Hardy-Weinberg Theorem

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 v0.36 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 v0.36 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
• 0.16 0.48 0.64
• Recessive phenotype aa 0.36