Talk:Hardy–Weinberg principle

formulas

What is going on here? You wikipedians have really screwed this up! There are dozens of fancy formulas but not once is the simple formula: (p^2 + 2pq+ q^2 = 1) mentioned. What are you guys doing!!! that should be the first thing on this page.

All these pages take 2 semesters of college calculus to understand. Seriously, take a look at the "set theory" page it's utterly incomprehensible!

It's in the lead as well as in the derivation paragraph. Also, that is algebra not calculus. StephenPCook (talk) 01:49, 31 October 2009 (UTC)

StephenPCook, what does lead mean? 1st paragragh? If so, it's not on there. Also, I cannot find it under the derivation paragraph. Even if I missed it, 99.999% of people who view this wikipedia article are simply looking for p^2 + 2pq+ q^2 = 1. I can't believe that a 10+ page article on HW has the equation mentioned once or twice (again, note that I even used the "find" function and still couldn't find this equation mentioned once).

I'm a first year medical student, with a B.S. in Chemistry and a master's in Biochemistry, and I can't understand more than half this article. I'm pretty sure I also have an average IQ. All I wanted was the equation. I had to use another website to get it! :) Boonshofter 13:51, 20 November 2010 (UTC) —Preceding unsigned comment added by Boonshofter (talk • contribs)

Agreed. I added {{technical}}, so hopefully someone who can translate this will fix it soon. Habstinat (talk) 03:32, 28 February 2012 (UTC)

Agreed, that the article uses only algebra, not one jot of calculus, that derivation of (p^2 + 2pq+ q^2 = 1) precedes statement and proof of the Hardy-Weinberg principle, and that the math is ordinary starting material for any second-year evolutionary biology class. Failure of chem / biochem majors and others to appreciate this is why Hardy needed to do it. Let's have a go at the first paragraph. Smcewincarr (talk) 19:44, 24 October 2012 (UTC)

Explanation

That formula is not descriptive of Hardy-Weinberg equilibrium or the Hardy-Weinberg principle, and does not deserve a more prominent place in the article. If you can provide a reliable source saying that "the Hardy-Weinberg principle states that p^2 + 2pq + q^2 = 1" (and I doubt it), I may eat my words, but more likely I will suggest that your source is sacrificing accuracy for a mathematical soundbite. Sometimes, people call "p^2 + 2pq + q^2 = 1" the Hardy-Weinberg EQUATION, but it only applies to a special case, and is potentially misleading to boot. A population that is not at H-W equilibrium will still have p^2 + 2pq + q^2 = 1.

Here is why:

If you have only two alleles, A and a, for a given gene, then every gamete (sperm or egg) has to have either one or the other. If 20% of gametes have A, then 80% must have allele a. In this case, we have p = .2 and q = .8. In general, the percentages have to add up to 100%. So p + q = 1. So... q = 1 - p.

Now, try substituting 1-p for q in that "p^2 + 2pq + q^2" expression...

p^2 + 2pq + q^2 = p^2 + 2p(1-p) + (1-p)^2 = p^2 + 2p - 2p^2 + 1 - p^2 - 2p = 1.

In other words... if you assume that you have only two alleles, then p^2 + 2pq + q^2 = 1 ALWAYS, no matter WHAT assumptions you make! It's algebra, not genetics.

The real Hardy-Weinberg principle is stated repeatedly in the article. It should be stated more clearly early on, but here it is, stated in the plainest English I can muster:

• In an idealized general case, allele and genotype frequencies reach a stable equilibrium VERY quickly, and stay stable across generations. They don't change unless something MAKES them change.

• In the special case where you have one gene locus with two alleles, which we'll call "A" and "a" with allele frequencies p and q, the genotype frequencies at this equilibrium end up being:

f(AA) = p^2

f(Aa) = 2pq

f(aa) = q^2

Of course, f(AA) + f(Aa) + f(aa) = 1, because that sum represents the entire population. The meat of H-W is in the individual terms, not in the fact that they sum to 1.

"p^2 + 2pq + q^2 = 1" is, at best, a way to check results. There are other problems with this article - the Hardy derivation is opaque and that the triangle diagram is woefully ambiguous. It could definitely be improved by cutting down the jargon and adding real-world examples taken from good genetics textbooks. — Preceding unsigned comment added by 75.6.252.67 (talk • contribs) 06:55, 10 February 2011

Old comments

I actually have not read Hardy and Weinberg's original work -- so this may be historically inaccurate; maybe it is theoretically inaccurate too, in which case I hope you will explain why, but: shouldn't the conditions for HWE include the absence of migration (I am not just asking about flow; if in G2 a selective group of people leave the population, or another group moves in, won't that immediately alter the frequencies)? Or is this implicit? Slrubenstein

Yes, lack of gene flow/migration is a prerequisite for HWP. I have added it. Thanks for pointing it out. -- Lexor 05:05 5 Jul 2003 (UTC)

Move

Hi. Moved to Hardy--Weinberg principle on the basis that this should be an em dash because the Hardy and Weinberg were unconnected. Had one person called Fred Hardy-Weinberg discovered it then the en dash would be okay. MediaWiki will implement this in the future. This also means that Hardy—Weinberg principle, should be a link - this is [[Hardy—Weinberg principle]] Dunc Harris | Talk 13:47, 26 May 2004 (UTC)

Should it not just be a hyphen? (I.e. ‘Hardy-Weinberg principle’.) —James Haigh (talk) 2013-12-08T04:45:55Z

Evolution in the assumptions

My objections to using evolution in the assumptions for H-W are twofold.

• The main result of the HWP is that the population does not evolve, in either a micro- or macro-evolutionary sense. Including evolution in the definition weakens this — it is no longer a result of H-W, the lack of evolution seems to cause HWP.
• On a macro-evolutionary scale, one of the forces listed is actually anti-evolutionary (works against the evolution of new species). It is still part of the assumptions, but can't truly be considered evolution.

There is enough mis-information about evolution that we need to be careful when writing about peripheral issues. Ted 00:01, 8 March 2006 (UTC)

F-Statistics

What F-Statistics are these? The F-Statistic given by Sewall Wright is

$F={\frac {\operatorname {E} {(f(\mathbf {Aa} ))}-\operatorname {O} (f(\mathbf {Aa} ))}{\operatorname {E} (f(\mathbf {Aa} ))}}\!$,

which is the normal inbreeding coefficient for a single population. I will change it unless someone can give me a reference to the equation in the article. Ted 21:29, 10 March 2006 (UTC)

Done. Ted 18:53, 11 March 2006 (UTC)

Polyploidy

It seems to me that the polyploid generalization is, in fact, wrong. The key to HWP is that each allele in an individual is selected independently at random from the allele frequency in the previous generation. However unless n-ploid mating actually involves n individuals, which I believe it doesn't, independence will fail. --Vfreeh

That is misreading HW. The key to random mating is that gametes are combined at random. For tetraploids, the gametes are diploid. What kind of polyploid it is will determine how the gametes are created in terms of independence of the alleles in the gametes. True amphidiploids would prove to be problematic. Ted^Talk/_{Contributions} 01:15, 1 August 2006 (UTC)

What I meant there was "what makes HWP true in the diploid case is that each allele in an individual is selected independently at random [which in the diploid case is equivalent to gametes being combined at random]". I have to admit that I don't know a whole lot about polyploidy but it seems that if you consider a tetraploid case in which the population is 50% AAAA and 50% aaaa, then the gametes produced will be 50% AA and 50% aa and random mating will result in a next generation which is 25% AAAA, 25% aaaa, and 50% AAaa. This is not what the current polyploid generalization predicts, nor is it even an equilibrium. --Vfreeh 04:58, 8 August 2006 (UTC)

That is the reason for the statement in the article: "Depending on whether the organism is a 'true' tetraploid or an amphidiploid will determine how long it will take for the population to reach Hardy-Weinberg equilibrium." It has grammatical problems, but it states that H-W proportions will be reached, asymptotically, not immediately (similar to sex-linked). With "true" amphidiploids, the alleles pair in pairs, while with a "true" tetraploid, they pair up at random from among the four alleles.

Degrees of freedom for Pearson's chi square

I think the description for the degrees of freedom for the Pearson's Chi-squared test needs modification.

Here's the statistical theory description of how to derive the degrees of freedom for the chi-squared distribution to which Pearson's statistic converges as the amount of data tends to infinity.

The degrees of freedom for Pearson's chi-squared is equal to the difference in the number of parameters associated with the statistical models that appear in the null hypothesis and the alternative hypothesis.

In the given example, the general probability model describing the proportions of the population bearing the three different genotype classes AA, Aa and aa is a multinomial with proportions p1, p2 and p3 respectively. However, p1 + p2 + p3 = 1.0 so p3 is just (1.0 - p1 - p2). Therefore, the general probability model contains two independent parameters, p1 and p2. The parameter space for this model is two dimensional.

Under the null hypothesis that the allele frequencies follow the Hardy-Weinberg law, the classes AA, Aa and aa occur with proportions p*p, 2*p*q and q*q where p + q = 1.0. Thus q = (1 - p) so the restricted probability model contains one independent parameter, p. Under Ho, p1 = p*p, p2 = 2*p*(1-p) and p3 = (1-p)*(1-p). The parameter space for this model is one dimensional.

The Null Hypothesis model has one degree of freedom associated with its model. The Alternative Hypothesis has two degrees of freedom associated with its model. Under the null hypothesis, Pearson's Chi-squared statistic has a distribution that converges to a Chi-squared distribution as the amount of data tends to infinity, and the degrees of freedom of that Chi-squared distribution equals the difference in the dimensions of the parameter spaces associated with the alternative and null hypotheses, or (2 - 1) = 1 degree of freedom in this case.

I know the above discussion is not ready for inclusion in the article. It needs some smoothing over, but it represents more accurately the statistical theory associated with determining the degrees of freedom.

The current discussion stating that a degree of freedom was lost because the expected values were estimated from the observed values is not relevant. The expected values for Pearson's chi-squared test statistic for contingency tables always use the observed values to calculate the expected values.

I will attempt to craft a description of how to determine the degrees of freedom by considering the number of independent parameters under the null and alternative hypotheses and propose a change to this article. If anyone more articulate than I can do this, that would be valuable.

Smckinney2718 23:47, 2 November 2006 (UTC)Steven McKinney, Statistician Nov 2, 2006

Reference: I.J. Good (1973) "What Are Degrees of Freedom?" The American Statistician, Vol 27, No. 5 pp. 227-228

"The expected values for Pearson's chi-squared test statistic for contingency tables always use the observed values to calculate the expected values." And, because of that, the degrees of freedom is (r-1)(c-1) and not rc-1. Most likely, the explanation is simply not needed. Genetics411 02:45, 8 November 2006 (UTC)

discrete generations?

I'm new to genetics and I'm not sure what a "discrete generation" is. I did a google on it but its mainly complex papers I don't understand. What is a discrete generation? Also, can this be clarified in the article, or at least create a page on the term and link to it from here? Thanks very much, --Urthogie 15:55, 6 February 2007 (UTC)

Discreet means that they are non-overlapping. So one generation cannot reproduce with the next. It just makes the maths a bit easier. --I am not a dog (talk) 00:18, 25 March 2008 (UTC)

Evolution

I don't think that "It is possible to represent the effects of Natural Selection and its effect on allele frequency on such graphs." really gets across one of the most useful conclusions one can make with a HWP. An additional comment, something in the vain of, "If there is a discrepancy between the HW prediction and an observed frequency of an allele in a population, especially if this discrepancy changes over multiple generations, then that is evidence that the population is evolving" might be appropriate, though (sadly) controversial. —The preceding unsigned comment was added by 66.24.17.198 (talk) 16:54, 3 March 2007 (UTC).

Subject-Appropriate information

I have the impression that this article includes superfluous information about statistics. Perhaps we should consider an example that is less verbose and simply reference the appropriate entries on statistical analysis. neffk 06:36, 14 April 2007 (UTC)

Image:Hardy-Weinberg.gif

I'm a bit confused about this graph. It seems to indicate that the frequency of A is q and the frequency of a is p, while the article (in the intro ("Their frequencies are p and q; freq(A)=p and freq(a)=q.") and the Derivation section) says the opposite. So which is right? Also, the graph is not very clear and it might be confusing to someone who didn't understand HWP. I think it should be replaced with something consistent with the article and easier to understand. --Anakata 22:33, 14 June 2007 (UTC)

The graph of the Hardy-Weinberg equation needs fixing

As far as I can see, the curves 1 and 2 on the graph should be based on P representing allele A and q representing allele a . I only discovered that the equation here is back to front when I tried to interpret the graph. Who else agrees with me? RogerWooller 11:32, 16 October 2007 (UTC)

Error in Hardy-Weinberg plot

Nucdesigner1 01:36, 4 December 2007 (UTC) I believe the H-W plot has an error in the legend, I do not know how to replace the plot. p2 line should be "AA" and q2 line is should be "aa", based on the discussion.

I corrected the error by making a new diagram, using Inkscape (SVG format). I see that I should have made the image area a few pixels larger on each side, and the colors might be a little garish, but it should do. --Johnuniq (talk) 08:43, 26 February 2009 (UTC)

Questions

1. Under "Example Chi-squared test ...": Where did the equation for p immediately under Table 3 come from? This website ([1]) does HWP differently. Which is correct?

2. The example deals with the genotype distribution in a given generation. How is the genotype distribution determined for succeeding generations? The assumption of constant allele frequencies is valid but each time the genetic pot is stirred to produce a new generation, the AA, Aa, aa distribution is going to change. Hardy's result seems to indicate this.

First impression. Question withdrawn Virgil H. Soule (talk) 17:25, 16 July 2009 (UTC)

3. Under History: Hardy says, "a little math of the multiplication-table type...". Could someone elucidate the math he's talking about? --Virgil H. Soule (talk) 04:28, 10 July 2009 (UTC)

Never mind, I worked out the derivation for myself. Turned out to be simpler than I would have thought. I added the derivation and a numerical example to the article to show that Hardy's math does in fact work.--Virgil H. Soule (talk) 17:25, 16 July 2009 (UTC)

4. Under Derivation at the top, the description given is not probabilistic. The Punnett Square has four possible outcomes. The probability of AA occurring is 1/4 or 0.25, Aa is 0.5, and aa is 0.25. These are not the values of p^2, 2pq, and q^2. (See Punnett Square.)--Virgil H. Soule (talk) 17:25, 16 July 2009 (UTC)

Mistake in "Derivation of Hardy’s Equations"

Shouldn't the line in the "Derivation of Hardy’s Equations" which reads

p_2 = (p_1+q_1)^2

be

p_2^2 = (p_1+q_1)^2

? —Preceding unsigned comment added by 155.198.157.29 (talk) 10:56, 29 September 2009 (UTC)

No. The text in the derivation is thoroughly confusing, but is correct. In generation 0, the frequencies of AA, Aa, aa are defined to be p, 2q, r (respectively, where p+2q+r = 1). The corresponding values in generation 1 are p₁, 2q₁, r₁ and in generation 2 are p₂, 2q₂, r₂. Under the HW assumptions, the Punnett square calculation applies and it shows that p₁ = (p+q)² and likewise p₂ = (p₁+q₁)². The calculations show that regardless of the initial frequencies, it is always the case that p₂ = p₁. In addition p₁ = p if and only if q² = pr.

Example: If p,2q,r = 0.5,0.2,0.3 (respectively), then p₁,2q₁,r₁ = 0.36,0.48,0.16 and p₂,2q₂,r₂ = 0.36,0.48,0.16. Johnuniq (talk) 11:44, 1 October 2009 (UTC)

I don't understand Hardy's equation to begin with. He assumes genome frequencies in the proportions p:2q:r, which seems arbitrary, and uses that to obtain the frequencies for the next generation. in contrast the Punnett square derivation begins with a priori allele frequencies. Does the Punnett square derivation yield the corresponding a priori genome frequencies or are they for the next generation? For example, is Hardy's p the same as the Punnett p²? (Personally, I think Hardy is a fraud but that's just me.)

The p:2q:r genotype ratio isn't an assumption at all; it works for any two-allele data you can get! If you saw an AA:Aa:aa ratio of .4:.3:.3, then you'd say that p = .4, q = .15, and r = .3. In his math, it is more convenient to say p:2q:r rather than p:q:r. If he called the frequencies p:q:r, he'd end up with a bunch of ".5 * q" floating around in the formulas. Hardy's p is the same as the Punnett square's p, his q is the equivalent of p*q in the Punnett square, and his r is the equivalent of the q in the Punnett square. That is because he came up with this argument before the convention of calling the frequencies "p" and "q" came about; his frequencies are "p" and "r". —Preceding unsigned comment added by 75.6.252.67 (talk) 05:56, 10 February 2011 (UTC)

The Derivation at the top of the article has a confusion between probabilities and frequencies. Punnett square is described in terms of probabilities. The second sentence under Derivation says, "... fraction of each is equal to the product of the row and column probabilities." How do you get from probabilities to frequencies? Very confusing.

What's confusing about the Hardy derivation? Seems concise and straight-forward to me. --Virgil H. Soule (talk) 17:41, 3 October 2009 (UTC)

requires mendelian inheritance.

The assumptions do not state that the need of mendelian inheritance, i.e. alleles are equally likely to be inherited. If this is violated (by selfish genes and such), the formulae and so HWP will fail, since if an allele A can act selfishly against a, the Aa hetrozygotes will be produce more AA's than with mendelian inheritance, and less aa's than with mendelian inheritance, and so forth. (138.38.228.25 (talk) 21:26, 16 January 2010 (UTC))

There is nothing to suggest - in selfish gene theories or anywhere else as far as I am aware - to support this (frankly bizarre) idea that alleles compete and may in some mysterious way change the ratios of mendelian inheritance. I hope no-one takes this suggestion seriously.

Random mating

Shouldn't the first item in "Deviations from Hardy-Weinberg equilibrium" be titled "Non-random mating" rather than "Random mating"? 128.97.70.203 (talk) 20:16, 27 April 2010 (UTC)

The wording could be improved, but the text makes the point accurately ("When violations of this provision occur...", meaning when mating is not random). Johnuniq (talk) 02:18, 28 April 2010 (UTC)

History -- mendelian genetics

Mendelian genetics "were" rediscovered..., but "it" remained controversial. Which one is it? 212.126.224.100 (talk) 16:14, 10 November 2010 (UTC)

"Genetics "was" rediscovered and "it was" controversial". Mendel's Laws were rediscovered and they remained controversial. Cf. Genomics, Linguistics, Hermeneutics, meteoritics, mechanics. Aristotle's "Ethics" is an interesting book, and Clinton's ethics are fine though his morals are suspect. Smcewincarr (talk) 15:12, 26 October 2012 (UTC)

Error in explanation of chi-squared test results

This page has been a great help in my calculation of a chi-squared statistic for a population distribution resulting from a genotyping experiment. However, I think there is a small (simple) error in the explanation of the chi-squared test results. The article states the following:

The 5% significance level for 1 degree of freedom is 3.84, and since the χ2 value is less than this, the null hypothesis that the population is in Hardy–Weinberg frequencies is rejected.

In the article on Chi-squared distribution, a table is given that relates χ2 to p-value. The χ2 for df=1 is indeed 3.84, but χ2 less than 3.84 are insignificant, not significantly significant. Doesn't this mean that a χ2 value less than 3.84 (and consequently a p>0.05) indicates the null hypothesis (population in HWE) CANNOT be rejected, and so the population is likely in HWE? Basically a χ2>3.84 (for df=1) should mean that the population differs significantly from HWE. Please clarify if I am not thinking about this correctly. If I am correct, the article could be modified to state "cannot be rejected" rather than "is rejected". Kelly42 (talk) 00:17, 12 December 2010 (UTC)

Dominance/Recessivity

I feel it's unnecessary to talk about alleles being dominant and recessive in relation to the Hardy-Weinberg principle. Hardy Weinberg describes alleles at the genotypic level rather than the phenotypic level. This means dominance has no effect on HWE, so describing alleles in this way is at best redundant. I would suggest changing the A and a alleles to a1 and a2 80.7.125.93 (talk) 16:16, 25 April 2012 (UTC)

Fine by me. Joannamasel (talk) 19:51, 25 April 2012 (UTC)

Error in deviations section

In the section titled "Deviations from Hardy-Weinberg Equilibrium" the author states that there are "three such violations." What it is that is being asserted that is violated is a "provision" of random mating. Not sure what a "provision" is with respect to a principle such as HWP. Don't you mean "assumption?"

At any rate, the next line asserts that there are 3 "violations" of the "provision" but then only lists 1, inbreeding.  ???

BabelBoy (talk) 14:05, 15 July 2012 (UTC)

Fixed Joannamasel (talk) 19:42, 17 July 2012 (UTC)

Recent major changes

I have again corrected the lead paragraph to be accessible to a general reader, by including the concepts of constancy between generations and expected genotype proportions given constant allele frequencies. The latter requires demonstration, which is deferred to the next section. I continue to object strongly to (and will edit out) any use of the word 'equilibrium', as pedagocially and mathematically flawed for phenomena in which allele frequencies are changing but display expected proprotions every generation (selection), or where allele frequencies are constant from generation to generation but heterozygotes are deficient (inbreeding with neutral markers)

Use of the term 'violations' is one of many unpleasantries in the original text. The statement of 'deviations' is inaccurate. The next section to be changed (back to my re-write) is the discussion of major population genetic and evolutionary factors that alter HW expectations. I did this once, I won't do it again until we agree what is to be included and what excluded.

The extension of HW to multiple alleles is not entirely out of place, but is more relevant to population genetics per se than the principle of constancy between generations. The polyploidy derivation is also generally irrelevant, and the conflating of these two not useful to the general reader [that being one of the original objections]

A better numerical example IMO would be the standard exercise that two populations, each showing HW proportions, when combined do not. This answers the usual objection that, of course population usually show HW, because the expected values are calculated from the observed.

Discussion of chi-square and monte carlo methods of testing deviations should be limited to a statement that they exist, with references. Discussion and an example of Fisher's exact test is overkill.

Hardy's (1908) derivation is historically interesting, but uses antiquated language and a non-standard notation (use of p, q and r for genotype frequencies, which is confusing when these are used elsewhere in the article for allele frequencies), and are thus of little value to the modern student of genetics. I'd drop them. Smcewincarr (talk) 14:43, 26 October 2012 (UTC)

Please, can we keep this at talk for now? You made many simultaneous bold changes, I reverted them saying that they created inaccuracies / deleted for no good reason etc and asked you to take them to talk before proceeding further, and then after a single talk post, you simply put them straight back with no modification, justifying your change with an argument from (your own) authority, and then continued further in the same vein. I don't want an edit war. This is not what is supposed to happen. Wikipedia's policy is bold-revert-discuss. We are up to discuss now. One talk post, without waiting for a reply, is not a discussion. Arguments from authority are not recognized as valid on wikipedia, and even if they were, that doesn't mean you would come out ahead. Let's sort things out and get consensus first on the talk page, one change at a time. There are some things the two of us can agree on (see below), others will require input from others. Take this slowly. Please set up a separate subsection on this talk page for each major change that you wish to make. When you have consensus for one of them, we can make that change. Making many disputed changes simultaneously is very unproductive in terms of improving the article.

The article was flagged as 'too technical' and quick scan showed it not so much too technical as badly organized and written, with multiple errors. The most obvious deficiency is the article nowhere shows that allele and genotype frequencies will remain constant in one generation of random mating. Since nobody else bothered to correct them, I did. I suggest any further efforts would be better spent in improving what I wrote, rather than simply reverting to a highly defective prior text. To do so is professionally insulting, as you must surely realize. This is the main reason why I do not waste much time on Wikipedia, preferring to spend the effort on peer reviewed research or my course notes.

Your statement is simply incorrect. One generation of random mating produces specific genotype frequencies, eg p^2, 2pq, q^2. It does not necessarily produce constant genotype frequencies, and certainly not constant allele frequencies. Your "correction" introduces rather than removes error. The content of the page is sound. Its technical nature is a more difficult matter. But it is better to be correct and difficult than accessible and wrong. Joannamasel (talk) 07:39, 1 November 2012 (UTC)

First, it is not sufficient that you object to the word "equilibrium". You need to use authoratitive sources to document that it is not in use. The problem is that it is in use. Your preference for avoiding it is original research.

It is sufficient to point out that use of the phrase 'HW equilibrium', even if in common use, is inaccurate if it is taken to mean that observation of HW proportions means that allele frequencies are not changing (selection) or that absence of HW proportions means that allele frequencies are inconstant (inbreeding or population structure).

No, according to wikipedia policies it is not sufficient. You are, however, welcome to find an appropriate source and cite it to say that "Some have suggested that the term equilibrium is not appropriate because...." But you can't do it without a source. Joannamasel (talk) 07:39, 1 November 2012 (UTC)

Similarly, it is standard usage to talk about an assumption being violated, and it is not sufficient just to label this as an "unpleasantry" to take it out. Ditto for deviations from expectations. Both are standard.

Would you accept "not met" ?

That depends. Can you suggest a whole sentence here? Joannamasel (talk) 07:39, 1 November 2012 (UTC)

This article is on the Hardy-Weinberg principle. The application of Hardy-Weinberg to multiple alleles and to polyploid populations is clearly relevant. I realise that the most common readers of this page are students encountering standard curricular materials. But Hardy-Weinberg is also a specialized population genetic tool used today to analyze population structure (where there are always multiple alleles and may be polyploidy). Hardy-Weinberg is also an extremely important development in the history of biology. The content of this page should be determined by "what is hardy-weinberg?", not "what does a typical course in biology / genetics teach about hardy-weinberg?" This material should not be deleted. Hardy-Weinberg has meaning and life outside the introductory classroom, and this meaning should not be excluded from this page.

The one notable extension to HW required beyond the diploid monoecious model is a diploid dioecious model, for which I cited [2], not wanting to reformat the table for Wikipeida.

Have you ever tested for HW in a real population? I assure you that real genes normally have more than two alleles. I don't see how the actual application of HW in practice could fail to be notable in a HW article. Joannamasel (talk) 07:39, 1 November 2012 (UTC)

I do not see the present article as a place for detailed discussion of any of the violating factors (the text lists them, but does not elaborate) that change allele and/or genotype frequencies. The introduction of multiple alleles is basic population genetics, and not relevant to HW as a principle, absent any proof that either phenomenon differs from what is true for a two-allele, diploid system. The equations included simply state the obvious, that frequencies are the product of their individual components. NB: the lead paragraph lists meiotic drive, but Deviations does not. Delete discussion of multiple alleles and especially polyploidy.

I would be happy for you to add to the article a section demonstrating that two populations, each showing HW proportions, when combined do not, as an illustration of population structure.

As you are aware, the intuitive objection to HW is that, as expected genotype frequencies are dervied from allele frequencies calculated from observed genotype frequencies, of course expected will match observed. The exercise of combining Australian and Eskimo (Inuit) MN freqs at [3] suffices to prove this, as would simple reference to the cod data under Wahlund effect. Please feel free to include them.

I am also happy to cut out statistical details concerning the methodology for testing HW proportions, replacing them with references and wikilinks.

Good. Please do so.

I strongly object to the removal of historical content from an article on a topic of such great historical importance. For this reason, Hardy's derivation should be left in. Those not interested in the history can easily skip it, it has its own section.

I disagree, at least if the article does not start front and center with the derivation of HW in modern notation. The historical summary is adequate (after it is corrected for accuracy along the lines I wrote). Hardy's derivation is easily available in the original MS online. Hardy was unaware of, and the original does not discuss, any of the modern phenomena that make HW useful.

The article does start front and center with modern notation, so your condition is met. If you want to edit this section, how about posting draft historical text on the talk page, so we can work on it here and reach consensus on this part in isolation from some of the more major disagreements.Joannamasel (talk) 07:39, 1 November 2012 (UTC)

Those are my replies to your points. In addition, here is one of my objections to your other changes, and one reason I revert them. In your edited lead text you say that The Hardy–Weinberg theorem provides a null hypothesis for an ideal state, against which the occurrence of other phenomena can be measured. where other phenomena, in the context of your sentence, include drift. The definition of testing a null hypothesis using a p-value is to detect deviations larger than those due to random sampling. The definition of drift is random sampling. Your lead statement, as written, is therefore false. In practice, Hardy-Weinberg is only used as a statistical null hypothesis to test for non-random mating, never for anything else. The previous version contained careful wordsmithing to keep the article accessible while avoiding the kind of incorrect statements that you have inserted. Joannamasel (talk) 07:41, 27 October 2012 (UTC)

Really. (1) 'Other phenomena' is open-ended. I said measured, not tested. HW as an algebraic model implicitly assumes infinite N. Against the null hypothesis of no random change in an infinite population, any finite population will show delta q, proportional to N. Thus the standard exercise of running a computer model with no selection, structure etc. but variable N, and measuring time to fixation. Smaller populations fix faster than larger, within stochastic limits. The degree of drift is testable. QED. (2) You said "Hardy-Weinberg is only used as a statistical null hypothesis to test for non-random mating, never for anything else." Ever heard of the General Selection Model?

With all due respect, if the previous version was an example of 'careful wordsmithing', it fails horribly on scientific and plain English criteria. It requires complete reworking. If the point now is to preserve the original as a privileged text, we're done. Smcewincarr (talk) 18:07, 28 October 2012 (UTC)

You cannot "measure" genetic drift, selection or mutation via a deviation from HW proportions. Your text was incorrect. Measuring delta q is very different from HW proportions. If "the degree of drift is testable", please cite references that have tested it. Will Provine, eg, believes otherwise.

Obviously I am not trying to preserve the original as a privileged text. I have given an all-clear on two of the points you have brought up, and am open to a third. But of course I will oppose changes that make the article inaccurate. And we need to work on one point at a time to make progress.Joannamasel (talk) 07:39, 1 November 2012 (UTC)

Pronunciation?

Does anyone know how to pronounce the first syllable of Weinberg? I've heard most people say /wain/, while some say /wen/ or /win/. The guy is German, does that mean it should be /vain/ ? (I don't speak German) Yel D'ohan (talk) 05:45, 26 April 2013 (UTC)

In German (I don’t speak it but I can read it and know basic pronunciation) it would be pronounced Vine-berg but in the US it’s often pronounced Wine-berg. I’m taking an advanced genetics class and the professor pronounces it wine-berg. --MadScientistX11 (talk) 20:02, 13 July 2019 (UTC)

Suggestions for addressing the "too technical" tag

Based in part on WP:TECHNICAL. Lead should address the following points in order (in normal prose, I'm not proposing a question and answer format):

• What is it? Bolded text that matches common redirects important, keep it as non-technical as possible, ideally no more than a short paragraph. Leave technical asides to a paragraph(s) at the end of the lead. I think the current lead is OK in this regard.
• Why is it important? IMO the lead doesn't address this well. Copying the text from the intro to the applications section would be a good start. Also the historical point that it disproved the theory that dominant alleles increase over time. Aside: Regarding earlier talk, I expect (WP:OR for now) that the word "equilibrium" got used precisely to constrast against that idea.
• Example to illustrate the preceding points. Keep it simple and concrete. In this context I think the current quadratic formula is OK as the basis, but the presentation could probably be simplified.
• Anything else non-technical?
• Anything technical that needs to be covered up front?

Regarding overall layout:

• Push derivations towards the end, but link to them as soon as a concept is introduced.
• Push history towards the end, it doesn't really matter where exactly, assume those who want it will use the table of contents to find it.
• Don't treat the general case as a generalisation of the quadratic case, instead treat the quadratic case as a concrete example of a general principle (and general formula).
• Bring the applications to the front, before the theory. Add more examples of how the principle has been used to prove or disprove interesting questions. No more than two examples (preferably only one) to illustrate each point of interest.

I have no immediate plans to implement any of this (busy with the article that led me here), so if there is consensus, or you want to be bold, anyone reading this should feel free to go ahead.TuxLibNit (talk) 23:51, 9 January 2014 (UTC)

Too technical for most readers to understand; (192.231.80.99 (talk) 15:36, 26 April 2016 (UTC))

The Hardy-Weinberg principle is not meant for high school biology projects. This is a principle specific to population ecology with regards to genetic dispersal. I suggest that the average reader researching the work of Mr. Hardy and Mr. Weinberg be directed to an easily read article discussing the fact that they DEVELOPED this principle. Advanced users, those who would understand the statistics of the principle in conjunction to mark-recapture expeditions upon a given population, would be directed to the page we are discussing.192.231.80.99 (talk) 15:36, 26 April 2016 (UTC)

Memes and cultural evolution

Long screed by blocked user

Anybody got a problem with "memes" ( Humean / Lockean "ideas", or Aristotelian/ Semon-ian "Mnemes"?) ? I made a fine edit today, fundamental, essential, and non controversial, with several external sources cited. And handle "Citation bot" gave it a summary dismissal. I must confess wikipedia is the last place I thought I'd have to fight to say something obvious. Let's discuss. DOES cultural evolution effect gene frequencies? We wouldn't want THE ENCYCLOPEDIA TO BE WRONG OR ILLOGICAL !!!!! I am going to edit it again ( and sue the government And science magazine and Harvard and etc) until I'm allowed to publish. And I will revert this article to the Hardy Weinberg Meyer equilibrium. "version", EVERY time I see it is VANDALIZED WITH FALSE INFORMATION. Sorry "Citation Bot". This ain't my first censorship rodeo. If you have a useful edit. I am happy to accept it. But if you are just a dick, let's take it to Jimmy Wales and see what he thinks about your attitude. I'm a real person. In the real world. Doing real scholarship. Encyclopedias cover the real world? Dont they? Your page is wrong. The science ( according to the "gatekeepers" who are too chicken / crooked to meet me in the "literature" and too chicken to meet me in court ) is wrong. And dismissive attitudes from lesser minds do not make my research incorrect. It makes your encyclopedia incorrect. Which is undesirable? Right? So yeah .. Citation bot ... Yeah, No! Dismissive. Small mind. Troll. Dranonymous2000 (talk) 20:04, 9 June 2022 (UTC) @Dranonymous2000: Actually, I was the user who reverted your change, not the Citation Bot. I did so because you added a novel hypothesis presented by someone named "Randall Meyer". Unfortunately, Meyer does not appear to have published his hypothesis in any reputable journal where such an idea might receive proper peer review. Wikipedia does not accept original research. Based on your use of first person pronouns in the above argument, I presume that you are, in fact, Randall Meyer. If you are a real person, in the real world, doing real scholarship, please go publish your real scholarship in a real journal. WikiDan61ChatMe!ReadMe!! 20:11, 9 June 2022 (UTC) Well. Ummm. Thanks? I think. I'm pretty fed up with academic censorship at the moment. It has RUINED my life. I live in a different country now. Seeking political asylum. So? While I like people and academicians .... I have developed a strong hatred for "Troglodytic philistines" and "semantic-pedantic jurisprudes". I HAVE published some of these ideas in COURT DOCUMENTS when I sued the US Federal government and several prominent academicians and universities for academic censorship ( violation of my rights and such ; is that "peer reviewed" enough for you? Or is a judge not your peer? Or the universities and Daniel Dennett abd Richard schacter ; and Peter Welch and Bernie Sanders; who dodge service of my documents ... Are they Not peers to you?) I will be glad to supply the numbers of the court cases and a link to the documents. I've been meaning to put them up on the internet in a retrievable place anyway. So. Thanks and no thanks. I think? You might be a frenemy. But if you are dispassionate and honest about knowledge, then my ideas won't be disappeared by the internet TOO !!! It IS original research. But it is ALSO common knowledge. And I AM me ... Always have been. And will continue to be. But I can't fight a war of attrition with entrenched academics.... And intetnet trolls too !!! And a dilatory negligent government. I'm not superman. Don't ask metro be. So be be a frenemy ... If you must ... But be a better wiki-editor. Find the loophole that let's the ideas be published here. After 20 years of pushing this one little idea , I am running out of steam. I have to go somewhere else and do something else. And be a different person. I added my idea to the history of ideas. If nobody accepts it? Their loss? Right? I will try to pop online here and do some good edits to other articles. I am a well trained academician. But? How likely am I to diligently do so? If there is no similar respect in return? P.S. what a fine irony that my "bitching complaints" on the "talk" pages require me to push a button that literally says "publish"? So my bitching complaints can be published? But my original research cannot? No intelligent thoughts published : not on the internet or in the "real" publishing world. That's sone kafkanian sh ..... Shtuff. It's equivalent to "you can only publish complaints. Not logic or facts or observations or ideas.". And even your complaints will not be in book form. They will be hidden in the nether regions of the internet and lorded over by the king of all internet trolls and his court of similar minded pendants. Let's not be that way. It's exhausting !!!! Dranonymous2000 (talk) 21:03, 9 June 2022 (UTC) @Dranonymous2000: So, if I can summarize: you've had some brilliant ideas, but no one else can see the brilliance of your ideas, so you've sued them for censorship. (No, your lawsuits cannot be used as reliable sources.) Perhaps, and I'm just spitballing here, the brilliance of your ideas is not as obvious to others as it is to you. This can mean one of two things: The entire world is populated by idiots who simply cannot perceive your brilliance. Your ideas are not as brilliant as you think they are. I'll let you decide which of these options might be true. In either case, you're unlikely to get Wikipedia to publish them if other journals have refused. WikiDan61ChatMe!ReadMe!! 21:11, 9 June 2022 (UTC) so let me summarize, for you. You had dreams of being a great author or an actor / actress or fill-in-the-blank-humanities-or-arts-person; so you majored in English and mommy and daddy paid for your degree and when you got out of school and you didn't turn into an immediate star you looked around for something to do and you found the internet. So you thought "Where can I go to torture and harass innocent people for fun and pleasure. And maybe profit. How can I find a smidgen of power when i am just this little itty bitty 46 chromosomes spinning on a rock in a giant void?" Aha !!! Wikipedia will provide me the gatekeeper / influencer status that I require ! Sorry. You bore me. If that is INDEED your psychological profile. But as I said. It's just as easy for you to malign and misunderstand me as it is for me to return the favor. No journals have refused. But to get published in journals you must do research. To do research you need at minimum time. But usually money and experimental apparatus and access to quality research materials. So publishing, for 10 or 15 years was not really an option for me. By age 42 I have some research materials collected and some apparatus. So I'm not ready to publish. I WAS making some progress, until everybody decided that they don't even have to meet me in court. No courtesy. No decorum. Chickens. Criminals. So haven't been rejected by journals. Rejected by schools and employers. But it still doesn't change the fact that I AM RIGHT AND EVERYBODY ELSE IS WRONG. And they are mostly wrong because they are intellectually lazy. ( or greedy. But that is a different accusation and also difficult to prove) Intellectually lazy, like YOU are being RIGHT NOW. Think about the article you are editing. Are there five assumptions to H-W law ( ok? 7 or 10 now. But I think some are duplicates of the standard five ... Splitting hairs ? Distinction without a difference?) Ask yourself if there MIGHT be a sixth "mechanism" that affects gene frequencies? Ask yourself if I've introduced one? Ask yourself if anybody else has suggested the same? Or similar? Ask yourself, both, if they haven't offered such AND its obviously a correct answer ; a valid sixth assumption... Ask yourself why nobody is concerned with this glaring error? Would Wikipedia publish 2+2=5 just because (a) all the experts say it's true AND (b) the only ( one of the only?) expert (s?) , the one (s?) that the other experts have shunned, has not been allowed to study 2+2=4 , can't afford a chalkboard or chalk or even a stick to scratch the equation in the dirt, and everytime he says "2+2=4" people either say (a) "oh that's obvious" or (b) "that's not what the experts say" or (c) (much more rarely) "you should publish, if it's wrong". "You should publish ..." . But not here. The last part barely whispered. Usually implied. You know what? I just read a short story the other day that your English lit. Mind just might appreciate. "A Hunger Artist" by Kafka. Are you familiar with it? Almost as good as "The Trial". Or "the castle" ( I confess I watched the eastern European movie of the last one. Did not read it.) If this is going to be my "average" experience with wikipedia, I might decide to not even edit anything. Maybe I'll stop using it at all !!! Which is a shame. I like it for topical everyday stuff. But it CAN be an excellent primer in fields that you are "soft" in. But if wikipedia will print 2+2=5 just because of a 30 second "psyche profile"-- armchair psychology and sloppier scholarship and logic than I care to describe--and simply because "The experts all claim 2+2=5" ... Well I'm sorry. I can't help you (wikipedia). You (wikipedia) , at that point, would be beyond help . And decidedly political. Not neutral. Which ... Is ANOTHER WIKIPEDIA RULE !!!! You must be neutral !!!! Come on other wiki editors?. Will anybody lean in and say "Hey ? Yeah !!! 2+2=4 !!! It's obvious !!! And FREQUENTLY IGNORED AND NOT EXPLICITLY STATED !!!!" Wjy is that? Does anybody know? Randall Meyer does ... Ohhhh .... Too bad. Dan called him a gadfly. It must be true. I guess 2+2 HAS to equal 5 ... Until Dan or the rest of academia and Uh?Muricuh apologize. And remove Randall Meyer's "gadfly" status? ( do I get a scarlett letter? Send me a big "G", Dan. I will wear it proudly on a shirt that also says "2+2=4") Yes I fled uh?Muricuh. Epistemological persecution. Maybe they will send me a "G" as a parting gift? Dranonymous2000 (talk) 22:10, 9 June 2022 (UTC) @Dranonymous2000: Whatever, dude. Wikipedia is not going to publish your hypothesis. I'm done here. WikiDan61ChatMe!ReadMe!! 23:02, 9 June 2022 (UTC) Yup Dan. Intellectual coward. Theory. Not hypothesis. There's a difference. And Hardy Weinberg Meyer Law. Like gravity. You can deny it. But it makes you look stupid. Dranonymous2000 (talk) 00:15, 10 June 2022 (UTC) Now we're done here .... Dranonymous2000 (talk) 00:15, 10 June 2022 (UTC)

Nonsensical footnote

I do not understand what note 1 is trying to say and suspect it is nonsense:

The term frequency usually refers to a number or count, but in this context, it is synonymous with probability.

No probability distribution was mentioned up to this point. Instead we only talked about a population. Given such a population, one can count the number of alleles of type A and divide it by the total to get a number between 0 and 1, which is a frequency and not a probability, since it indeed refers to a count.

Does this footnote really intend to say that in spite of this, the Hardy-Weinberg theory uses the word "frequency" to refer to something else? If so that something else needs to be properly defined, so that we know which probability distribution is being referred to. If not then the footnote is just wrong and should either be removed or replaced by something more correct such as

by "frequency" we mean the number of alleles of a given type at the given locus, divided by the size of the population.

I'm not an expert on this topic but I sincerely expect that this is what is actually meant.

Although, after that the text refers to an expectation, despite still not having defined any probability distribution. (Perhaps an average was meant, rather than an expectation.) I suspect that the author doesn't know any probability theory and is fundamentally confused about the difference between probabilities and frequencies. This is unfortunate because any model in population genetics involves both, and if you don't know the difference then nothing you say or calculate will make any sense. I will look elsewhere for information on this topic. This needs attention from an expert.

Nathaniel Virgo (talk) 04:07, 21 May 2023 (UTC)

My guess is that the note (which is old, before 2019) was from someone used to the electrical engineering term frequency. There should be a link to Frequency (statistics) somewhere in the article but I'm not sure where it should go as "frequency" is used, well, frequently. Perhaps asking at one of the above wikiprojects would bring help. Johnuniq (talk) 04:35, 21 May 2023 (UTC)

Assumptions listed after they are used

The maths in the 'Derivation' section relies on a bunch of assumptions that are not even mentioned until the 'Deviations from Hardy–Weinberg equilibrium' section. In particular, none of the maths makes any sense at all unless you know that we're assuming an infinite population. I was completely confused by that and didn't have a clue what was going on. The assumptions need to at least be mentioned before they are used, in order for the article to be any use. I will edit to at least mention the infinite population assumption, which is crucial.

Nathaniel Virgo (talk) 04:40, 21 May 2023 (UTC)

OK. Hardy's discussion of the principle is short and can be seen in the sources and here. It lists the assumptions. Johnuniq (talk) 05:40, 21 May 2023 (UTC)