1. Hardy-Weinberg Theorem
Excerpts from Chapter 23

2. 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)

3. 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

4. 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

5. 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”

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

7. 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

8. 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

9. 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

10. 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
= 0.64
Recessive phenotype – aa = 0.36