Skip to main content
Log in

Asymptotic line-of-descent distributions

  • Published:
Journal of Mathematical Biology Aims and scope Submit manuscript

Abstract

Asymptotic distributions are derived for the number of non-mutant ancestors, at time t in the past, of a sample of n from a neutral infinite alleles model. Either the number of non-mutant ancestors L n (t) has a normal distribution or n-Ln(t) has a Poisson distribution as n → ∞, t → 0.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Billingsley, P.: Probability and Measure. New York: Wiley, 1979

    Google Scholar 

  • Donnelly, P.: The transient behaviour of the Moran model in population genetics. Math. Proc. Cambridge Philos. Soc. 95, 349 (1984)

    Google Scholar 

  • Griffiths, R. C.: Lines of descent in the diffusion approximation of neutral Wright-Fisher models. Theoret. Population Biology 17, 37–50 (1980)

    Google Scholar 

  • Kingman, J. F. C.: On the geneology of large populations. J. Appl. Probability 19A, 27–43 (1982a)

    Google Scholar 

  • Kingman, J. F. C.: The coalescent. Stochastic Processes Appl. 13, 235–248 (1982b)

    Google Scholar 

  • Tavaré, S.: Line-of-descent and genealogical processes, and their applications in population genetics. Theoret. Population Biology 26, 119–164 (1984).

    Google Scholar 

  • Tier, C., Keller, J. B.: Asymptotic analysis of diffusion equations in population genetics. SIAM J. Appl. Math. 34, 549–576 (1978)

    Google Scholar 

  • Voronka, R., Keller, J. B.: Asymptotic analysis of stochastic models in population genetics. Math. Biosci. 25, 331–362 (1975)

    Google Scholar 

  • Watterson, G. A.: Lines of descent and the coalescent. Theoret. Population Biology 26, 77–92 (1984).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Griffiths, R.C. Asymptotic line-of-descent distributions. J. Math. Biology 21, 67–75 (1984). https://doi.org/10.1007/BF00275223

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00275223

Key words

Navigation