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ALLELE FREQUENCY

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HARDY - WEINBERG

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  • A population that is not changing genetically is said to be at Hardy–Weinberg equilibrium
  • The assumptions that underlie the Hardy–Weinberg equilibrium are
    • population is large
    • mating is random
    • There is no migration (no immigration or emigration)
    • There is no mutation of the alleles
    • natural selection is not acting on the population. (all genotypes have an equal chance of surviving and reproducing)
  • Sets up a reference point at equilibrium

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HARDY-WEINBERG & EVOLUTION

  • Biologists can determine whether an agent of evolution is acting on a population by comparing the population’s genotype frequencies with Hardy–Weinberg equilibrium frequencies.
  • If there is no change in frequencies, there is no evolution
  • Conversely, if there have been changes in the frequencies, then evolution has occurred.
  • Evolution is change of allelic frequencies

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HARDY - WEINBERG

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  • In a population at Hardy–Weinberg equilibrium, allele frequencies remain the same from generation to generation, and genotype frequencies remain in the proportions p2 + 2pq + q2 = 1.
  • Two equations
    • p + q = 1
      • A + a = 1, where A and a equal gene percentages
      • All dominant alleles plus all recessive alleles add up to all of the alleles for a particular gene in a population
      • Allele frequencies
    • p2 + 2pq + q2 = 1
      • AA + 2Aa + aa = 1
      • For a particular gene, all homozygous dominant individuals plus all heterozygous individuals plus all homozygous recess individuals add up to all of the individuals in the population
      • Genotype frequencies

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TWO EXAMPLES OF HARDY WEINBERG

A

A

A

a

a

a

0.49 AA

0.42 Aa

0.09 aa

0.49 + 0.21

0.21 + 0.09

0.7A

0.3a

AA(p2)

Aa(pq)

Aa(pq)

aa(q2)

A

p

a

q

A

p

a

q

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HARDY-WEINBERG

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HARDY-WEINBERG PROBLEM

  • Given: In a population of 100 individuals (200 alleles), sixteen exhibit a recessive trait.
  • Problem:
    • Find the allele frequencies for A and a.
    • Find the genotypic frequencies of AA, Aa, and aa.
  • Allele frequency
    • p + q = 1 or A + a = 1
    • ?/200 + 32/200 = 200/200 (You need total alleles)
    • ?% + 16% = 100% or 16% = aa and 84% = AA +Aa
    • aa = qq or q2 = .16 or q = .4
    • 1 - q = p 1 - .4 = .6 or A = .6 and a = .4

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HARDY - WEINBERG PROBLEM

  • Phenotypic frequencies
    • If: p = .6 and q = .4, then
      • p2 = (.6)(.6) = .36
      • q2 = (.4)(.4) = .16
      • 2pq = 2(.6)(.4) = .48
  • Therefore, in the population:
    • Homozygous dominant = 36/100 or 36%
    • Heterozygous dominant = 48/100 or 48%
    • Recessive = 16/100 or 16%

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ANOTHER PROBLEM

  • Fraggles are mythical, mouselike creatures that live beneath flower gardens.
  • Of the 100 fraggles in a population, 91 have green hair(F) and 9 have grey hair(f).
  • Assuming genetic equilibrium:
    • What are the gene frequencies of F and f?
    • What are the genotypic frequencies?

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ANSWERS TO PROBLEM

  • Gene frequencies:
    • F = 0.7 and f = 0.3
  • Genotypic frequencies
    • FF = 49% or 0.49
    • Ff = 42% or 0.42
    • f f = 9% or .09

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HARDY-WEINBERG EQUILIBRIUM

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ALLELE FREQUENCY VARIATIONS

  • Hardy-Weinberg applies only if there is genetic equilibrium or NO allele frequency changes
  • Causes of allele frequency variations
    • Mutation
    • Migration
    • Non-random mating
    • Genetic drift
    • Natural selection
  • How often in nature do NONE of these occur?
    • Rarely, if ever.

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GENOTYPE & ALLELE FREQUENCIES

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GENOTYPE & ALLELE FREQUENCIES

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GENOTYPE & ALLELE FREQUENCIES

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GENOTYPE & ALLELE FREQUENCIES

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GENOTYPE & ALLELE FREQUENCIES

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GENOTYPE & ALLELE FREQUENCIES

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GENOTYPE & ALLELE FREQUENCIES

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HARDY - WEINBERG LAW