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Hardy-Weinberg Principle Hardy-Weinberg Principle Hardy-Weinberg Principle – enables us to calculate and predict allelic and genotypic frequencies Allelic frequency – the frequency of an allele in a population Genotypic frequency – the frequency of a genotype in a population Hardy-Weinberg We use p to represent the dominant allele, and q to represent the recessive allele For allelic frequency: p + q = 1 So if the frequency of the dominant allele (p) is 0.75, then the frequency of the recessive allele (q) is…0.25 Hardy-Weinberg For genotypic frequency: p2 + 2pq + q2 = 1 Where: p2 = frequency of homozygous dominant 2pq = frequency of heterozygous q2 = frequency of homozygous recessive Hardy-Weinberg SO…for example, if we know the frequency of the homozygous recessive genotype (q2), we can find the frequency of the recessive allele [√(q2) = q] THEN…since we know q, we can find p, then p2, then 2pq! Hardy-Weinberg Hardy-Weinberg predicts that gene frequencies will remain the same from one generation to the next However, certain conditions must be met Hardy-Weinberg – the frequencies of the alleles do not change and – as long as the mating is random, the genotypic frequencies will remain in the proportions p2 (frequency of AA), 2pq (frequency of Aa) and q2 (frequency of aa) where p is the frequency of A and q is the frequency of a – The sum of the genotypic frequencies should be: p2 + 2pq + q2 = 1 Hardy-Weinberg Assumptions 1) Large population 2) Random mating 3) No mutation 4) No migration (in or out of population) 5) No selective pressure Brachydactyly and evolutionary change We know the gene for brachydactyl fingers is dominant to normal fingers A man named Yule suggested that short-fingered people should become more common through time Godfrey Hardy showed this inference was wrong Wilhelm Weinberg derived the same solution to the problem independently The Hardy-Weinberg Law - the most important principle in population genetics The law is divided into three parts: a set of assumptions and two major results – In an infinitely large, randomly mating population, free from mutation, migration and natural selection (note there are five assumptions here) The Hardy-Weinberg Law - the most important principle in population genetics The incidence of albinism is remarkably common (0.0043 or 13 in every 3000 Hopis) Assuming Hardy-Weinberg equilibrium, we can calculate q as the square root of 0.0043 = 0.066 p is therefore equal to 0.934 The frequency of heterozygotes in the population is 2pq = 0.123 In other words, 1 in 8 Hopis carries the gene for albinism! Take-home Lesson: For a rare allele, heterozygotes can be relatively common Albinism in Hopi Native Americans The incidence of albinism is remarkably common (0.0043 or 13 in every 3000 Hopis) Assuming Hardy-Weinberg equilibrium, we can calculate q as the square root of 0.0043 = 0.066 p is therefore equal to 0.934 The frequency of heterozygotes in the population is 2pq = 0.123 In other words, 1 in 8 Hopis carries the gene for albinism! Take-home Lesson: For a rare allele, heterozygotes can be relatively common Hardy Weinberg Problem I Sickle Cell Anemia – SS = susceptible to malaria but no SCA – ss = non-susceptible but SCA mortality – Ss = non-susceptible and no SCA What do we expect proportions of ss? Ss? • E.g. 4% ss - what are proportions of Ss – .04 = ss = q2 q = √.04 = .2 – p = 1 - q = 1 - .2 = .8 – Ss = 2pq = 2(.8)(.2) = .32 Hardy Weinberg Problem II What would it take to increase Ss proportion to 50% (from 32%)? – Ss = 2pq = .5 pq = .25 – q = 1 - p p (1-p) = .25 p = .5 – Which means aa goes to .25 from .04, over 6x Hardy Weinberg Problem III How many of you can roll your tongues? – A - Yes –B-N Hardy Weinberg Problem III What is the percentage of heterozygous tongue-rollers? – Yes = p2 + 2pq – No = q2 – q = √No – p = 1- q – Heterozygous = 2pq