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The post Solving Hardy Weinberg problems offers an easy explanation of Hardy-Weinberg rule. The current top answer explicitly does not talk about the assumptions of Hardy-Weinberg. A model makes sense only if one is able to tell its domain of definition and therefore it is critical to understand the assumptions underlying Hardy-Weinberg assumptions.

What are the assumptions of Hardy-Weinberg rule?

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Here are the assumptions to the standard Hardy-Weinberg rule (HWr) formulation

$$p^2 + 2p(1-p) + (1-p)^2 = 1$$

See Solving Hardy Weinberg problems for more info about this formulation.

Assumptions

The locus of interest is bi-allelic

This is an obvious assumptions, however it is very easy to extrapole HWr to any number of loci.

Organisms are diploid

This is another obvious assumption that is very easy overcome. This also means that HWr does not hold for loci present on sexual chromosomes as those chromosomes do not display a simple diploid behaviour.

Only sexual reproduction occurs

If some individuals are able to undergo non-sexual reproduction, then the rule does not hold anymore. See also Panmixia as these two assumptions are related.

Panmixia

Panmixia is often called "random mating". Panmixia is the state where each individual is equally to mate with any other individual in the population (including itself). There is therefore no population structure and no mate choice.

Let $N$ be the number of individuals in the population, in absence of selection (see If selection, it must be on fecundity alone), the probability to mate with any given individual (including itself) is $\frac{1}{N}$. You will note that it requires that individuals are able to self (but not clone as reproduction must still be sexual).

If selection, it must be on fecundity alone

If selection occurs, then it must on fecundity (right before reproduction). If selection occurs on survival during the lifetime, then the selected genotypes will be in excess in comparison to Hardy-Weinberg expectations.

If migration, it must be right before reproduction only

For the same reason as above, if there is migration, then it must be right before fecundity. If migration occur during the lifetime, then it will have a very similar effect than selection. Selection would increase the frequency of selected genotypes above HR expectations. Migration would increase the frequency of incoming genotypes above HR expectations.

Non-overlapping generations

This means that everyone reproduce in the exact same time and die right afterward. Very few species would qualify for such assumptions.

Population of infinite size

If previous assumptions already seemed hard to meet in the real world, the assumption of infinite population is absolutely impossible to meet.

Deviation from this assumption will cause deviations from expectations. Such deviations are often tested via a Chi squared goodness-of-fit test.

Note by the way that if the population is of infini size, there is no mutation, no migration and no selection, then there is no evolution.

Other assumptions

Biology is a science of complex systems. There are always other assumption one might want to consider. For example I did not talk about sex-specific selection or sex-specific mutation rate. But I am hoping that with the above I went over the most important assumptions.

So what's the point of HWr?

All models are wrong but some are useful. There exist no real life example of a population that perfectly fit into HWr assumptions but it does not mean the model isn't useful. Actually most population approximate HW expectations quite well. You will note also that it is by understanding how a scenario lead to a specific observation that we can interpret how derivation from the expectations can be achieved.

So yes, HWr is one of the most basic and most important rule in population genetics. It is so basic, that I would hardly name it in any fancy way as it is just the simple application of basic probability theory. See Solving Hardy Weinberg problems for more info.

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  • $\begingroup$ You missed that (i) generations are assumed to be discrete and without overlap and that (ii) allele frequencies are unbiased between sexes. $\endgroup$ – AlexDeLarge Apr 17 '17 at 21:03
  • $\begingroup$ @AlexDeLarge Thanks. I added "Non-overlapping generations". When you say "allele frequencies are unbiased between sexes", is it any different from what I meant in his also means that HWr does not hold for loci present on sexual chromosomes as those chromosomes do not display a simple diploid behaviour.? $\endgroup$ – Remi.b Apr 17 '17 at 21:12
  • $\begingroup$ It just means that males and females do not differ in allele frequencies. If they did - and given the assumptions mentioned in your answer there is no obvious reason (you can construct it implicitly from the panmixia assumption, I guess, but this is too vague) why they would not -, the population would not be in HWE. $\endgroup$ – AlexDeLarge Apr 17 '17 at 21:30
  • $\begingroup$ Yes... "males and females do not differ in allele frequencies" sounds more like a consequence of the violation of specific assumptions that we should make sure to include. I see the mention of this assumption in the wikipedia article. I would not know how to justify the addition of this assumption so I'll leave it out for the moment until someone can teach me more on it. $\endgroup$ – Remi.b Apr 17 '17 at 21:36
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    $\begingroup$ @canadianer: That's why I don't like Euler's identity. 0=0 ... come on. $\endgroup$ – AlexDeLarge Apr 18 '17 at 7:24

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