Coalescent patterns in diploid exchangeable population models

J Math Biol. 2003 Oct;47(4):337-52. doi: 10.1007/s00285-003-0218-6. Epub 2003 May 15.


A class of two-sex population models is considered with N females and equal number N of males constituting each generation. Reproduction is assumed to undergo three stages: 1) random mating, 2) exchangeable reproduction, 3) random sex assignment. Treating individuals as pairs of genes at a certain locus we introduce the diploid ancestral process (the past genealogical tree) for n such genes sampled in the current generation. Neither mutation nor selection are assumed. A convergence criterium for the diploid ancestral process is proved as N goes to infinity while n remains unchanged. Conditions are specified when the limiting process (coalescent) is the Kingman coalescent and situations are discussed when the coalescent allows for multiple mergers of ancestral lines.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Algorithms
  • Animals
  • Diploidy*
  • Female
  • Genetics, Population*
  • Genotype
  • Humans
  • Male
  • Models, Genetic*
  • Pedigree*
  • Reproduction / genetics
  • Sex Distribution
  • Stochastic Processes