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If a population isn't evolving because it's in Hardy-Weinberg (HW) equilibrium, then I know that both genotype and allele frequencies must stay constant.

My question is, can evolution still not occur even if Hardy-Weinberg conditions aren't met? In all of my books, the conclusion seems to be that if HW conditions are met, then evolution doesn't occur. However, they don't clarify if HW conditions being met is both a necessary and sufficient condition for evolution to not occur (they only imply that it's sufficient).

Any thoughts?

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    $\begingroup$ Could you clarify what specially you mean by 'evolution'? Are you referring to the evolution of a morphological trait, molecular evolution, evolution as a general response to selection? I'm also a little bit confused as to how this relates to the title of the post. $\endgroup$
    – user438383
    Jul 27 '20 at 17:26
  • $\begingroup$ That’s important because by definition, if HWE assumptions are all met then there can’t be any selection occurring. $\endgroup$
    – user438383
    Jul 27 '20 at 17:40
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At the risk of further confusing the issue (there are already 2 answers focusing on different aspects!!), I am going to focus on a somewhat different aspect of this question that I think we need to nail down before it can be addressed.

Going mostly off your question title, it would help to know what you mean by genotype vs. allele frequencies. These are quite different, and it's not clear how you are trying to employ them. Speaking strictly, we use alleles to talk about genetic variation within a locus, and genotype variation to also mean variation across loci as well (how alleles across loci are sorted into individuals; this is sometimes also called "gamete frequency"). Of course, people generally talk about HWE in the context of only a single locus, which means that it is easy to get tripped up here.

It is possible for us to have non-equilibrium genotypes while also having equilibrium allele frequencies, in direct response to your question title. A trivial example of this is linkage: when two loci are very close to each other on a chromosome, their alleles will be more closely correlated than genes on different chromosomes. This yields the phenomenon with the unfortunate name linkage disequilibrium (LD), which implies nothing about evolution or HWE but rather about a non-equilibrium mixing of alleles into genotypes.

For context, it is quite common to apply tests of HWE locus-by-locus in genomics, as a sort of quality control or preprocessing step. It is also common to measure LD for relevant pairs of loci, but there is not much biological relationship between these measures (even though LD can be thought of as an extension of Hardy-Weinberg to a multilocus case, for historical perspective see here.). In any realistic case, global linkage equilibrium across the genome is very unlikely, whereas HWE for most loci is very likely.

As a thought experiment, imagine that a (neutral) inversion arises, and then starts segregating. All of the alleles remain at HWE, but suddenly you have new LD (genotypic disequilibrium) that wasn't there before.

With all that out of the way, I see no reason why evolution could not happen at the level of overall genotypes even in the case that HWE is maintained statistically. This can be achieved by the evolution of e.g. sign epistasis, I am sure there are other examples as well that would yield apparent HWE while trait evolution is technically still going on.

I think that it might be fair to say that monogenic evolution isn't happening with apparent HWE, I don't think that you can say the same thing for polygenic evolution.

I'll finish by just saying that I refer specifically to the statistical phenomenon of HWE, and not to the assumptions themselves (which would be tautological; "can evolution happen if you assume there's no evolution?" as commenters point out). After all, You can violate most of the assumptions of HWE and still end up with allele frequencies that look like HWE:

Although statistical deviation from Hardy-Weinberg expectations generally indicates violation of the assumptions of the theorem, the converse is not necessarily true. Some forms of natural selection (e.g., balancing selection, which maintains multiple alleles in a population) can generate genotypic frequency distributions that conform to Hardy-Weinberg expectations. It may also be true that migration or mutation is occurring, but at such low rates as to be undetectable using available statistical methods. And, of course, all real populations are finite and thus susceptible to at least some evolution via genetic drift.

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Where do you get that populations aren't evolving?

A population might be in HWE for a particular trait if there is no selection on that trait, but that doesn't mean that there is no selection or drift happening on any trait!

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  • $\begingroup$ True but that wasn't the main purpose of my question. The more important part is regarding whether HW is necessary not just sufficient $\endgroup$
    – Ally
    Jul 27 '20 at 17:14
  • $\begingroup$ @Ally Maybe an example of what you are thinking of would be helpful. As-is, to me this question just raises my eyebrows. I think you might have confusion somewhere but I'm having trouble pinpointing where that is. $\endgroup$
    – Bryan Krause
    Jul 27 '20 at 17:24
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    $\begingroup$ If a trait is under selection, by definition it's not in HWE. $\endgroup$
    – swbarnes2
    Jul 27 '20 at 17:33
  • $\begingroup$ Yeah so reiterating the question in an if..then format might make it more clear. Right now, I'm getting that "if HW, then no evolution", which also implies "if evolution (aka if a trait is under selection), then no HW". However, from the original premise it does not necessarily follow that "if no evolution, then HW". So my question was basically asking if there was no evolution occurring, would that necessitate the population being in HW or if there was some other mechanism / set of conditions that would allow no evolution to occur $\endgroup$
    – Ally
    Jul 28 '20 at 18:07
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    $\begingroup$ The HW principle is not a mechanism. They are equations that build a rather simplistic model that sometimes is applicable and useful in real life. $\endgroup$
    – swbarnes2
    Jul 28 '20 at 20:57
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Let me focus on the necessary and sufficient part: such a language is suitable in mathematics, but does not really have much meaning in evolutionary/statistical context. Instead we talk about rejecting the null hypothesis, which does not mean accepting the alternative hypothesis. Equally, a failure to reject the null hypothesis does not mean that this hypothesis is true.

Hardy-Weinberg is a null model of evolution with about a dozen of assumptions. It is not a model of "no evolution", but rather a model of how evolution happens all the time (but it seems like "no evolution" in the sense that not much interesting is happening). Rejecting this null model/hypothesis means that some of its assumptions are violated. However, if the genotype frequencies do satisfy HWE, it doesn't automatically mean that the assumptions of this model are satisfied.

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