Measuring Evolution in Populations using Hardy-Weinberg Theorem

Introduction

• The Hardy-Weinberg theorem is used to determine if a population is evolving.
• Evolution is defined as a change in allele frequencies over time.

Five Mechanisms of Evolution

1. Natural Selection
2. Sexual Selection
3. Mutations
4. Genetic Drift
5. Gene Flow

Hardy-Weinberg Equilibrium

• A population is in Hardy-Weinberg equilibrium if it is not evolving, meaning allele frequencies remain constant from one generation to the next.
• Conditions for equilibrium:
  • No natural selection
  • Random mating (no sexual selection)
  • No new mutations
  • Large population size (to mitigate effects of genetic drift)
  • No migration (no gene flow or introduction of new genes)

Calculating Allele Frequencies

• Formula: ( p + q = 1 )
  • ( p ): frequency of the dominant allele
  • ( q ): frequency of the recessive allele

Example: Deer Population

• Phenotypes: Orange (recessive), Brown (dominant or heterozygous)
• Start by solving for ( q ) using recessive phenotypes, then solve for ( p ).

Homozygous and Heterozygous Individuals

• Formula: ( p^2 + 2pq + q^2 = 1 )
  • ( p^2 ): frequency of homozygous dominant individuals
  • ( 2pq ): frequency of heterozygous individuals
  • ( q^2 ): frequency of homozygous recessive individuals

Practical Example Calculations

1. Original Population:
   • 24 deer, 48 alleles (diploids)
   • 24 dominant alleles, 24 recessive alleles
   • ( p = 0.5 ), ( q = 0.5 )
2. Natural Selection Example:
   • Orange phenotype selected against
   • New generation: ( p = 0.59 ), ( q = 0.41 )
   • Population evolved (allele frequencies changed)
3. Sexual Selection Example:
   • Orange deer have shorter antlers, less reproductive success
   • Original: ( p = 0.29 ), ( q = 0.71 )
   • New generation: ( p = 0.47 ), ( q = 0.53 )
   • Change in allele frequencies indicates evolution

Summary

• Changes in allele frequencies from one generation to the next indicate evolution.
• Hardy-Weinberg equations allow us to calculate allele and genotype frequencies to determine if evolution is occurring.
• Future discussions will cover more styles of Hardy-Weinberg problems and solutions.