Dost thou know the equilibrium at panmixia?

If you read a blog about Biblical criticism from a Christian perspective it would probably be best if you were familiar with the Bible. You don’t have to have read much scholarly commentary, rather, just the New Testament. Barring that, at least the synoptic gospels!

At this point, with over 400 individuals responding to the reader survey, it is strange to consider that more people believe they have a handle on what Fst is than the Hardy-Weinberg Equilibrium. First, Fst is a more subtle concept than people often think it is. And second, because the HWE is so easy, important, and foundational to population genetics. I mean [latexpage] $p^2 + 2pq + q^2 = 1$. Could it be simpler???

So a quick ask. If you are one of the people who doesn’t understand HWE or why it is important, please get yourself a copy of John Gillespie’s Population Genetics: A Concise Guide. I understand that not everyone has the time, interest, or money for Principles of Population Genetics, or any of the more “hardcore” texts. But Population Genetics: A Concise Guide will surely suffice to follow anything on this blog.

Or, barring that, please review the online resources which you have available. Two examples:

Graham Coop’s Notes on Population Genetics or Joe Felsenstein’s unpublished textbook Theoretical Evolutionary Genetics.

10 thoughts on “Dost thou know the equilibrium at panmixia?

  1. I wonder if you might be over-interpreting that question. I’m one of your lay readers, science background, even worked in a molecular genetics lab once upon a time, but not a scientist let alone a geneticist. You’ve used Fst so many times in your posts over the years that at some point I had to go look it up and learn what it was. Knowing what it is allows many posts to be comprehensible that otherwise wouldn’t be. HWE is something I actually knew once (or at least was supposed to know on a test) but have long since forgotten the details of and I’d say it’s never been necessary to know the equation form to understand your blog posts. The qualitative meaning, sure, but the question was if we could translate from the eponym to the equation.

    Of course, maybe you have looked at the cross-tabs and your geneticist readers don’t know it either.

  2. I’d would similarly add that there were several concepts that you asked about (such as HWE) that I am somewhat familiar with but don’t know by name. I have a hard enough time keeping track of which notable person goes with which concept in mathematics, physics, psychiatry, law and political science to have much room left for to match names and theories in genetics as well.

    I would observe, however, that physicists seem to fight much more over what gets named after whom than any other discipline. There must be half a dozen significant physics concepts with multiple competing naming claims, while I can’t think of even one right off in any of the other disciplines that I’m familiar with.

  3. I’ll give it a go. I tried starting with Principles of Population Genetics but found it heavy going(Ive only been reading here for a few years and mainly got into it for the posts about religion, but the genetics stuff is quite interesting)
    Btw, Ive bought a few of your recommended books and will probably buy some more in the future. I buy through Amazon UK though, which I assume you dont get compensated for. Dont know if it’s possible or worthwhile to add links to other non US amazon sites aswell, so just a suggestion.

  4. agree. Fst often used. HWE is substrate, not explicitly called out very much. But there’s a bit more to this.

    I’d also say that Fst has a clear intuition as genetic distance. Even if in reality it’s a more complicated stat about population genetic differentiation. So a small number means populations are more alike. Big is different. Near small. Far big. This is a very very easy idea to grasp. Even if the math is subtle.

    So my two cents is…
    Fst: simplified concept easy, math hard, true understanding hard
    HWE: simplified concept medium, math easy, true understanding easy/medium

    Or even simpler: lay readers (like me) never do the math anyway. So we’ll report understanding things based on simplified concepts, not on ability to actually do the work (which requires knowing and really using the math). So there’s real signal here in why people say they understand what they do. Practitioners who can do the math and calculations will report understanding level against doing, well, the actuall math and calculations and problems. Lay readers report knowledge against simplified concepts or often just analogies (physical distance = Fst).

  5. Could it be simpler?
    Sure it could: (p+q)^2=1. or even 1^2=1. When I first encountered the HWE in high school my opinion of biologists plummeted. Who would give (two) names to something that trivial.
    (Also, there is an unnecessary square in your version.)

    [thanks for the typo. so didactically representing the 2pq is pretty important, as a lot of time we’re focusing on genotypes, not just allele frequencies -Razib]

  6. There’s also the irony that Fst is actually defined in terms of the HWE formula–i.e., the decrease of average heterozygosity of subpopulations in ratio to that which HWE would predict if the subpopulations were combined in the total population.

    [bingo, that’s the weird thing. HWE is a null for so many tests/stats -razib]

  7. Hm — I put down that I didn’t know HWE because I didn’t remember all the conditions for it to be valid.

    Also, echoing Nador’s comment above. The nontrivial part of HWE isn’t that p^2+2pq+q^2=1; that’s automatic from p+q=1. The nontrivial part is that (supposing it’s P that has frequency p and Q that has frequency q) that PP occurs with frequency p^2, that QQ occurs with frequency q^2, and that heterozygosity occurs with frequency 2pq. (I too had a high school biology teacher that didn’t seem to be able to grasp this point…)

  8. What’s interesting about the history of the HW formula is that it took a while for scientists to come up with it. Several scientists produced the correct outcome for specific values of p and q, but the general formula was not stated. One might say that that reflected the mathematical ineptness of biologists, but I think that’s not really right. The famous statistician Karl Pearson in a 1904 paper on Mendelian heredity stated the correct proportions for p=.5, but didn’t state a general formula.

    You really have to think about the problem HW solved with some real care to come up with the formula: you need to get the basic model right. The beauty of HW is that it predicts that (infinite) randomly mating populations will generate genotypes in HW proportions in one generation, no matter the previous proportion of genotypes. The previous generation might have been entirely homozygotes, or the maximum possible proportion of heterozygotes, or anywhere in between, and one round of random mating will get them to HW proportions. This certainly isn’t obvious at first blush.

    The most direct way of establishing the HW result is to assemble into a table the proportion of genotypes in the first generation against the various possible mating combinations, calculate the frequencies of combinations into genotypes of progeny, assemble those terms at the end, and then, via some algebraic simplification, prove that the HW proportions are found in the progeny. One might also derive far more simply HW by starting with the assumption that the genotypes randomly mate iff all of their gametes taken together are randomly matched. But this conceptual leap is not so obvious, and probably requires the more detailed approach for inspiration, if not justification.

  9. And I thought it was a reference to F1 F2 hybridization.

    Sorry….just knock one off of that survey.

Comments are closed.