Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-04T20:13:41.786Z Has data issue: false hasContentIssue false
  • English
  • Français

Drift variances of heterozygosity and genetic distance in transient states

Published online by Cambridge University Press:  14 April 2009

Wen-Hsiung Li  and
Masatoshi Nei
Wen-Hsiung Li
Affiliation:
Centre for Demographic and Population Genetics University of Texas at Houston, Texas 77025
Masatoshi Nei
Affiliation:
Centre for Demographic and Population Genetics University of Texas at Houston, Texas 77025

Summary

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Using the moments of gene frequencies, the drift variances of heterozygosity and genetic distance in transient states have been studied under the assumption that all mutations are selectively neutral. Interestingly, this approach provides a simple derivation of Stewart's formula for the variance of heterozygosity at steady state. The results obtained indicate that if all alleles in the initial population are equally frequent, the standard derivation of heterozygosity is very small and increases linearly with time in the early generations. On the other hand, if the initial allele frequencies deviate appreciably from equality, then the standard deviation in the early generations is much larger but increases linearly with the square root of time. Under certain conditions, the standard deviation of genetic distance also increases linearly with time. Numerical computations have shown that the standard deviations of heterozygosity and genetic distance relative to their means are so large that a large number of loci must be used in estimating the average heterozygosity and genetic distance per locus.

Type
Research Article
Information
Genetics Research , Volume 25 , Issue 3 , June 1975 , pp. 229 - 247
Copyright
Copyright © Cambridge University Press 1975

References

REFERENCES

Avise, J. C. & Selander, R. K. (1972). Evolutionary genetics of cave-dwelling fishes of the genus Astyanax. Evolution 26, 1–19.Google ScholarPubMed
Bernstein, S. C., Throckmorton, L. H. & Hubby, J. L. (1973). Still more genetic variability in natural populations. Proceedings of the National Academy of Sciences (U.S.A.) 70, 3928–3931.CrossRefGoogle ScholarPubMed
Cavalli-Sforza, L. L. (1969). Human diversity. Proceedings of the XIIth International Congress of Genetics (Tokyo) 3, 405–416.Google Scholar
Cavalli-Sforza, L. L. & Edwards, A. W. F. (1967). Phylogenetic analysis: models and estimation procedures. American Journal of Human Genetics 19, 233–257.Google ScholarPubMed
Chakraborty, R. & Nei, M. (1974). Dynamics of gene differentiation between incompletely isolated populations of unequal sizes. Theoretical Population Biology 5, 460–469.CrossRefGoogle ScholarPubMed
Crow, J. F. & Kimura, M. (1956). Some genetic problems in natural populations. Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability 4, 1–22.Google Scholar
Hedrick, P. W. (1971). A new approach to measuring genetic similarity. Evolution 25, 276–280.CrossRefGoogle ScholarPubMed
Kimura, M. (1955). Random genetic drift in a multi-allelic locus. Evolution 9, 419–435.CrossRefGoogle Scholar
Kimura, M. (1968). Genetic variability maintained in a finite population due to mutational production of neutral and nearly neutral isoalleles. Genetical Research 11, 247–269.CrossRefGoogle Scholar
Kimura, M. & Crow, J. F. (1964). The number of alleles that can be maintained in a finite population. Genetics 49, 725–738.CrossRefGoogle Scholar
Kimura, M. & Ohta, T. (1971). Protein polymorphism as a phase of molecular evolution. Nature 229, 467–469.CrossRefGoogle ScholarPubMed
Latter, B. D. H. (1972). Selection in finite populations with multiple alleles. III. Genetic divergence with centripetal selection and mutation. Genetics 70, 475–490.CrossRefGoogle Scholar
Malécot, G. (1948). Les Mathématiques de l'hérédité. Paris: Masson et Cie.Google Scholar
Nei, M. (1972). Genetic distance between populations. American Naturalist 106, 283–292.CrossRefGoogle Scholar
Nei, M. (1973). The theory and estimation of genetic distance. Genetic Structure of Populations (ed. Morton, N. E.), pp. 45–54. Honolulu: University of Hawaii Press.Google ScholarPubMed
Nei, M. (1975). Molecular Population Genetics and Evolution. Amsterdam: Elsevier, Excerpta Medica and North-Holland.Google ScholarPubMed
Nei, M. & Chakraborty, R. (1973). Genetic distance and electrophoretic identity of proteins between taxa. Journal of Molecular Evolution 2, 323–328.CrossRefGoogle ScholarPubMed
Nei, M. & Feldman, M. W. (1972). Identity of genes by descent within and between populations under mutation and migration pressures. Theoretical Population Biology 3, 460–465.CrossRefGoogle ScholarPubMed
Nei, M. & Roychoudhury, A. K. (1972). Gene differences between Caucasian, Negro, and Japanese populations. Science 177, 434–436.CrossRefGoogle ScholarPubMed
Nei, M. & Roychoudhury, A. K. (1974 a). Genic variation within and between the three major races of man, Caucasoids, Negroids, and Mongoloids. American Journal of Human Genetics 26, 421–443.Google ScholarPubMed
Nei, M. & Roychoudhury, A. K. (1974 b). Sampling variances of heterozygosity and genetic distance. Genetics 76, 379–390.CrossRefGoogle ScholarPubMed
Ohta, T. & Kimura, M. (1973). A model of mutation appropriate to estimate the number of electrophoretically detectable alleles in a finite population. Genetical Research 22, 201–204.CrossRefGoogle Scholar
Ohta, T. & Kimura, M. (1974). Simulation studies on electrophoretically detectable genetic variability in a finite population. Genetics 76, 615–624.CrossRefGoogle Scholar
Rogers, J. S. (1972). Measures of genetic similarity and genetic distance. Studies in Genetics: VII. University of Texas Publication no. 7213, pp. 145–153.Google Scholar
Sanghvi, L. D. (1953). Comparison of genetic and morphological methods for a study of biological differences. American Journal of Physical Anthropology 11, 385–404.CrossRefGoogle ScholarPubMed
Stewart, F. M. (1974). Variability in the amount of heterozygosity maintained by neutral mutations. Theoretical Population Biology (in press).Google Scholar