Population Genetics

Population genetics is the fusion of Darwin's theory of evolution by natural selection with Mendel's principles of genetics. Mendel's priciples for how traits are inherited when individuals mate must be extended to populations of interbreeding organisms (Hardy-Weinberg). The effects of selection for a phenotype can then be modeled and and the consequences for the population (evolution?) can be determined.

Hardy-Weinberg (1908)

Two approaches to extending Mendelian genetics to populations, the "gene pool" or "randomly mating individuals". In both the frequency of the different genotypes and alleles is determined for each generation.

  • Genotypic frequencies
    • The fequency of a genotype is equal to the # of individuals with the genotype divided by the total # of individuals in the population.
    • Thus the frequency X of the genotype AA in a population is the # of AA individuals divided by the population size.

  • Allelic frequencies
    • The frequency of an allele in a population is equal to the # of copies of that allele divided by the total # of all alleles for that gene in the population
      • p = f(A) = (2 x AA + Aa)/(2 x total)
      • or p = f(AA) + 0.5 x f(Aa)

The "gene pool" concept

  • The frequency of an allele in a population will determine the proportions of gametes carrying that allele
  • If there is random mating then the frequency of gametes carrying an allele will determine the proportions of the different genotypes in the next generation
    • i.e., if p=the frequency of the A allele and q = the frequency of the a allele then,
      the frequency of AA individuals in the next generation is equal to the probability of two A gametes fusing, f(AA) = p*p = p2, f(aa) = q2, and f(Aa) = 2pq.

      as all of the indivivduals are either AA, Aa, or aa, then p2 + 2pq + q2 = 1

"Random mating"

  • Start with the frequency of the three different genotypes (AA, Aa, aa)
  • Determine the probability of all of the different possible matings (AA with AA, AA with Aa, etc.)
  • Determine the proportions of the different genotypes produced by each of the "matings", i.e. AA with AA produce all AA progeny, Aa with Aa produce 1/4 AA, 1/2 Aa, and 1/4 aa
  • Add up all of the AA, Aa, and aa produced by the different matings
  • The result is that the frequency of AA in the next generation = p2, f(Aa) = 2pq and f(aa) = q2

Hardy-Weinberg Principle

In a large randomly mating population with no mutation, migration or differential reproductive success, the frequencies of alleles in a population will not change.

  • Evolution objectively defined
  • Identifies causes of evolution

Conditions under which there will be no changes in allelic frequencies

  1. No selection
  2. Infinite population
  3. Random mating
  4. No mutation
  5. No migration

Deviations from Hardy-Weinberg

  • Selection - the only one of these that causes adaptive change
    • directional, stabilizing or disruptive
  • Small population size leads to sampling error(founder effect, genetic drift)
  • nonrandom mating (inbreeding, assortive or disassortive mating, sexual selection) - only sexual selection changes the allelic frequencies, the others change genotypic frequencies (changes in heterozygosity)
  • Mutation - the ultimate source of all new alleles
    • by itself mutation has little effect because typical mutation rates are so small (less then 10-5) - thus genetic drift eliminates most new mutations
  • Migration - the addition of alleles from other populations - tends to average things out (the melting pot effect)

You can see how some of this works by doing the exercises in the Population Genetics Simulation handout which uses the popualation genetics simulator kindly provided by the University of Chicago.

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This document is maintained by: Jeff Bell
Last Update: Wednesday, August 12, 1998