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II.—Non-Associative Algebra and the Symbolism of Genetics

Published online by Cambridge University Press:  11 June 2012

I. M. H. Etherington
I. M. H. Etherington
Affiliation:
Mathematical Institute, University of Edinburgh.
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Extract

The statistical material of genetics usually consists of frequency distributions—of genes, zygotes and mating couples—from which new distributions referring to their progeny arise. Combination of distributions by random mating is usually symbolised by the mathematical sign for multiplication; but this sign is not taken literally for the simple reason that the genetical laws connecting the distributions of progenitors and progeny are inconsistent with the laws governing multiplication in ordinary algebra. This is explained more fully in § 2.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh, Section B: Biological Sciences , Volume 61 , Issue 1 , 1941 , pp. 24 - 42
Copyright
Copyright © Royal Society of Edinburgh 1941

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References

References to Literature

Dahlberg, G., 1929. “Inbreeding in man,” Genetics, vol. xiv, pp. 421–454.Google Scholar
Etherington, I. M. H., 1939 a. “On non-associative combinations,” Proc. Roy. Soc. Edin., vol. lix, pp. 153–162.Google Scholar
Etherington, I. M. H., 1939 b. “Genetic algebras,” Proc. Roy. Soc. Edin., vol. lix, pp. 242–258. (Referred to as “G.A.”)Google Scholar
Etherington, I. M. H., 1941. “Duplication of linear algebras,” Proc. Edin. Math. Soc. (In press.)CrossRefGoogle Scholar
Geppert, H., and Koller, S., 1938. Erbtnathematik, Leipzig.Google Scholar
Hogben, L., 1931. Genetic Principles in Medicine and Social Science, London.Google Scholar
Hogben, L., 1933. “A matrix notation for mendelian populations,” Proc. Roy. Soc. Edin., vol. liii, pp. 7–25.Google Scholar
Jennings, H. S., 1916, 1917. “The numerical results of diverse systems of breeding,” Genetics, vol. i, pp. 53–89; vol. ii, pp. 97–154.CrossRefGoogle Scholar
Robbins, R. B., 1917, 1918. “Some applications of mathematics to breeding problems,” Genetics, vol. ii, pp. 489–504; vol. iii, pp. 73–92, 375–389.CrossRefGoogle Scholar
Wentworth, E. N., and Remick, B. L., 1916. “Some breeding properties of the generalised mendelian population,” Genetics, vol. i, pp. 608–616.Google Scholar