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Hardy-Weinberg Principle SBI3UP What is it? • Method to quantify a gene pool (total of all alleles within a population) by measuring each allele frequency • Changes in allele frequencies may help measure evolutionary change within populations In order to apply the Hardy-Weinberg Equilibrium/Population Equilibrium the following conditions are required: – Large populations – Random mating – No mutation – No migration – Equal viability, fertility, and mating ability of all genotypes The H-W equations: p+q=1 p2 + 2pq +q2 = 1 p frequency of allele A in popl’n q frequency of allele a in popl’n p2 frequency of AA genotype q2 frequency of aa genotype 2pq frequency of Aa genotype • If a pop’n is in Hardy-Weinberg equilibrium (not evolving) the frequency of the dominant and recessive alleles is 0.5 each (50%) – E.g. p + q = 1 • so, 0.5 + 0.5 = 1 • If white (b) is recessive to black (B) and 34% of the alleles are b, what is the frequency of B? – – – p= 1- q p = 1 – 0.34 p = 0.66 A Little Math 1 unit 1 unit A 1 unit by 1 unit square has an area of 1 unit2 p2 pq p 1 unit pq q2 q If the sides are (p+q) units long then the area is q p 1 unit (p+q)2 = p2 + 2pq +q2 Add the squares and rectangles to get this formula Ex. • If p = 0.8 then q = 0.2 • What is the frequency of the dominant phenotype? – p2 + 2pq (both represent dominant phenotype – 0.96 or 96% • What is the frequency of heterozygous individuals? – 2pq – 0.32 or 32% p+q=1 p2 + 2pq +q2 = 1 0.8 0.2 p2 0.64 pq 0.16 p pq 0.16 q2 0.04 q p q 0.8 0.2 Ex. If 98 out of 200 individuals in a population express the recessive phenotype, what percent of the population would you predict would be heterozygotes? Dominant allele Recessive allele t Heterozygous Dominant phenotype Homozygous recessive p q p2 2pq p2+2pq q2 0.1 0.8 0.09 0.64 0.25 0.16 0.91 0.96 0.99 For extra practice, complete the table… Dominant allele Recessive allele Homozygous dominant Heterozygous Dominant phenotype Homozygous recessive p q p2 2pq p2+2pq q2 0.1 0.9 0.01 0.18 0.19 0.81 0.2 0.8 0.04 0.32 0.36 0.64 0.3 0.7 0.09 0.42 0.51 0.49 0.4 0.6 0.16 0.48 0.64 0.36 0.5 0.5 0.25 0.50 0.75 0.25 0.6 0.4 0.36 0.48 0.84 0.16 0.7 0.3 0.49 0.42 0.91 0.09 0.8 0.2 0.64 0.32 0.96 0.04 0.9 0.1 0.81 0.18 0.99 0.01