Lecture 9

• Hardy–Weinberg Equilibrium


  Allele frequencies and genotype frequencies remain at equilibrium (i.e., constant) when there is no mutation, no selection, no migration, no genetic drift, and random mating

  
• Hardy–Weinberg Equilibrium


  • Genotype frequencies for a diallelic locus are expected to be: p^2 (AA), 2pq (Aa), q^2 (aa)

  
• Population Genetics


  The study of populations' allele frequencies and their changes over time

  
• Population Genetics and Quantitative Genetics were the cornerstones of the modern synthesis
• Population Geneticists


  • Study evolution using theoretical models, computer simulations, laboratory experiments, and by observing natural populations
• Population


  Localized group of individuals of the same species
• Theodosius Dobzhansky: 'Nothing in biology makes sense except in the light of evolution'
• Michael Lynch: 'Nothing in evolutionary biology makes sense except in the light of population genetics'
• Evolution


  A change in allele frequencies over generations

  
• Calculating genotype and allele frequencies

  1. Observe genotypes of a sample

  2. Calculate observed genotype frequencies

  3. Calculate allele frequencies from genotype frequencies

  
• Homozygotes carry two identical allele copies, heterozygotes carry one copy of each allele
• Allele frequencies p and q must sum to 1
• Genotype frequencies fr(AA), fr(Aa), fr(aa) must sum to 1

  
• Allele frequencies can be calculated from genotype frequencies, but the reverse is usually impossible without additional information

  
• Idealized population


  • Random mating, infinitely large, discrete non-overlapping generations
• Life cycle of an idealized population

  1. Gene pool

  2. Zygote formation

  3. Zygotes to adults

  4. Adults creating gametes

  
• Genotype frequencies among zygotes are p^2 (AA), 2pq (Aa), q^2 (aa)

  
• Genotype frequencies among adults are the same as zygotes if there is no selection or gene flow

  
• Allele frequencies in gametes produced by adults are the same as the original allele frequencies in the population
• Hardy-Weinberg Principle


  Allele and genotype frequencies remain constant over generations if there is no mutation, selection, migration, drift, and random mating

  
• With more than two alleles, the Hardy-Weinberg equilibrium formula is more complex
• Allele frequencies produced when adults make gametes

  1. p2 + 2pq/2 = p2 + pq = p2 + p(1–p) = p

  2. q2 + 2pq/2 = q2 + pq = q2 + (1–q)q = q
• The allele frequencies produced are the same as the original allele frequencies. If allele frequencies didn't change over a generation, evolution hasn't happened.

  
• Hardy-Weinberg principle


  States that allele frequencies and genotype frequencies remain at equilibrium (i.e., constant) when these conditions hold true: No mutation, No selection, No migration, No genetic drift, Random mating

  
• Genotype frequencies at Hardy-Weinberg equilibrium for a diallelic locus

  • AA: p2
  • Aa: 2pq
  • aa: q2

  
• Hardy-Weinberg equilibrium with more than two alleles


  For a triallelic locus (with allele frequencies of p, q, and r), the genotype frequencies are: A1A1: p2, A1A2: 2pq, A1A3: 2pr, A2A2: q2, A2A3: 2qr, A3A3: r2

  
• Hardy-Weinberg principle


  • It is the null model for evolution
  • If all the conditions hold true, evolution will not happen
  • It identifies the "forces" that cause evolution
  • Genotype frequencies in real populations can be examined to determine whether they are in Hardy-Weinberg equilibrium

  
• Testing whether a population is in Hardy-Weinberg equilibrium

  1. Calculate observed genotype frequencies

  2. Calculate allele frequencies

  3. Calculate expected genotype frequencies assuming Hardy-Weinberg equilibrium

  4. Compare observed and expected genotype counts

  
• If a locus does not match Hardy-Weinberg expectations, we can reject the null model. One or more assumptions may be substantially violated for this locus; something interesting may be happening.
• If a locus matches Hardy-Weinberg expectations, we cannot necessarily conclude that the null model is true. The assumptions may be only slightly violated, or a balance of the forces might keep the genotypes approximately in Hardy-Weinberg proportions.
• How mutation affects allele frequencies

  1. p' = p - μp

  2. Δp = -μp

  3. q' = 1 - p'

  
• Mutation, by itself, is a weak evolutionary force. Even with a high mutation rate iterated over many generations, the allele frequency only changes slightly.