Gene Expression

Size matters, or it doesn’t….

Over at my other blog I reaffirm Richard Dawkins’ criticism of Freeman Dyson’s off the cuff opinions about evolutionary genetics. Dyson is basically asserting that the rate of evolution is inversely proportional to the square root of population size. In short, small populations evolve fast in his mind because of stochastic fluctuations, clearly drift. I’ve posted a fair amount about stochastic dynamics…and it’s complicated. Science is complicated. That’s just life.

Now, Dyson is pretty much wrong. But his intuition is conventional; I’ve met many people who believe that somehow evolution can operate more effectively, faster, on small populations. I can’t even count up how many people seem to believe that population bottlenecks are always the critical events in changing the character of a species. In a very primitive way I think people have a general sense that Sewall Wright’s Shifting Balance model captures the essence of evolutionary dynamics; though like most interpreters of Wright’s views they incorrectly place greater emphasis on random drift as opposed to genetic interactions.

But why are people struck by the idea that small population sizes can change faster and more easily than large ones? I believe I held this intuition as well before engaging in a serious study of evolutionary process. Here are some thoughts. Consider that we normally talk of “gene pools.” In other words, we conceptualize genes as floating in a mass, physically embedded within the “population.” I suspect in our mind’s eye we’re conceiving of evolution as physically operating upon the mass of the gene pool somehow. Assuming that evolution is a constant pressure or force, a small mass would be more malleable and easier to shift because of the ratio between the force and the object which it operates upon increases. This fits pretty well with the impact of stochasticity, it isn’t like deviation from generation to generation of allele frequencies isn’t an issue, it is simply that the deviation is proportionately smaller because of increased sample size. The stochasticity is there, but it becomes less effective in “moving” the gene pool over time as it increases in size. Similarly with selection we’re imagining that it takes more time to makes its force felt in a large population. Humans don’t think in terms of population genetic parameters, rather, unless straight-jacketed into a precise formalism they’ll make recourse to physical analogs. Now, you say “No shit Sherlock!” But remember that this post was triggered by the musings of one Freeman Dyson, no tard is he. A cautionary tale on the unnaturalness of science….


  1. #1 colugo
    September 8, 2007

    I have an alternative explanation for why these beliefs are widely held. A lot of educated, professional class non-biologists got much of their understanding of evolutionary biology from reading Stephen Jay Gould’s popular science books. That’s changing of course, so it’s probably much less the case for people born after 1975, but Gould was America’s popular authority on evolution for decades.

  2. #2 razib
    September 8, 2007

    that’s a simpler explanation. but i also think it is more proximate. i.e., i think gould’s attraction was in part that his verbal models gelled with intuition.

  3. #3 Joseph W.
    September 8, 2007

    Also, the idea that small, inbred populations are going to mutate into something strange fits a common cultural idea about backwoodsmen and hillbillies.

  4. #4 agnostic
    September 8, 2007

    I can see the intuition behind random perturbations of equal amplitude being more noticeable in a glass of water than in a lake.

    But my spatial intuition about selection shows the opposite of it taking longer to take effect in a larger pop. Selection isn’t random perturbations — it’s deliberate stretching, pulling, tearing, etc. With a smaller mass of silly putty, you can’t mold it into as wide a variety of shapes, so it’ll take longer to produce something truly perceptibly different. With a larger mass of silly putty, it only takes a handful of manipulations to produce something bizarre.

    If selection is a sculptor, it will find it easier to work with a large slab of clay than a puny one. (And yes, it lacks forethought and is more experimental, but the point remains.)

  5. #5 Matthew MacManes
    September 8, 2007

    I haven’t read the Dyson piece yet, although it is next in the pile, It seems as if he is probably right on this one- assuming you hold the simplistic (but technically correct) definition of evolution: change in gene frequency over time.. Drift in small pops can cause alot of fluctuation in gene frequencies, fixing some/eliminating others.. especially thinking about the 1st few generation.. There is a nice graph of his in Futuymas Evolution text (probably Drift Chapter). Now it is true that after the 1st few generations there will be almost no evolution- most every locus is fixed…

    Now the large pop, gene frequencies are pretty constant (assuming pop is at equilibrium) basically by a process analogous to inertia.. Selection has to potential to enact change (i.e. selective sweep) but these events are the exceptions, not the rules.. Can very fast evolution happen- sure.. But if I was to have to pick a scenario where rapid evolution was likely to happen, it would be the small pop not at equilibrium.

    Now having taken a quick look at Dyson’s essay, I agree that the way he applied basic population genetics is ridiculous, and clearly mistaken.. He had a similarly wacky essay about “car eating termites” earlier in the summer which I commented on here.

  6. #6 agnostic
    September 8, 2007

    But if we’re going to be generous and say, OK he was talking about neutral changes, then he’s still wrong since across taxa there isn’t tons of difference in amount of variation, despite astronomical differences in pop size.

    Not being a molecular pop gen guy, I don’t know where the consensus is today (if any), but Gillespie has been pushing for draft being more important than drift, and the former is pretty insensitive to pop size.

  7. #7 Matt
    September 8, 2007

    Web of Science says the term “genetic draft” has been used in papers 5 times since Gillespie proposed it… I guess that means people don’t really think too highly of it…

    I don’t know if there has ever been a study that tests the predictions of the neutral theory on allelic variation… It would be cool to look at, say cytB in a number of independent populations that vary in Ne.. I bet there is variation as predicted..

  8. #8 razib
    September 8, 2007

    matt, just another word for hitch-hiking on selective sweep.

  9. #9 Matthew MacManes
    September 8, 2007

    yes, I know- nevertheless, if people thought highly of Gillespies idea, the paper would have been cited a little more frequently.. I think the draft does happen, but considering the likelihood of selective sweep vs. a bottleneck event, drIft is probably more likely to be an important process in populations than drAft.

  10. #10 razib
    September 8, 2007

    I think the draft does happen, but considering the likelihood of selective sweep vs. a bottleneck event, drIft is probably more likely to be an important process in populations than drAft.

    depends on context though (as does all of evo bio….). i’m not a big believer in the attempts to one-size-catchall as to the one parameter to rule them all ;-)

  11. #11 agnostic
    September 8, 2007

    Well, it’s easier for me to point to Gillespie’s papers and books rather than rehearse the whole thing here. One thing, though: selection happens whenever the environment changes and throw a pop of its optimum, or changes pay-off matrices, or anything else. Environmental change is more likely than pop bottlenecks.

    If we are keeping score based on citations, the relevant one to check is his 1991 book which ties a lot of the threads together (although the term “draft” isn’t there, it is conceptually there). The Causes of Molecular Evolution.

  12. #12 agnostic
    September 8, 2007

    Google Scholar says iTCoME is cited by 567 sources. Ohta’s Nearly Neutral revised paper of 1 year later has less than half that number, and the original 1973 Nearly Neutral paper has 1/3 as many as TCoME.

  13. #13 windy
    September 9, 2007

    I don’t know if there has ever been a study that tests the predictions of the neutral theory on allelic variation… It would be cool to look at, say cytB in a number of independent populations that vary in Ne.. I bet there is variation as predicted…

    cytb being mitochondrial, it does not conform to the expectations:

    Population Size Does Not Influence Mitochondrial Genetic Diversity in Animals
    Eric Bazin, Sylvain Glémin, Nicolas Galtier
    Within-species genetic diversity is thought to reflect population size, history, ecology, and ability to adapt. Using a comprehensive collection of polymorphism data sets covering 3000 animal species, we show that the widely used mitochondrial DNA (mtDNA) marker does not reflect species abundance or ecology: mtDNA diversity is not higher in invertebrates than in vertebrates, in marine than in terrestrial species, or in small than in large organisms. Nuclear loci, in contrast, fit these intuitive expectations. The unexpected mitochondrial diversity distribution is explained by recurrent adaptive evolution, challenging the neutral theory of molecular evolution and questioning the relevance of mtDNA in biodiversity and conservation studies.

  14. #14 Rich Lawler
    September 11, 2007

    I saw a talk by Sean Rice (who is a brilliant evolutionary theorist) at the evolution meetings two years ago in Stony Brook. He showed from first principles that directional selection can, in fact, be stronger in very small populations. It blew me away and was convincing–the talk was called directional stochastic evolution. I’m not sure if/where it’s published.