Lopez-Sanchez, Jesus; Perez de Vargas, Alberto Zygotic algebra for two linked loci with sexually different recombination rates. (English) Zbl 0586.92016 Bull. Math. Biol. 47, 771-782 (1985). The author studies the properties of a zygotic algebra of two linked loci with different recombination rates in male and female gametes. The algebras obtained have some similarities to those obtained from sex linkage in that there are separate elements for male and female types. However, the loci are autonormal, i.e., both sexes are diploid for the genes considered, thus the algebras are closely related to algebras obtained by duplication. The main theorem says that such an algebra is a genetic algebra and it is a special train if and only if both recombination rates are 0. Reviewer: H.Gonshor Cited in 2 ReviewsCited in 3 Documents MSC: 92D10 Genetics and epigenetics 17D92 Genetic algebras Keywords:random mating; genetic subalgebra; train roots; zygotic algebra of two linked loci; different recombination rates; duplication; genetic algebra PDFBibTeX XMLCite \textit{J. Lopez-Sanchez} and \textit{A. Perez de Vargas}, Bull. Math. Biol. 47, 771--782 (1985; Zbl 0586.92016) Full Text: DOI References: [1] Etherington, I. M. H. 1939. ”Genetic Algebras.”Proc. R. Soc. Edinb. 59, 242–258. · Zbl 0027.29402 [2] —- 1941a. ”Non-associative Algebra and the Symbolism of Genetics.”Proc. R. Soc. Edinb. B61, 24–42. · JFM 67.0501.01 [3] —- 1941b. ”Special Train Algebras.”Q. J Math. 12, 1–8. · JFM 67.0093.04 · doi:10.1093/qmath/os-12.1.1 [4] Gonshor, H. 1960. ”Special Train Algebras Arising in Genetics.”Proc. Edinb. math. Soc. 12, 41–53. · Zbl 0249.17003 · doi:10.1017/S0013091500025037 [5] —- 1965. ”Special Train Algebras Arising in Genetics II.”Proc. Edinb. math. Soc. 14, 333–338. · Zbl 0139.03102 · doi:10.1017/S0013091500009020 [6] —- 1971. ”Contributions to Genetic Algebras.”Proc. Edinb. math. Soc. 17, 289–298. · Zbl 0247.92002 · doi:10.1017/S0013091500009548 [7] Gonshor, H. 1973. ”Contributions to Genetic Algebras II.”Proc. Edinb. math. Soc. 18, 273–279. · Zbl 0272.92012 · doi:10.1017/S001309150001004X [8] Heuch, I. 1972. ’k Loci Linked to a Sex Factor in Haploid Individuals.”Biometr. Z. 13, 57–68. · Zbl 0236.92002 · doi:10.1002/bimj.19720140108 [9] —-. 1973. ”The Linear Algebra for Linked Loci with Mutation.”Math. Biosci. 16, 262–271. · Zbl 0251.17001 · doi:10.1016/0025-5564(73)90034-5 [10] —-. 1975. ”Partial and Complete Sex Linkage in Infinite Populations.”J. math. Biol. 1, 331–343. · Zbl 0301.92013 [11] —-. 1977. ”Genetic Algebras for Systems with Linked Loci.”Math. Biosci. 34, 35–47. · Zbl 0361.92015 · doi:10.1016/0025-5564(77)90034-7 [12] Holgate, P. 1968. ”The Genetic Algebra ofk Linked Loci.”Proc. Lond. math. Soc. 18, 315–327. · Zbl 0157.26703 · doi:10.1112/plms/s3-18.2.315 [13] —-. 1979. ”Canonical Multiplication in the Genetic Algebra for Linked Loci.”Linear Alg. App. 26, 281–286. · Zbl 0408.92004 · doi:10.1016/0024-3795(79)90182-4 [14] —-. 1981. ”Population Algebras.”J. R. statist. Soc. B43, 1–19. · Zbl 0472.92008 [15] Reiersøl, O. 1962. ”Genetic Algebras Studied Recursively and by Means of Differential Operators.”Math. Scand. 10, 25–44. · Zbl 0286.17006 [16] Schafer, R. D. 1949. ”Structure of Genetic Algebras.”Am. J. Math. 71, 121–135. · Zbl 0034.02004 · doi:10.2307/2372100 [17] Wörz-Busekros, A. 1974. ”The Zygotic Algebra for Sex Linkage.”J. math. Biol. 1, 37–46. · Zbl 0407.92012 · doi:10.1007/BF02339487 [18] —-. 1975. ”The Zygotic Algebra for Sex Linkage II.”J. math. Biol. 2, 359–371. · Zbl 0327.92010 · doi:10.1007/BF00817393 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.