Absorption and fixation times for neutral and quasi-neutral populations with density dependence

Todd L. Parsons, Christopher Quince, Joshua B. Plotkin

Research output: Contribution to journalArticlepeer-review

29 Citations (Scopus)


We study a generalisation of Moran's population-genetic model that incorporates density dependence. Rather than assuming fixed population size, we allow the number of individuals to vary stochastically with the same events that change allele number, according to a logistic growth process with density dependent mortality. We analyse the expected time to absorption and fixation in the 'quasi-neutral' case: both types have the same carrying capacity, achieved through a trade-off of birth and death rates. Such types would be competitively neutral in a classical, fixed-population Wright-Fisher model. Nonetheless, we find that absorption times are skewed compared to the Wright-Fisher model. The absorption time is longer than the Wright-Fisher prediction when the initial proportion of the type with higher birth rate is large, and shorter when it is small. By contrast, demographic stochasticity has no effect on the fixation or absorption times of truly neutral alleles in a large population. Our calculations provide the first analytic results on hitting times in a two-allele model, when the population size varies stochastically.

Original languageEnglish
Pages (from-to)302-310
Number of pages9
JournalTheoretical Population Biology
Issue number4
Publication statusPublished - Dec 2008


  • Absorption
  • Allele
  • Asymptotic
  • Competition
  • Density-dependent
  • Drift
  • Fixation
  • Logistic
  • Moran
  • Neutral
  • Stochastic
  • Wright-Fisher

Cite this