Hardy-Weinberg Theorem Excerpts from Chapter 23

Population Genetics Population – a localized group of individuals belonging to the same species Species – a group of populations whose individuals can interbreed and produce fertile offspring Gene pool – total aggregate of genes (all alleles at all gene loci)

Hardy-Weinberg Theorem The gene pool of a non-evolving population will remain constant over generations For the theorem to work, the following conditions must be met: Large population size No gene flow (no immigration or emigration) No mutations Random mating No natural selection

Hardy-Weinberg Theorem Two formulas for Hardy-Weinberg must be learned: p2 + 2pq + q2 = 1 and p + q = 1 p = frequency of the dominant allele in the population q = frequency of the recessive allele in the population p2 = percentage of homozygous dominant individuals q2 = percentage of homozygous recessive individuals 2 pq = percentage of heterozygous individuals

Hardy-Weinberg Theorem Problem: 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 frequencies of the two possible phenotypes if “A” is completely dominant over “a”

Hardy-Weinberg Theorem “the percentage of the homozygous recessive genotype (aa) is 36%” The frequency of the “aa” genotype Given: 36% or 0.36

Hardy-Weinberg Theorem “the percentage of the homozygous recessive genotype (aa) is 36%” The frequency of the “a” allele The frequency of aa (q2) is 0.36; therefore the frequency of a (q) is √0.36 = 0.60

Hardy-Weinberg Theorem “the percentage of the homozygous recessive genotype (aa) is 36%” The frequency of the “A” allele The frequency of aa (q2) is 0.36; therefore the frequency of a (q) is √0.36 = 0.60 If q = 0.60 and p + q = 1; then p = 1 – 0.60 = 0.40

Hardy-Weinberg Theorem “the percentage of the homozygous recessive genotype (aa) is 36%” The frequencies of the genotypes “AA” and “Aa” If p = 0.40 and q = 0.60 AA = p2 = 0.16 Aa = 2pq = (2)(0.40)(0.60) = 0.48

Hardy-Weinberg Theorem “the percentage of the homozygous recessive genotype (aa) is 36%” The frequencies of the two possible phenotypes if “A” is completely dominant over “a” Dominant phenotype – AA and Aa 0.16 + 0.48 = 0.64 Recessive phenotype – aa = 0.36