Abstract
The fundamental quantity which is used in population genetics to describe the genetic composition of a Mendelian population (i.e. reproductive community) is the gene frequency, or the proportion of a given gene in the population. Thus, a population is characterized by a set of gene frequencies.
Contribution No. 697 from the National Institute of Genetics, Misima, Shizuoka-ken, Japan.
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References
Crow, J. F.: Breeding structure of populations. II. Effective population number. In: Statistics and mathematics in biology, pp. 543–556. Ames, Iowa: Iowa State College Press 1954.
-, and N. Morton: Measurement of gene frequency drift in small populations. Evolution 9, 202–214 (1955).
-, and M. Kimura: An introduction to population genetics theory. New York: Harper and Row 1970.
Deevey, E. S. Jr.: The human population. Sci. Am. 203, 195–204 (1960).
Ewens, W. J.: The probability of a new mutant in a fluctuating environment. Heredity 22, 438–443 (1967).
Fisher, R. A.: On the dominance ratio. Proc. Roy. Soc. Edinburgh 42, 321–341 (1922).
- The genetical theory of natural selection. Oxford: Clarendon Press 1930.
Haldane, J. B. S.: A mathematical theory of natural and artificial selection. Part V: Selection and mutation. Proc. Cambridge Phil. Soc. 23, 838–844 (1927).
Hill, W. G., and A. Robertson: Linkage disequilibrium in finite populations. Theor. Appl. Genet. 38, 226–231 (1968).
Karlin, S., and J. McGregor: On some stochastic models in genetics. In: Gurland, J. (Ed.): Stochastic models in medicine and biology, pp. 245–271. Madison: University of Wisconsin Press 1964.
Kerr, W. E.: Multiple alleles and genetic load in bees. J. Apicult. Res. 6, 61–64 (1967).
Kimura, M.: Solution of a process of random genetic drift with a continuous model. Proc. Natl. Acad. Sci. U.S. 41, 144–150 (1955a).
- Random genetic drift in multi-allelic locus. Evolution 9, 419–435 (1955b).
- Random genetic drift in a tri-allelic locus: Exact solution with a continuous model. Biometrics 12, 57–66 (1956).
- Some problems of stochastic processes in genetics. Ann. Math. Stat. 28, 882–901 (1957).
- On the probability of fixation of mutant genes in a population. Genetics 47, 713–719 (1962).
-, and J. F. Crow: The measurement of effective population number. Evolution 17, 279–288 (1963).
-, T. Maruyama, and J. F. Crow: The mutation load in small populations. Genetics 48, 1303–1312 (1963).
- Diffusion models in population genetics. J. Appl. Prob. 1, 177–232 (1964).
-, and J. F. Crow: The number of alleles that can be maintained in a finite population. Genetics 49, 725–738 (1964).
- Evolutionary rate at the molecular level. Nature (Lond.) 217, 624–626 (1968a).
- Genetic variability maintained in a finite population due to mutational production of neutral and nearly neutral isoalleles. Genet. Res. 11, 247–269 (1968b).
- The number of heterozygous nucleotide sites maintained in a finite population due to steady flux of mutations. Genetics 61, 893–903 (1969).
-, and T. Ohta: The average number of generations until fixation of a mutant gene in a finite population. Genetics 61, 763–771 (1969).
Kojima, K., and T. M. Kelleher: Survival of mutant genes. Amer. Natur. 96, 329–346 (1962).
Miller, G. F.: The evalution of eigenvalues of a differential equation arising in a problem in genetics. Proc. Cambridge Phil. Soc. 58, 588–593 (1962).
Moran, P. A. P.: The survival of a mutant under general conditions. Proc. Cambridge Phil. Soc. 57, 304–314 (1961).
Muller, H. J.: Evolution by mutation. Bull. Am. Math. Soc. 64, 137–160 (1958).
Nei, M., and Y. Imaizumi: Effects of restricted population size and increase in mutation rate on the genetic variation of quantitative characters. Genetics 54, 763–782 (1966).
Ohta, T.: Effect of initial linkage disequilibrium and epistasis on fixation probability in a small population, with two segregating loci. Theor. Appl. Genet. 38, 243–248 (1968).
-, and M. Kimura: Linkage disequilibrium due to random genetic drift. Genet. Res. 13, 41–55 (1969).
Robertson, A.: A theory of limits in artificial selection. Proc. Roy. Soc. B, 153, 234–249 (1960).
- Selection for heterozygotes in small populations. Genetics 47, 1291–1300 (1962).
Watterson, G. A.: Some theoretical aspects of diffusion theory in population genetics. Ann. Math. Stat. 33, 939–957 (1962).
Wright, S.: Evolution in Mendelian populations. Genetics 16, 97–159 (1931).
- The distribution of gene frequencies in populations. Proc. Natl. Acad. Sci. U.S. 23, 307–320 (1937).
- The distribution of gene frequencies under irreversible mutation. Proc. Natl. Acad. Sci. U.S. 24, 253–259 (1938).
- Statistical genetics in relation to evolution. Actualités Scientifiques et Industrielles 802. Exposés de Biométrie et de Statistique Biologique. Paris: Hermann et Cie. 1939.
- Statistical genetics and evolution. Bull. Am. Math. Soc. 48, 223–246 (1942).
- The differential equation of the distribution of gene frequencies. Proc. Natl. Acad. Sci. U.S. 31, 382–389 (1945).
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Kimura, M. (1970). Stochastic Processes in Population Genetics, with Special Reference to Distribution of Gene Frequencies and Probability of Gene Fixation. In: Kojima, Ki. (eds) Mathematical Topics in Population Genetics. Biomathematics, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46244-3_6
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DOI: https://doi.org/10.1007/978-3-642-46244-3_6
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