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Finding Variation Gene frequency Richard Lewontin To understand evolution we must identify changes in gene frequency within populations. Population Genetics is the branch of Biology explicitly concerned with gene frequencies. • In the 1960’s, electrophoresis was first employed as a method for examining protein diversity. • The astounding finding of this early work was the ubiquity of genetic diversity. • genetic diversity extensive: many protein alleles and high levels of polymorphism within populations. • protein estimates << DNA sequence reality PCR Thermus aquaticus • Polymerase Chain Reaction technique has revolutionised molecular biology. – TAQ polymerase DNA polymerase + specific primers used to amplify specific sequence DNA – Thermal cycles used to melt target DNA, allow primers to attach, and then replica of target DNA to be formed. – Cut the DNA with restriction enzymes & run fragments on gel. Kary Mullis 4 Calculating Gene Frequencies . • How common is CCR5-D32? • Example: In Icelanders, 102 people were see Table 5.3 F&H screened for this genotype. 75 +/+; 24 +/D32; 3 D32/D32 • 204 alleles, 24 + 6 = 30 of which were D32. • i.e., 14.7% D32 in the population. Genetic Diversity • Several measures exist, e.g., • heterozygosity (frequency of heterozygotes in a population) • proportion of genes polymorphic • F&H first emphasize classical allelomorph data from protein electrophoresis. • allozyme heterozygosity data suggest that 1/3 - 1/2 of loci coding for enzymes are polymorphic in a typical population. • average individual is heterozygous at 4-15% of loci. Genetic Diversity • Sequencing of DNA is a more direct method • of course many changes in sequence are silent & do not present themselves as a phenotype • CFTR is a gene linked to cystic fibrosis. • helps cells in lung destroy Pseudomonas aeruginosa. • over 500 different loss of function mutants found in screen of 30 000 chromosomes of CF-sufferers. • an example of how dozens or hundreds of alleles may be typical for a given locus. • • neutralists maintain that most alleles are equivalent; diversity results from genetic drift. selectionists argue that forces like shifting NS, heterozygote advantage, frequencydependence (advantage to being rare) supports variation. Genes in Populations Loss-of-function mutations in the human CFTR gene Godfrey Hardy the equilibrium principle Wilhelm Weinberg “A fundamental principle in population genetics stating that the genotype frequencies and gene frequencies of a large, randomly mating population remain constant providing that mutation, immigration, and selection do not take place” -- American Heritage Dictionary SCIENCE JULY 10, 1908 DISCUSSION AND CORRESPONDENCE Mendelian Proportions in a Mixed Population To The Editor of Science: I am reluctant to intrude in a discussion concerning matters of which I have no expert knowledge, and I should have expected the very simple point which I wish to make to have been familiar to biologists. However, some remarks of Mr. Udny Yule, to which Mr. R. C. Punnett has called my attention, suggest that it may still be worth making. In the Proceedings of the Royal Society of Medicine (Vol I., p. 165) Mr. Yule is reported to have suggested, as a criticism of the Mendelian position, that if brachydactyly is dominant “in the course of time one would expect, in the absence of counteracting factors, to get three brachydactylous persons to one normal.” It is not difficult to prove, however, that such an expectation would be quite groundless. Suppose that Aa is a pair of Mendelian characters, A being dominant, and that in any given generation the numbers of pure dominants (AA), heterozygotes (Aa), and pure recessives (aa) are as p:2q:r. Finally, suppose that the numbers are fairly large, so that the mating may be regarded as random, that the sexes are evenly distributed among the three varieties, and that all are equally fertile. A little mathematics of the multiplication-table type is enough to show that in the next generation the numbers will be as 2 2 (p + q) : 2(p + q)(q + r) : (q + r) , or as p1:2q1:r1, say. The interesting question is – in what circumstances will this distribution be the same as that in the generation before? It is easy to see that the condition for this is q2 = pr. And since q = p1r1, whatever the values of p, q, and r may be, the distribution will in any case continue unchanged after the second generation. Suppose, to take a definite instance, that A is brachydactyly, and that we start from a population of pure brachydactylous and pure normal persons, say in the ratio of 1:10,000. Then p = 1, q = 0, r = 10,000 and p1 = 1, q1 = 10,000, r1 = 100,000,000. If brachydactyly is dominant, the proportion of brachydactylous persons in the second generation is 20,001:100,020,001, or practically 2:10,000, twice that in the first generation; and this proportion will afterwards have no tendency whatever to increase. If, on the other hand, brachydactyly were recessive, the proportion in the second generation would be 1:100,020,001, or N. S. Vol. XXVIII:49-50 Allele vs. Genotype practically 1:100,000,000, and this proportion would afterwards have no tendency to decrease. In a word, there is not the slightest foundation for the idea that a dominant character should show a tendency to spread over a whole population, or that a recessive should tend to die out. I ought perhaps to add a few words on the effect of the small deviations from the theoretical proportions which will, of course, occur in every generation. Such a distribution as p1:2q1:r1, which satisfies the condition q = p1r1, we may call a stable distribution. In actual fact we shall obtain in the second generation not p1:2q1:r1 but a slightly different distribution p:2q:r, which is not “stable.” This should, according to theory, give us in the third generation a “stable” distribution p2:2q2:r2, also differing from p1:2q1:r1; and so on. The sense in which the distribution p1:2q1:r1 is “stable” is this, that if we allow for the effects of casual deviations in any subsequent generation, we should, according to theory, obtain at the next generation a new “stable” distribution differing but slightly from the original distribution. I have, of course, considered only the very simplest hypotheses possible. Hypotheses other that [sic] that of purely random mating will give different results, and, of course, if, as appears to be the case sometimes, the character is not independent of that of sex, or has an influence on fertility, the whole question may be greatly complicated. But such complications seem to be irrelevant to the simple issue raised by Mr. Yule’s remarks. G. H. Hardy Trinity College, Cambridge, April 5, 1908 A a A AA Aa a aA aa Allele frequencies a=0.5 A=0.5 Genotype frequencies aa=0.25 Aa=0.50 AA=0.25 P. S. I understand from Mr. Punnett that he has submitted the substance of what I have said above to Mr. Yule, and that the latter would accept it as a satisfactory answer to the difficulty that he raised. The “stability” of the particular ratio 1:2:1 is recognized by Professor Karl Pearson (Phil. Trans. Roy. Soc. (A), vol. 203, p. 60). Reprinted from Hardy, G. H. 1908. Mendelian proportions in a mixed population, Science, N. S. Vol. XVIII:49-50. (letter to the editor) Available from: Electronic Scholarly Publishing http://www.esp.org A a A AA Aa a aA aa A a A p2 pq a pq q2 p = 0.6 q = 0.4 population of zygotes = 100 Allele frequencies a=0.5=q A=0.5=p Genotype frequencies AA=p2 Aa=2pq aa=q2 p + q = 1.0 p2 = 0.36 2pq = 0.48 q2 = 0.16 p2 + 2pq + q2 = 1.0 Assume complete mixing & no mate choice. The next generation Using H-W • Assume each zygote grows up, produces 10 • we may use the H-W principle to determine if gametes and mates randomly. the population is in equilibrium. • AA = 36 x 10 = 360 • Aa = 48 x 10 = 480 • aa = 16 x 10 = 160 • The frequency of A = 360 + 1/2*480 = 600/1000 = 0.6 • count allele (gene) frequencies • calculate expected genotype frequencies • compare observed number of homozygotes with expected number. • The frequency of A = 160 + 1/2*480 = 400/1000 = 0.4 Human Blood Groups Human Blood Groups African American Obs. Exp. % Exp. # MM MN NN 79 138 61 ! 278 Euro. American freq. M 0.532 freq. N 0.468 African American Obs. Exp. % Exp. # MM MN NN 79 0.28 78.8 138 0.5 138.7 61 0.22 60.8 ! 278 freq. M freq. N 0.532 0.468 Euro. American Amerind Amerind freq. M = (79 + 0.5*138)/278 = 0.532 freq. N = (61 + 0.5*138)/278 = 0.468 expected # of MM = 0.5322 * 278 = 0.28 * 278 = 78.8 expected # of NN = 0.4682 * 278 = 0.22 * 278 = 60.8 expected # of MN = 2 * 0.532 * 0.468 * 278 = 138.7 Human Blood Groups So who cares? MM MN NN ! freq. M freq. N African American Obs. Exp. % Exp. # 79 0.28 78.8 138 0.5 138.7 61 0.22 60.8 278 0.532 0.468 Euro. American Obs. Exp. % Exp. # 1787 0.292 1787.2 3039 0.497 3044.9 1303 0.211 1296.9 6129 Amerind Obs. Exp. % Exp. # 123 0.602 123.3 72 0.348 71.4 10 0.05 10.3 205 • H-W is important for three major reasons: • practically, it serves as a null model. Deviations from H-W equilibrium point to interesting problems for investigation. 0.540 0.776 H-W often violated • The interest value of the H-W calculation is rarely predictive. • Populations will often violate one or more of 0.460 0.224 • conceptually, it solved a major dilemma for early population genetics: how variation can be maintained. Sources of Non-Equilibrium “... the genotype frequencies and gene frequencies of a large1, randomly mating2 population remain constant providing that mutation3, immigration4, and selection5 do not take place” its assumptions. • the mechanism of deviation generally of much greater interest to researchers. - deviation from equilibrium helps point out evolution and its sources