Infinite Allele Model with Varying Mutation Rate (Protein Polymorphism/Heterozygosity/Genetic Distance) MASATOSHI Nei, RANAJIT CHAKRABORTY, and PAUL A
Proc. Natl. Acad. Sci. USA Vol. 73, No. 11, pp.4164-4168, November 1976 Genetics Infinite allele model with varying mutation rate (protein polymorphism/heterozygosity/genetic distance) MASATOSHI NEi, RANAJIT CHAKRABORTY, AND PAUL A. FUERST Center for Demographic and Population Genetics, University of Texas at Houston, Houston, Tex. 77030 Communicated by Motoo Kimura, September 7, 1976 ABSTRACT Available data suggest that the variation in tone IV which has an unusually low rate of amino acid substi- mutation rate among protein loci follows the gamma distribu- tion. Thus, taking. into account this variation, formulae are de- tution. The mean and standard deviations of this distribution veloped for the distribution of allele frequencies, mean and are 2.47 X 10-7 and 2.51 X 10- per year, respectively. We variance of heter'ozygosity, expected number of alleles, pro- fitted the following gamma distribution to these data: portion of polymorphic loci, and genetic distance. These for- mulae should be more appropriate for the analysis of gene fre- quency data for protein loci than equivalent formulae with f(z) r(a) e Zi, [1] constant mutation rate. where a = i2/V5 and , = z/V,, in which z and V. are the In the last 10 years statistical methods based on the so-called mean and variance of the variate in question (z), respectively. infinite allele model (1, 2) have been used extensively to study The maximum likelihood estimates of a and ,3 obtained are 0.95 the mechanism of maintenance of protein polymorphism. and 3.9 X 106, respectively. It is clear that the gamma distri- Because each allele in a population behaves in a random fashion bution fits the data reasonably well (Fig.
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