Finite populations

Introduction

Hardy-Weinberg assumptions

  • Diploid
  • 2 alleles
  • Sexual reproduction
  • Mating is random
  • Same allele / genotype frequencies in both sexes
  • Very large population
  • Discrete generations
  • No mutation
  • No migration
  • No natural selection

All populations are finite

Model of finite populations

  • “Wright-Fisher” model
  • Named for:
    • Sewal Wright
    • Sir Ronald A Fisher

Basis of Wright-Fisher model

  • Individuals produce many gametes
  • Gametes contribute to gamete pool

  • Genes sampled from infinite gamete pool
  • Each gene in generation \(g\) can have \(0\) - \(2N\) descendents in generation \(g+1\)
  • Descendents a binomial random variable with \(p = \frac{1}{2N}\)

Genealogies

Identity by descent

  • Gustave Malécot (1911 - 1998)
  • Identical by descent: derived from the same ancestor.

Reading

Textbook: page 55

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