb" individual, since its offspring will be 25% "aabb" (average fitness), 25% "aAbb" (10% lowered fitness), 25% "aAbB" (10% higher fitness), and 25% "aabB" (average fitness). Nevertheless, over time, the "A" allele will increase and eventually fix (together with the "B" allele). (Those of you who want to quibble about the percentages can adjust them accordingly.)

Now that seems like an interesting result to me! We talk a lot about average fitness here, but if I am not mistaken, average fitness can tell a story that's very different from what's really going on. Increasing the fitness of winners seems to count a lot more than decreasing the fitness of losers - and in evolution it's the winner's story that will eventually be told.

Labels: epistasis, Evolution, Genetic

Recently Razib walked readers through a scenario where a population passing through a bottleneck would, by sampling error, experience a change in allele frequencies and thereby convert some of the variance due to dominance into additive genetic variance -- the kind that matters most for a population to respond to selection. If we recall the Breeder's Equation -- R = S*h^2 -- the increase in the population mean for a trait (R) equals the mean of the sub-population selected for breeding (S), multiplied by a fraction between 0 and 1 that shows how fully the potential for change is exploited by selective breeding (h^2). This fraction is called the heritability and equals the fraction of the entire phenotypic variance that is accounted for by just additive genetic effects. Clearly, this fraction increases as additive variance increases.

To review a key difference between additive vs multiplicative scenarios, the components in an additive case don't interact, or the context in which they appear doesn't matter. Since such effects are blind to all other contingencies, they matter most in trying to breed a trait in a desired direction. Non-additive effects throw sand in the gears: for instance, if the alleles within a particular locus interact, we have dominance. The other type is due to epistasis, or the interactive effects between loci. Since these effects blunt the power of directional selection, we ask what if we could magically convert the retarding type into the promoting type? Razib's post linked above has already showed how, in detail, this could happen when a bottleneck converts dominance variance into additive variance. Now, to see how a bottleneck could convert epistatic variance into additive variance, consider the following table*:

---- AA -- Aa -- aa
BB.. 8....... 6...... 4
Bb.. 2....... 4...... 4
bb.. 1........ 1..... 3

Let's call the locus with the A and a alleles locus 1, and that with the B and b alleles locus 2. We'll say the entries correspond to a phenotype that depends on the genotypes at both loci, and that fitness is positively correlated with this phenotype. Consider locus 1: the A allele is associated with greater fitness if you look just at the first row, where it interacts with just the BB genotype. In fact, A's effect is perfectly additive: each copy of A adds 2 units to the baseline, and the heterozygote's value is the average of those of each homozygote. If the b allele were lost somehow, then the only possible genotype at locus 2 would be BB (only the top row would show up), and the greater fitness of A combined with its non-trivial heritability (i.e., greater additive variance) would then drive A to fixation. The trouble is that when A teams up with the Bb and bb genotypes, its effect is non-additive and it's associated with lower fitness. We therefore have epistatic variance in this trait: the fitness of the alleles at locus 1 depend on the larger genetic context in which they appear.

For readers not used to this jargon, consider a real-world case of the market success of musical styles. Let's say that locus 1 represents the musical styles, such that AA is a pure classical, Aa is classical-jazz fusion, while aa is pure jazz. Now, locus 2 represents the critics, such that BB prefers classical and increasingly winces as he hears more jazz intrude into a style; Bb prefers music that has even a hint of jazz; while bb is a jazz purist. Here, the success of a particular style depends on who's judging it, and since the judges have dissimilar opinions, a diversity in musical styles will be maintained.

But suppose that, due to the whims of fashion in criticism, the pool of critics was suddenly depleted of those who valued jazz at all, leaving only the classically minded critics (BB). Then we would quickly see jazz musicians removed from the concert halls and record stores, replaced by pure classical musicians. This loss of diversity in the pool of critics wouldn't have to result from caprice -- maybe somebody important in the world of criticism fired all of the critics even somewhat sympathetic to jazz.

To bring this back to genetics, the loss of the b allele at locus 2 could result from a population bottleneck, which increases sampling error, or it could result for more selective forces. We already see that b is associated with lower fitness (values descend as you move down any of the three columns), so it could also be lost due to selection against it. In the past 10,000 years, it has been possible for a few people to affect large numbers of others -- maybe a satrap decides that he doesn't like people with blue eyes and tries to kill them off. Or perhaps an imperial ruler or ruling elite make good on a promise to execute anyone who steals. By purging a locus or loci of their diversity in any of these ways, any other loci that had been interacting with the suddenly homogenous loci are now more free to undergo directional selection. Crucially for humans, the new socio-cultural and institutional structures that came into being only after agriculture probably rubbed out some diversity at loci that were only of marginal importance in a hunter-gatherer society, but whose diversity could not be tolerated in an agricultural one. This applies equally to loci affecting traits above the neck as well as below.

* Shamelessly using the same numbers as Table 2.3 on p.21 of Mazer & Damuth (2001). Evolutionary significance of variation, in Fox, Roff, & Fairbairn (eds.). Evolutionary ecology: Concepts and case studies. New York: OUP.

Labels: epistasis, Evolution, Genetics