Journal of Mathematical Biology

, Volume 29, Issue 2, pp 131–159

On the two-locus sampling distribution

  • S. N. Ethier
  • R. C. Griffiths

DOI: 10.1007/BF00168175

Cite this article as:
Ethier, S.N. & Griffiths, R.C. J. Math. Biol. (1990) 29: 131. doi:10.1007/BF00168175


Two methods are discussed for evaluating the distribution of the configuration of unlabeled gametic types in a random sample of size n from the two-locus infinitely-many-neutral-alleles diffusion model at stationarity. Both involve finding systems of linear equations satisfied by the desired probabilities. The first approach, which is due to Golding, is to include additional probabilities in the system that allow some members of the sample to be specified at only one locus. The second approach, which is new, considers the joint distribution of the sample configuration and the number of recombination events since the time of the most recent common ancestor. The first approach is used for numerical computation, whereas the second approach is used to derive a two-locus version of Hoppe's urn model. The latter permits efficient simulation of the two-locus sampling distribution, provided the recombination parameter is not too large.

Key words

Measure-valued diffusion Infinitely-many-neutral-alleles model Recombination Complete linkage Independent loci Ewens' sampling formula 

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • S. N. Ethier
    • 1
  • R. C. Griffiths
    • 2
  1. 1.Department of MathematicsUniversity of UtahSalt Lake CityUSA
  2. 2.Department of MathematicsMonash UniversityClaytonAustralia