Gene Expression

Previously I discussed the probability of extinction across one generation for a new mutant allele. To review, there is ~1/3 chance that a new mutant will go extinct within one generation of its origination (i.e., a de novo mutation is not replicated and transmitted to the next generation of organisms). If there is positive selection on the mutant allele there is a reduction in the probability of extinction, but only a mild one. Consider that if s is 0.10, a 10% increase in fitness vis-a-vis population median fitness, that is likely to be swamped out in many cases by the stochasticity inherent in reproductive output for any given individual carrying a novel variant. In other words, favored alleles are rewarded by persistence.

But what about an allele which makes it past this cordon of extinction and eventually fixes, that is, goes from 1 mutant to ~99% of the alleles at a locus (a gene substitution)? We know that in a large population (where drift is ignored) the probability of fixation is 2s, which agrees with out intuition that even strong selection coefficients (e.g., 0.10) don’t guarantee escape from extinction. So, if a new mutant confers a 10% greater fitness upon an individual carrying the allele there is only a 20% chance that that allele will sweep and fix in the population. In the case of neutrality the probability of fixation is 1/(2N), in other words, the probability of fixation is inversely proportional to population size. This agrees with our intuition insofar as a new mutant in a population of 10 has fewer stochastic “steps” to make before reaching 100% vs. another mutant which arises in a population of 1000. Of course, conventional neutral theory does tell us that the rate of substitution is invariant of population size because even though the probability of ultimate fixation of a given allele decreases with increases effective population the number of mutants within the genetic background increases proportionally, ergo, the rate of neutral substitution is proportional only to the rate of mutation. This idea was a basis for the “molecular clock” in regards to genome evolution.

Interjection:
Please read Everything You Learned in Introductory Genetics was Wrong at some point. It is a good “reality” check for anyone reading these posts!
End Interjection

But in this section Gillespie is exploring a somewhat different model. He contends that “the mean time until the first substitution” from a mutant from the “mutational caldron” is:

t = 1/(2Nvs, where N and s are as above, and v is the mutational rate, where Nvs << 1 (that is, the mutational rate is very low, which should be implicit in that it is a poisson distribution)

If one assumes that the parameters for originating mutations for substitutions are held equal, the rate of substitution then is simply the recipocral:

ρ = 2Nvs

In other words, the rate of substitution in this model is proportional to population size, selection coefficient and mutational rate! Jumping out of the “caldron” exhibits a sensitivity to population size.

Of course, there is a serious problem with this. Starting with R.A. Fisher’s conception of adaptation in the 1920s, and proceeding up to contemporary models such as H. Allen Orr’s, theories of evolution driven by selection upon mutations have emphasized that selection coefficients for subsequent mutations should decrease as the fitness optimum is approached. This is the classic “overshoot” problem which Fisher illustrated geometrically, as you near a phenotypic ideal, excessive genetical deviation via mutation is far more likely to result in a decrease in fitness as you jump over the optimum and go careening down the adaptive hill. As Gillespie notes these models imply a burst of substitutions driven by positive selection and then equilibration at the adaptive peak. This was the reasoning behind the “Classical School” of evolutionary genetics and their argument for why polymorphism should be minimally extant within most populations, evolution would occur in dramatic sweeps to fixation followed by fallow periods of genetic stagnation (this is similar to Punctuated Equilibrium). Many of these models also exhibit a property of relative insensitivity to mutational rate, population size or selection coefficients, as the evolutionary dynamics work quickly over short periods of time with the raw material on hand and proceed to the same optimum (some models depend on the logarithm of the population size). It must be cautioned that these models are based on assumptions (e.g., poisson distribution) which do not always hold in all, or many, cases. Clearly large regions of the genome are neutral or nearly neutral, while other portions seem to be under positive selection, and other regions are subject to balancing selection of various kinds. The important point of the models is to offer insight into the dynamics in particular situations which gives us a piece of the greater puzzle.

And yet there is another issue which Gillespie covers, and which is really the heart of the issue, and that is environmental variation. Why do the substitutions toward an optimum occur? One presumes that there might be an exogenous factor, or, there might be a coevolutionary interspecies “arms race” at work, or perhaps intraspecies dynamics. Whatever the reality, fitness is a difficult parameter to reify in a universal sense, as opposed to a local value. Clearly a fitness landscape can be reworked dramatically if there is environmental impetus, and a new regime of selection coefficients may drive an immediate burst of adaptive evolution from the genetic background in response to exogenous inputs. So in this scenario you have evolution proportional simply to the rate of environmental change, with the genetic substitutions being derived from the ambient genetic background, with varying mutational rates, population sizes and selection coefficients being sufficient and of little concern. In paleoanthropology one might consider The Turnover Pulse Hypothesis as an example.

I think that these sort of models are probably relevant, or not, contingent upon the species you are speaking of. Clearly humans have less reproductive variance than salmon, for example. Since I’m pretty homocentric I look at these models as guides that can aid us in elucidating our own evolutionary past, and present, and ultimately, future. Some keep that in mind, I’m not talking about Newton’s Three Laws or the Laws of Thermodynamics, fixed and precise truths, but models which are an aid into understanding the general processes bubbling under the surface of the rich texture of life’s variation.

Note: Adapted from chapter 5 of Evolutionary Genetics: Concepts & Case Studies.

Comments

  1. #1 Agnostic
    November 7, 2006

    Re: environmental change driving most adaptation regardless of pop size, etc. etc. and relevance to humans — consider the relative paucity of data on genes of large effect on phenotypic IQ (which would be the nice way of saying it). Compare this situation with that of genes clearly implicated in personality (DRD4, MAO-A, 5HTT, etc.), resistance to infectious disease (sickle-cell among a billion others), digestion (lactose tolerance, alcohol tolerance, etc.), skin and eye color (MCR1 inter alia), and so on.

    In either Fisher’s geometric model or the Gillespie-Orr models based on Maynard Smith’s discrete model, a few substitutions of large effect on fitness occur first and are followed by many of smaller effect. Presumably the early ones would show up in tests for “major genes,” so to the extent that such large-effect substitutions are not found, this implies that the population may not have been thrown so far off the optimum and simply needed the small-effect substitutions to regain equilibrium.

    If true, this says that over recent history (10 kya to present), populations were blasted away from the optimum by environmental changes regarding diet, climate, infectious disease, social relations (where personality traits are strategies for social interaction), as shown by the large-effect genes above. However, the apparently large 1 SD difference in mean IQ between Europeans and s-S Africans may not be of equal “equilibrium disruption” effect compared to the 1 SD difference between Europeans and Ashkenazi Jews. For the latter, there are all the genetic neurological diseases that almost surely cause higher IQ.

    Perhaps there’s a non-linear relationship between IQ and fitness in the range of human environments so far encountered. An increase of 1 SD from 85 to 100 allows you to go from unskilled worker to skilled worker (or bumbling peasant to adept peasant), but a similar 1 SD jump from 100 to 115 allows you to go from skilled worker to college graduate / professional. If true, that might account for why there don’t seem to be large-effect genes relating to phenotypic IQ in Europeans, but why there are for Ashkenazim.

    Alternatively, it could be that comparing Europeans to modal s-S Africans is flawed since the latter are mostly agricultural — for a far shorter time, for sure, but again, most large-effect substitutions happen early on. It would be worthwhile, then, to compare Europeans to H-Gs reared in the modern world.

  2. #2 razib
    November 7, 2006

    relationship between IQ and fitness

    extant heritable variation implies weak correlation over time between IQ and fitness, else positive selection would have expunged all genetic variation on this trait.

  3. #3 Agnostic
    November 7, 2006

    Well, the key word there being “positive [directional] selection.” I was just talking about a population reaching an optimum, which doesn’t imply that it got there one way or another. Sub-Saharan Africans in malaria zones are at an optimum re: sickle-cell, but that’s sure not due to directional selection. There are all sorts of reasons why IQ might be under real or apparent stabilizing selection — too high or low may make you an outcast, there could be antagonistic pleitropy, or environmental heterogeneity (not everyone in a society of type X will occupy the exact same role in it), etc.

    I was just talking about the magnitude of the genome-environmental mismatch in the case of 1) Europeans who transitioned to complex agricultural societies, vs 2) Ashkenazim who transitioned from this to professional-managerial niches within host societies. It seems this mismatch is larger in 2) than 1), judging by detection of large-effect genes.

  4. #4 razib
    November 7, 2006

    I was just talking about the magnitude of the genome-environmental mismatch in the case of 1) Europeans who transitioned to complex agricultural societies, vs 2) Ashkenazim who transitioned from this to professional-managerial niches within host societies. It seems this mismatch is larger in 2) than 1), judging by detection of large-effect genes.

    hm. i’m not sure i get you re: ‘mismatch.’ re: detection of large-effect genes greg’s hypothesis last i checked was that that was due to the fact that the deleterious impact of these large effect genes (e.g., recessive diseases) don’t impinge on fitness in the ashkenazi EEA. over time one assumes that other genes, or modifying genes, would arise to mask this and the genes of large effect would fix so that you wouldn’t see the large effect behind the wall of the genetic background. therefore, the ‘overclocking’ title.

  5. #5 Agnostic
    November 7, 2006

    By “mismatch” I mean, in phenotypic space, how far off the optimum the population has been thrown due to recent environmental change. Say that IQ 85 is ideal pre-agriculture (though real H-Gs won’t even reach that due to insufficient environmental stimulation), and that some change occurs so that now IQ 86 is ideal. The pop isn’t thrown far away from the target, so little tweaks will readjust the pop to optimum. The farther off the optimum they’re thrown, the adjustments needed to regain the optimum will be more major in effect. I don’t think there’s any principled distinction between major & minor genes, but at some distance away from the optimum, the effects of the genes that bring it back will show up as “major” genes. A pop just introduced to ubiquitous malaria, for example, exceeds this threshold distance from the optimum, and their adjustments (sickle-cell etc.) show up as major genes.

    I’m sure the H-G to agriculture transition was a mismatch w.r.t. intelligence demands, but compared to the agriculture to moneylending transition was smaller in magnitude, despite the IQ gains being the same (roughly 1 SD). That, or the agricultural transition wasn’t as rapid and intense as the moneylending transition — my mental image of the former is that it was rapid enough, but I could be wrong about that.

    If I’m wrong about that — if the agricultural pops were only thrown off a small amount each generation as agricultural become gradually more and more complex, then at each step the tweaks would’ve been minor; ergo, no major genes. So, guess it depends on how rapid & intense the agricultural transition was.

  6. #6 windy
    November 8, 2006

    I’m sure the H-G to agriculture transition was a mismatch w.r.t. intelligence demands

    I don’t think we can automatically assume that agriculture was always connected with intelligence gains. IIRC, brain size went down in the Neolithic so you would need to sort out the nutritional and genetic processes there, but to me it doesn’t look like the early farmers were getting smarter in an obvious way.

    Perhaps selection managed to over-compensate for decreasing brain size (what was that gene with the most recent selective sweep? ASPM?) but was the cause agriculture or something else? Whether the complex civilizations made possible by agriculture later selected for intelligence in some way, at least for some parts of society, is a slightly different question IMO.