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The multilocus Hardy-Weinberg law. (English) Zbl 0757.92013
Summary: Work on the genetic algebra of multilocus genetic systems is reviewed, with particular emphasis on aspects of Hardy-Weinberg theory, including existence and stability of equilibria, global convergence and disequilibrium functions. It is pointed out that the non-uniqueness of the disequilibrium functions does not necessarily invalidate the proof of the multilocus Hardy-Weinberg law.

MSC:
92D10 Genetics and epigenetics
17D92 Genetic algebras
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[1] Abraham, V. M.: Linearising quadratic transformations in genetic algebras. Proc. Lond. Math. Soc., III. Ser. 40, 346-363 (1980) · Zbl 0418.92010
[2] Abraham, V. M.: The induced linear transformation in a genetic algebra. Proc. Lond. Math. Soc., III. Ser. 40, 364-384 (1980) · Zbl 0418.92009
[3] Bennett, J. H.: On the theory of random mating. Ann. Eugen. 184, 311-317 (1954)
[4] Geiringer, H.: On the probability theory of linkage in Mendelian heredity. Ann. Math. Stat. 15, 25-57 (1944) · Zbl 0063.01560
[5] Gonshor, H.: Special train algebras arising in genetics. Proc. Edinb. Math. Soc., II. Ser. 12, 41-53 (1960) · Zbl 0249.17003
[6] Heuch, I.: k loci linked to a sex factor in haploid individuals. Biom. Z. 13, 57-68 (1972) · Zbl 0236.92002
[7] Heuch, L: The linear algebra for linked loci with mutation. Math. Biosci. 16, 263-271 (1973) · Zbl 0251.17001
[8] Heuch, L: Genetic algebras for systems with linked loci. Math. Biosci. 34, 35-47 (1977) · Zbl 0361.92015
[9] Hill, W. G.: Disequilibrium among several linked neutral genes in finite populations. I. Theor. Popul. Biol. 5, 366-392 (1974) · Zbl 0291.92024
[10] Holgate, P.: Sequences of powers in genetic algebras. J. Lond. Math. Soc., 42, 489-496 (1967) · Zbl 0163.03103
[11] Holgate, P.: The genetic algebra of k linked loci. Proc. Lond. Math. Soc., III. Ser. 18, 315-327 (1986) · Zbl 0157.26703
[12] Holgate, P.: Direct products of genetic algebras and Markov chains. J. Math. Biol. 3, 289-295 (1976) · Zbl 0356.92013
[13] Holgate, P.: Canonical multiplication in the genetic algebra for linked loci. Linear Algebra Appl. 26, 281-287 (1979) · Zbl 0408.92004
[14] Holgate, P.: Linearisation of quadratic operators in genetic algebras. Cah. Math. 38, 23-33 (1989) · Zbl 0760.17025
[15] Holgate, P.: Bibliography of genetic algebras and related topics. Typescript (1991)
[16] Karlin, S, Liberman, U.: Global convergence properties in multilocus viability selection models: the additive model and the Hardy-Weinberg law. J. Math. Biol. 29, 161-176 (1990) · Zbl 0744.92024
[17] Peresi, L. A.: The derivation algebra of gametic algebra for linked loci. Math. Biosci. 91, 151-156 (1988) · Zbl 0662.92014
[18] Reiersol, O.: Genetic algebras studied recursively and by means of differential operators. Math. Scand. 10, 25-44 (1962) · Zbl 0286.17006
[19] Wörz-Busekros, A.: Algebras in genetics. (Lect. Notes Biomath., vol. 36) Berlin Heidelberg New York: Springer 1980 · Zbl 0431.92017
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