Evolution disproven — by Hardy and Weinberg?

Over at Uncommon Descent, “niwrad” has argued that the equations of theoretical population genetics show that evolution is unlikely.  niwrad says that the equations of theoretical population genetics

consist basically in two main equations: the Hardy-Weinberg law and the Price equation.

Furthermore niwrad says that

The Hardy-Weinberg law mathematically describes how a population is in equilibrium both for the frequency of alleles and for the frequency of genotypes. Indeed because this law is a fundamental principle of genetic equilibrium, it doesn’t support Darwinism, which means exactly the contrary, the breaking of equilibrium toward the increase of organization and the creation of entirely new organisms.

I just finished teaching my course in theoretical population genetics (with lots of equations, but actually not the Price Equation, as it happens). And I can say that the statement about the Hardy-Weinberg law shows niwrad to be mixed up about the import of Hardy-Weinberg proportions. Let me explain …

If we have a gene with two alleles whose gene frequencies are p and q, random mating in effect brings together a pair of randomly chosen copies in each individual. Thus the probability of genotype AA is p2. The probability of the heterozygote is 2pq, and the probability of aa is q2. The genotype frequencies depend on the gene frequencies in the previous generation.

These proportions are sometimes called Hardy-Weinberg “equilibrium”, because if you change the genotype frequencies in a population in a way which does not alter the gene frequencies random mating will bring the genotypic composition of the population back to the same Hardy-Weinberg proportions. Thus if you have a gene frequency of 0.2 for A, the Hardy-Weinberg proportions will be 0.04 : 0.32 : 0.64. Now if we take half of the heterozygotes and replace them by a 50:50 mixture of the two homozygotes, we would have genotype frequencies of 0.12 : 0.16 : 0.64. In that population the gene frequency of A is unchanged, still 0.2. Now if these individuals mate randomly and have offspring, we once again get the Hardy-Weinberg proportions 0.04 : 0.32 : 0.64.

But what happens if we change the gene frequency?  For example if we kill off all the AA individuals, we then have a population with genotype frequencies 0 : 0.32/0.96 : 0.64/0.96 which is 0 : 0.3333 : 0.6667.  In that population of survivors, the gene frequency of A is now 0.16667 instead of 0.2. After they mate randomly and have offspring, the genotypes are in Hardy-Weinberg proportions at the new gene frequency, and their genotype frequencies are 0.027778 : 0.27778 : 0.694444. The gene frequency is now still 0.16667, and has not gone back to 0.2. So evolutionary forces that change gene frequencies are not counterposed by Hardy-Weinberg “equilibrium”. The gene frequency has no tendency to return to previous values. Thus continued natural selection can gradually change the gene frequencies.

In my (free, online) textbook Theoretical Evolutionary Genetics this is covered on page 7. Chapter II is devoted to the (many) equations for change of gene frequencies under natural selection. I hope that niwrad will taken a look at that chapter, and let us know whether it shows that the Hardy-Weinberg “equilibrium” is a force preventing response to natural selection.

19 thoughts on “Evolution disproven — by Hardy and Weinberg?

  1. Is it dumb to ask why it’s called gene frequency instead of allele frequency?

  2. Not a dumb question at all. What it really is, is an allele frequency. Although sometimes called that, the term “gene frequency” became established years ago and can’t be dislodged.

    The phrase “a gene” is itself ambiguous. Does “a gene” mean a particular copy, such as the copy of Hemoglobin Beta that I got from my mother? Or does it mean a particular allele, such as the normal allele of Hemoglobin Beta? Or does it mean a locus, such as the Hemoglobin Beta locus? (It means all of these, at different times).

  3. On that thread at UD there are:

    3 comments (TLDR) from BA77
    One from Joe who says “Mother Nature + Father Time + some unknown process = the diversity of life” but who fails to realize “some unknown process” is ID’s current claim.
    Then Phinehas says “But how does one measure reproductive success?”. I wonder how many brothers and sisters he has.
    JDH then points out that “Number of rigorous mathematical models of evolution = 0.” then “There probably are rigorous mathematical models for micro-evolution, but no serious person denies the existence of that, and personally I believe it is a feature put in by the Designer.”.
    Lastly Axel wonders when the Darwinists will give up: “When will they finally emerge, hands in the air, from the jungle-canopy of Darwinian fantasmagoria, which they have endlessly elaborated upon in the teeth of all the extraordinary advances in mathematical and empirical studies, refuting it, shouting, ‘Long live the (naked) Emperor!’”.

    And last comment is from Mung.


    The plaintive cry of the ignored.

    So, evolution disproved? If so, not much of a reaction from the UD crowd. But then again they already *know* evolution is bunk. They knew it before they knew anything about it. Even after too.

  4. The niwrad thread about Hardy-Weinberg “equilibrium” showing that natural selection does not work continues, but no one there is addressing the question. No one is trying to defend niwrad’s actual argument. If niwrad had shown that Hardy-Weinberg “equilibrium” was a barrier to the effectiveness of natural selection, then you’d think that they would be driving home the point, explaining in great detail why the argument of this thread is wrong and niwrad is right.

    Instead the only direct mention of our thread is a dismissal on grounds that it is just microevolution. Well, niwrad’s argument was an argument that natural selection within a population would not work. They don’t seem to have figured that out. Or else they’re implicitly acknowledging that niwrad is wrong, but doing so really quietly.

  5. Joe Felsenstein,

    Therein lies the beauty and attraction of ID!

    Nobody get’s to be wrong at all. The only person who is wrong was Darwin and his followers.

    The “big tent” entrance fee is simply to keep your mouth shut and not point out the errors that others make. In return they will do the same for you. They will even keep up the pretense by creating their own “peer reviewed journals” which while they don’t publish very often they exist, don’t they? Therefore ID = science and all is well in the big tent.

  6. Raising the issue “how does one measure reproductive success” is relevant, but the UD crowd seems to be unaware that there have been hundreds of papers on the topic. In 1981 I published the only complete bibliography of theoretical population genetics ever attempted. It listed 7,982 papers. (You can download it from here). How one gets models to fit complex life cycles has been worked on a lot (Google “Fisher” “reproductive value” for example).

    Meanwhile advocates of ID repeatedly try to give their readers the impression that evolutionary biologists refuse to be quantitative.

  7. Joe Felsenstein,

    Misrepresentation of reality is in fact the only tool in their toolbox. You can see this every day at UD as they take somebody else’s work and spin it in an ID way.

  8. niwrad: As known, Darwin introduced no math whatsoever in his theory of origin of species.

    That’s not quite accurate. Darwin provided a diagram that encapsulates the mathematics of bifurcating descent.

    niwrad: The Hardy-Weinberg law mathematically describes how a population is in equilibrium both for the frequency of alleles and for the frequency of genotypes. Indeed because this law is a fundamental principle of genetic equilibrium, it doesn’t support Darwinism, which means exactly the contrary, the breaking of equilibrium toward the increase of organization and creation of entirely new organisms. To claim that the Hardy-Weinberg law explains evolution is as to say that in mechanics a principle of statics (immobility) explains dynamics (movement and the forces causing it).

    Actually, it does just that. By static physics, a column will support a beam, but disturb the column, and the beam may fall.

    Joe Felsenstein provides an important case above. More generally, Hardy-Weinberg assumes an infinite population, random mating, independence of traits, no mutation, and no selection. If any of these conditions are changed, then there is no equilibrium. A finite population results in genetic drift, for instance.

  9. If evolution has been “disproved” are there any signs of what the IDers would like to replace it with?

    I don’t think textbook publishers will be too happy to replace their larger tomes with a single sheet of paper that simply notes “design”.

  10. Barry creates a OP noting that TSZ is a “symbiotic site”.

    The “Skeptical” Zone, Where You Can Be Skeptical of Anything (Except Currently Fashionable Intellectual Dogmas)

    It seems that the regular posters at TSZ are skeptical of everything but the received wisdom, accepted conventions and cherished dogmas of the academic left.

    Is that right Barry? Well Casey Luskin has something to say about that also:

    Politically speaking, the debate over ID and Darwinism does not pit right against left. Rather, it is about free speech vs. censorship. There are folks on the left, and the right, who support free speech and freedom of scientific inquiry, advocating the rights of scientists and educators to dissent from the orthodox Darwinian viewpoint.

    But anyway. barry goes on to say:

    The true skeptics of the early twenty-first century are those willing to take on the dogmas of the academic elite, people like Bill Dembski, Michael Behe, and Jonathan Wells.

    But the problem Barry is that they tackled the dogma of the academic elite. And failed. If Dembski really had something, really had something that universal acid of truth would have ate away at the dogma (who does not like better results?) and replaced it.

    But it did not. It is not. And it will not.

    Why? Have you ever considered that they were just plain wrong? You can’t win every case, not every new idea challenging dogma is actually right.

    They had a fair crack at it. Books have been published. Films have been made.

    Yet all that remains for all that effort, quite literally, is UncommonDescent where ID supporters band together and mutually support each other’s contradictory ideas.

    Why don’t the posters at TSZ see the glaringly obvious irony of their enterprise?

    If you had the guts to come over here, perhaps you could explain on the record where the posters at TSZ are wrong. You see Barry, I can’t post at UD but you can post here.

    The first comment on your post Barry:

    No surprise here, unfortunately. Most so-called skeptics lack the courage and the vision to question all paradigms and would rather retreat into their comfort zones of hypocrisy.

    What amazes me is that you cannot see that is you. TSZ is not a comfort zone of hypocrisy for the single reason that anybody and everybody is welcome to post here. Yet the same is not true of UD. So OldArmy94 is talking about you, I’m laughing and the only person in the room who does not get the joke is you, Barry.

  11. Barry also notes:

    Emerson writes about how the dogmas of secularism act as a type of “revelation” that boxes in thinking in a way that the thinkers probably don’t even perceive at a conscious level.

    It seems to me that “boxed in thinking” is much more productive then any other sort in that case.
    If Barry etc are thinking outside the box then they’ve produced some books and films in support of ID.

    As of June 2012 there are 318,926 scientific papers in PubMed that mention ‘evolution’.
    To date however, there are no scientifically peer-reviewed research articles that disclaim evolution listed in the scientific and medical journal search engine Pubmed.

    So Barry, you keep on thinking outside that box. It seems to be protecting the rest of us from bad, unproductive and unoriginal ideas.

  12. The irony for me is that Barry has never shown any ability to be skeptical about his own position.

    Despite the fact I’ve got Joe, only today, to basically say that ID is totally unsupported and tells us nothing about anything Barry never addresses that and proclaims that the people with the data and evidence on their side should be more skeptical.

    Ever occurred to you Barry that you are in fact in error? That your utter certainty in your position might be based on, well, nothing much at all really?

    Ever wonder Barry why the whole “ID Enterprise” never seems to actually go anywhere or do anything? Never wonder why each ID journal, without fail, comes and goes after a few issues? Ever wonder why even in those journals there were no “this is the evidence for ID” type papers?

    Never wonder why ID seems to be built on what Darwinism can’t do Barry?

    Never wonder why people like Joe are among the most vocal proponents of ID?

    Never wonder why KF is too scared to come here and argue his case on the basis of “rudeness” when Joe is told off by KF for “rudeness” constantly?

    Tone Joe

    Nah, I guess you never have wondered any of those things Barry. You don’t seem to have the imagination for it to be honest, if you can’t see the irony in doubting the ability of posters here to consider fairly another’s viewpoint when you run a site where you ban people for speaking out of turn.

  13. OMagain,

    Darwin upended thousands of years of conventional thinking by thinking outside the box. Just as Copernicus and Galileo and Hutton had done.

    ID is the older, conventional idea, replaced by Darwins ideas. ID was firmly established as the conventional idea, Fully accepted by Darwin at the beginning of his career.

    So regardless of who’s right, let’s at least get the sequence of ideas right.

  14. petrushka,

    I suppose what I’m getting at how Barry perceives “boxed in thinking” to be what I talk about when I say “thinking outside the box”

    Barry said:

    Emerson writes about how the dogmas of secularism act as a type of “revelation” that boxes in thinking in a way that the thinkers probably don’t even perceive at a conscious level.

    And what I’m saying if that “evolutionism” is the result of “boxed in thinking” as in the above quote then give me boxed in thinking.

    I’m not sure where you are getting from what I wrote that the sequence of events was not as you note.

  15. . . .
    Never wonder why KF is too scared to come here and argue his case on the basis of “rudeness” when Joe is told off by KF for “rudeness” constantly?

    Tone Joe

    So Joe is still allowed to post at UD despite behaving in a way that would get any ID opponent banned? Barry’s double standard and kairosfocus’ hypocrisy know no bounds.

    ETA: This probably belongs in the Sandbox.

  16. OMagain,

    Sorry, I didn’t catch the reference to Emerson.

    It’s true that many people accept conventions without thing them through. Most of us accept the Copernican model of the solar system without thinking it through and without verifying it independently.

    For someone in 1913 it would be reckless to accept evolution without thinking it through. And acceptance would best be provisional.

    A hundred years later, most people can safely accept it.

    As for “secularism,” I can’t say one way or another what the correct attitude should be. My transformation from confirmed Episcopalian to agnostic began at age 11 with the discovery of books on world religions. It became obvious to me that faith in a particular religion was an accident of birth.

    My own attitude toward teaching the controversy is that everyone should be exposed in school to the history of great discoveries. Everyone should be at least minimally aware that things like the solar system are relatively new ideas and that the arguments for and against them can be made without expensive or modern instruments.

    Same with much of Darwin’s arguments.

  17. petrushka,

    I think much of it is about how you delegate trust. You can’t verify everything, rather you can make rational decisions about who is trustworthy. Until shown otherwise, that source is trusted.

    And that seems to be the way of it. I certainly agree that schools should teach that not everybody thinks the way we do now, and that our knowledge is based on generations of ideas layered upon each other, not all right.

    I think the Simpsons episode where Marge ended up reading “Origin” is a great example – I once had an argument back in the day of ‘overwhelming evidence’ with ‘Troutmac’ where he did not believe that Darwin addressed the origin of life (to say he’s not dealing with it) in his book. When he finally read the relevant pages he backed down and admitted he was wrong. He verified it himself, and (surprise surprise) he’d been fed wrong information by the ID cabal 😛

  18. A curious strawman. On a 105-year-old equation!

    To claim that the Hardy-Weinberg law explains evolution is as to say that in mechanics a principle of statics (immobility) explains dynamics (movement and the forces causing it).

    Is that claim made? As I understand it, it gives the baseline position in which NO evolution can be said to occur, and the inevitable result that provided there is no change in allele frequency, random allele pairs from any starting mix of pairs, however far from ‘equilibrium’, will result in the same genotype frequencies in the next generation, because ultimately it does not matter how they are linked this generation if they assort independently in making the next.

    It only holds if

    1. mutation is not occurring
    2. natural selection is not occurring
    3. the population is infinitely large
    4. all members of the population breed
    5. all mating is totally random
    6. everyone produces the same number of offspring
    7. there is no migration in or out of the population

    It ‘explains’ evolution in relief, by demonstrating the restrictive and unrealistic conditions necessary to turn evolution off.

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