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Equilibrium behavior of population genetic models with non-random mating. Part I: Preliminaries and special mating systems

Published online by Cambridge University Press:  14 July 2016

Samuel Karlin*
Affiliation:
Stanford University, California

Abstract

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Type
Review Paper
Copyright
Copyright © Applied Probability Trust 1968 

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References

Bailey, N. T. J. (1961) Introduction to the Mathematical Theory of Genetic Linkage. Oxford University Press.Google Scholar
Bartlett, M. S. and Haldane, J. B. S. (1935) The theory of inbreeding with forced heterozygosis. J. Genet. 31, 327340.Google Scholar
Bennett, J. H. (1954) The distribution of heterogeneity upon inbreeding. J. R. Statist. Soc. B 16, No. 1, 8899.Google Scholar
Bennett, J. H. and Binet, F. E. (1956) Association between Mendelian factors with mixed selfing and random mating. Heredity 10, 5155.CrossRefGoogle Scholar
Bennett, J. H. (1956) Lethal genes in inbred lines. Heredity 10, 263270.CrossRefGoogle Scholar
Bodmer, W. F. (1960a) The genetics of homostyly in populations of Primula vulgaris. Phil. Trans. Roy. Soc. B 242, 517549.Google Scholar
Bodmer, W. F. (1960b) Discrete stochastic processes in population genetics. J. R. Statist. Soc. B 22, 218236.Google Scholar
Bodmer, W. F., Feldman, M. W. and Karlin, S. Theoretical Population Genetics. Manuscript in preparation.Google Scholar
Crow, J. F. (1967) Genetic Notes. 6th Edition, Burgess Publishing Company.Google Scholar
Crow, J. F. (1969) Population Genetics. Harper and Row (in press).Google Scholar
Darwin, C. (1859) The Origin of Species.Google Scholar
East, E. M. and Mangelsdorf, A.J. (1925) A new interpretation of the hereditary behaviour of self sterile plants. Proc. Nat. Acad. Sci. USA 11, 166–17.Google Scholar
Finney, D. J. (1952) The equilibrium of a self incompatible polymorphic species. Genetica 26, 3364.CrossRefGoogle ScholarPubMed
Fisher, R. A. (1949) The Theory of Inbreeding. Oliver and Boyd, Edinburgh.Google Scholar
Fisher, R. A. (1958) The Genetical Theory of Natural Selection. Second revised edition, Dover, New York.Google Scholar
Fisher, R. A. and Mather, K. (1943) The inheritance of style length in Lythrum salicaria Ann. Eugenics 12, 123.Google Scholar
Gale, J. S. (1964) Some applications of the theory of junctions. Biometrics 20, 85117.CrossRefGoogle Scholar
Garber, M. J. (1951) Approach to genotypic equilibrium with varying percentage of self fertilization. J. Heredity 42, 299300.CrossRefGoogle Scholar
Ghat, G. L. (1967) Loss of heterozygosity in populations under mixed random mating and selfing. J. Indian Soc. Agr. Statist. 18, 7381.Google Scholar
Haldane, J. B. S. (1956) The conflict between inbreeding and selection. J. Genet. 54, 5663.Google Scholar
Hayman, B. I. (1953) Mixed selfing and random mating when homozygotes are at a disadvantage. Heredity 7, 185192.CrossRefGoogle Scholar
Hayman, B. I. and Mather, K. (1953) Progress of inbreeding when homozygotes are at a disadvantage. Heredity 7, 165183.CrossRefGoogle Scholar
Jennings, H. S. (1916) The numerical results of diverse systems of breeding. Genetics 1, 5389.Google Scholar
Kalmus, H. and Maynard-Smith, Sheila (1966) Some evolutionary consequences of pegmatypic mating systems (imprinting). Amer. Naturalist 100, 619635.Google Scholar
Karlin, S. (1966) A First Course in Stochastic Processes. Academic Press, New York and London.Google Scholar
Karlin, S. and Feldman, M. W. (1968a) Analysis of models with homozygote x heterozygote matings. Genetics 59, 105116.CrossRefGoogle ScholarPubMed
Karlin, S. and Feldman, M. W. (1968b) Further analysis of negative assortative mating. Genetics 59, 117136.Google Scholar
Karlin, S. and Scudo, F. (1968) Assortative mating based on phenotype II: Two autosomal alleles without dominance. To appear.Google Scholar
Kempthorne, O. (1957) An Introduction to Statistical Genetics. Wiley, New York.Google Scholar
Kimura, M. (1957) Overdominant genes in a partially self-fertilizing population. Annual Report Nat. Inst. Genet. (Japan) 105106.Google Scholar
Lerner, I. M. (1950) Population Genetics and Animal Improvement. Cambridge University Press.Google Scholar
Li, C. C. (1955) Population Genetics. The University Press, Chicago.Google Scholar
Mainardi, D. (1968) La Scelta Sessuale Nell' Evoluzione Della Specie. Boringhieri, Torino.Google Scholar
Moran, P. A. P. (1962) The Statistical Processes of Evolutionary Theory. Clarendon Press, Oxford.Google Scholar
O'Donald, P. (1959) Possibility of assortive mating in the Arctic Skua. Nature 182, 12101211.Google Scholar
O'Donald, P. (1960a) Inbreeding as a result of imprinting. Heredity 15, 79.Google Scholar
O'Donald, P. (1960b) Assortive mating in a population in which two alleles are segregating. Heredity 15, 389396.Google Scholar
Page, A. R. and Hayman, B. I. (1960) Mixed sib and random mating when homozygotes are at a disadvantage. Heredity 14, Parts 1 and 2, 187196.Google Scholar
Parsons, P. A. (1957) Selfing under conditions favouring heterozygosity. Heredity, 11, Part 3, 411421.Google Scholar
Parsons, P. A. (1962) The initial increase of a new gene under positive assortative mating. Heredity 17, 267276.Google Scholar
Parsons, P. A. (1963) Complex polymorphisms where the coupling and repulsion double heterozygote viabilities differ. Heredity 18, 369374.Google Scholar
Parsons, P. A. (1963) Polymorphisms and the balanced polygenic combination. Evolution 17, 564574.Google Scholar
Parsons, P. A. (1965) Assortative mating for a metrical characteristic in drosophila. Heredity 20, 161167.Google Scholar
Scudo, F. M. (1964) Sex population genetics. Ri. Sci. 34, II–B, 93146.Google Scholar
Scudo, F. M. and Karlin, S. (1968) Assortative mating based on phenotype; I. Two alleles with dominance. To appear.Google Scholar
Scudo, F. M., Mainardi, D. and Barbieri, D. (1965) Assortative mating based on early learning: population genetics. Acta Bio-medica 36, Fasc. 5 583605.Google Scholar
Stern, Curt (1960) Principles of Human Genetics. 2nd edition. Freeman, San Francisco.Google Scholar
Wentworth, E. H. and Remick, B. L. (1916) Some breeding properties of generalized Mendelian populations. Genetics 1, 608616.Google Scholar
Workman, P. L. (1964) The maintenance of heterozygosity by partial negative assortative mating. Genetics 50, 13691382.Google Scholar
Wright, S. (1921) Systems of mating. Genetics 6, 111178.CrossRefGoogle ScholarPubMed