Wright-Fisher model

Shafiey H & Waxman D 2017 Exact results for the probability and stochastic dynamics of fixation in the Wright-Fisher model. J Theor Biol 430:64-77.

  • 6.2. fixing trajectories for a neutral fixation probability
  • Yt + 1 = Bin(N − 1, Yt) / N + 1 / N ... (17)
  • fixing trajectories
  • the presence of the term 1 / N in Eq. (17) ensures that loss of the A allele can never occur
  • the second term on the right hand side Eq. (17) can simply be interpreted as the injection, every generation, of a single carrier of the A allele into a population of size N − 1
  • in the diploid case it is a bit more complicated
  • if we repeat the analysis we have already presented, but conditional on ultimate loss of the focal allele, then 1 / N term is absent
  • in the simplest case of neutrality, this is the only change
  • Zt + 1 = Bin(N − 1, Zt) / N
  • 2 since the population of juveniles is effectively infinite, it makes no difference whether we pick N individuals with or without replacement
  • 4 genic selection, by its definition, exhibits no dominance on a logarithmic scale
  • the log fitness of the heterozygote lies at the mean of the log fitnesses of the two homozygotes
  • if genic selection is weak, it can be approximated by additive selection
  • the fitness of the heterozygote then lies at the mean fitness of the two homozygotes, and exhibits no dominance on a linear scale
  • 5 when selection is not genic, the number of A alleles in adults in generation t + 1, conditional on the value of Xt, will deviate from a binomial random variable (Nagylaki, 1992, p252; see also Waxman, 2009)