Talk:Hardy-Weinberg principle

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	To-do list for Hardy-Weinberg principle:	edit  · history  · watch  · refresh
Things to do: Add a de Finetti diagram with line through (I have equations, just need something that'll plot them with same scale on x and y axes. Have added a diagram from the de finetti diagram section and some more info on this, could do with bulking out the maths (from memory I think the HW parabola is m2 = 4ln), I do think however that the graph should be replaced with one with scales on the axis, will try and get something from the site I linked uploaded to replace this. Slack---line 04:43, 15 January 2007 (UTC). Improve the generalisation section and put in about generalising to n-ploidy Tidy the maths up(!) Add an example of the use of Fisher's exact test.

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Contents 1 Migration 2 Move 3 Evolution in the assumptions 4 F-Statistics 5 Polyploidy 6 Degrees of freedom for Pearson's chi square 7 discrete generations? 8 Evolution

[edit] Migration

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)

[edit] 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)

[edit] 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)

[edit] F-Statistics

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

,

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)

[edit] 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.

[edit] Degrees of freedom for Pearson's chi square

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

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

The degrees of freedom for Pearson's chi-square 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-square statistic has a distribution that converges to a Chi-square distribution as the amount of data tends to infinity, and the degrees of freedom of that Chi-square 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-square 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-square 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)

[edit] 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)

[edit] 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).