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How to: Hardy - Weinberg. What is Hardy-Weinberg?. Hardy-Weinberg says that the frequency of alleles and genotypes remain constant in a population generation after generation when certain conditions are met . What are the conditions?. No Mutations No Gene Flow Random Mating
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What is Hardy-Weinberg? • Hardy-Weinberg says that the frequency of alleles and genotypes remain constant in a population generation after generation when certain conditions are met.
What are the conditions? • No Mutations • No Gene Flow • Random Mating • No Genetic Drift • No Selection *note that these conditions are rarely met*
Hardy-Weinberg Equation p + q = 1 p= frequency of dominant allele q= frequency of recessive allele
Example 1 If 60 people out of 100 can roll their tongues, and tongue rolling is dominant, then what is the frequency of the recessive alleles? 60/100 = .60 or 60% can roll tongues p + q = 1 .60 + q = 1 -.60 -.60 q= .40 or 40% cannot roll their tongues
Your turn • If 23 out of 100 people do not have a hitchhikers thumb, and possessing a hitchhikers thumb is recessive, then what is the frequency of the dominant allele? Click here for the answer.
But… we know that we can have a mixture of dominant and recessive alleles (heterozygous)
Hardy-Weinberg Equation p2 + 2pq + q2 = 1 or (p x p) + (2 x p x q) + (q x q) = 1
p2 + 2pq + q2 = 1 =frequency of homozygous dominant genotypes =frequency of homozygous recessive genotypes 2pq = frequency of heterozygous genotypes
Example 2 • You have sampled a population in which you know that the percentage of the homozygous recessive genotype (aa) is 36%. Using that 36%, calculate the following: • The frequency of the "aa" genotype. • The frequency of the "a" allele. • The frequency of the "A" allele. • The frequencies of the genotypes "AA" and "Aa."
The frequency of the "aa" genotype. Answer: 36%, as given in the problem itself. • The frequency of the "a" allele. Answer: The frequency of aa is 36%, which means that q2 = 0.36, by definition. If q2 = 0.36, then q = 0.6, again by definition. Since q equals the frequency of the a allele, then the frequency is 60%. • The frequency of the "A" allele. Answer: Since q = 0.6, and p + q = 1, then p = 0.4; the frequency of A is by definition equal to p, so the answer is 40%. • The frequencies of the genotypes "AA" and "Aa." Answer: The frequency of AA is equal to p2, and the frequency of Aa is equal to 2pq. So, using the information above, the frequency of AA is 16% (i.e. p2 is 0.4 x 0.4 = 0.16) and Aa is 48% (2pq = 2 x 0.4 x 0.6 = 0.48).
Your turn • You have sampled a population in which you know that the percentage of the homozygous dominant genotype (AA) is 25%. Using that 25%, calculate the following: • The frequency of the “AA" genotype. • The frequency of the "a" allele. • The frequency of the "A" allele. • The frequencies of the genotypes “aa" and "Aa." Click here for the answer.
.25 (given in the problem) • .5 (take the square root of .25 and subtract from 1) • .5 (take the square root of .25) • .25, .50 (your number from C and D into the Hardy-Weinberg equation)