Estimation of the Characteristics of Rare Variants

  • E. A. Thompson
Conference paper
Part of the Lecture Notes in Biomathematics book series (LNBM, volume 19)


This paper arises in connection with a study of the data on rare protein variants in American Indian populations. Several American Indian tribes have been extensively sampled (Neel 1973), and the variants found range from those present only in a single individual or nuclear family, through those that have spread through a village or to several villages, to one which has achieved polymorphic frequencies in a single tribe. It is perhaps doubtful whether this last should be considered a “rare variant”, but we include it since it is fairly certain that it has arisen since tribal differentiation, and in spite of inter-tribal migration it has not spread to neighbouring tribes. For variants apparently localised in areas where sampling has been intensive, accurate estimates of the total number of individuals carrying the variant allele may be made.


Rare Variant Offspring Distribution Neutral Allele American Indian Population Migration Matrix 
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  1. Crump, K. S. and Gillespie, J.H. 1976. The dispersion of a neutral allele considered as a branching process. J. Appl. Prob. 13: 208–218.CrossRefGoogle Scholar
  2. Ewens, W.J. 1972. Sampling theory of selectively neutral alleles. Theor. Pop. Biol. 3: 87–112.CrossRefGoogle Scholar
  3. Ewens, W.J. 1973. Testing for increased mutation rate for neutral alleles. Theor. Pop. Biol. 4: 251–258.CrossRefGoogle Scholar
  4. Harris, T.E. 1963. The theory of branching processes. Springer Verlag, Berlin.Google Scholar
  5. Karlin, K. and MacGregor, J. 1966. The number of mutant forms maintained in a population. Proc. V Berk. Symp. 4: 415–438.Google Scholar
  6. Kimura, M. and Ohta, T. 1974. The age of a neutral mutant persisting in a finite population. Genetics 75: 199–212.Google Scholar
  7. Kojima, K. and Kelleher, T.M. 1962. Survival of mutant genes. Am. Nat. 96: 329–346.CrossRefGoogle Scholar
  8. Li, W.H. 1975. The first arrival time and mean age of a deleterious mutant in a finite population. Am. J. Hum. Genet. 27: 274–286.PubMedGoogle Scholar
  9. MacCluer, J.W., Neel, J.V. and Chagnon, N. 1971. Demographic structure of a primitive population; a simulation. Am. J. Phys. Anthrop. 35: 193–208.PubMedCrossRefGoogle Scholar
  10. Maruyama, T. 1974. The age of a rare mutant gene in a finite population. Am. J. Hum. Genet. 26: 669–673.PubMedGoogle Scholar
  11. Moran, P.A.P. 1975. Wandering distributions and the electrophoretic profile. Theor. Pop. Biol. 8: 318–330.CrossRefGoogle Scholar
  12. Neel, J.V. 1973. “Private” genetic variants and the frequency of mutation. Proc. Nat. Acad. Sci. USA 70: 3311–3315.PubMedCrossRefGoogle Scholar
  13. Neel, J.V. and Chagnon, N. 1968. Demography of two tribes of primitive relatively unacculturated American Indians. Proc. Nat. Acad. Sci. USA 59: 680–689.PubMedCrossRefGoogle Scholar
  14. Stigler, S. 1970. Estimating the age of a Galton-Watson process. Biometrika 57: 505–512.Google Scholar
  15. Thompson, E.A. 1976. Estimation of the age and rate of increase of rare variants. Am. J. Hum. Genet. 28: 442–452.PubMedGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 1977

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  • E. A. Thompson

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