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Sequences in genetic algebras for overlapping generations

Published online by Cambridge University Press:  20 January 2009

I. Heuch
I. Heuch
Affiliation:
Institute of General Genetics, University of Oslo, Norway
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When Etherington (2) introduced linear commutative non-associative algebras in connection with problems in theoretical genetics, he pointed out that various sequences of elements in these algebras represented different mating systems. In all such systems it was however assumed that the generations did not overlap, and this restriction has been kept in later work in this field. In this paper we treat sequences which make it possible to find the probability distribution in successive generations in a discrete time model where the generations may be overlapping. We also consider idempotents in genetic algebras and outline how the method used on the overlapping generation sequence may be applied to other sequences.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 18 , Issue 1 , June 1972 , pp. 19 - 29
Copyright
Copyright © Edinburgh Mathematical Society 1972

References

REFERENCES

(1) Etherington, I. M. H., On non-associative combinations, Proc. Roy. Soc. Edinburgh 59 (1939), 153–162.CrossRefGoogle Scholar
(2) Etherington, I. M. H., Genetic algebras, Proc. Roy. Soc. Edinburgh 59 (1939), 242–258.CrossRefGoogle Scholar
(3) Etherington, I. M. H., Commutative train algebras of ranks 2 and 3, J. London Math. Soc. 15 (1940), 136–149.CrossRefGoogle Scholar
(4) Etherington, I. M. H., Special train algebras, Quart. J. Math. Oxford Ser. (2) 12 (1941), 1–8.CrossRefGoogle Scholar
(5) Etherington, I. M. H., Non-commutative train algebras of ranks 2 and 3, Proc. London Math. Soc. (2) 52 (1950), 241–252.CrossRefGoogle Scholar
(6) Gonshor, H., Special train algebras arising in genetics, Proc. Edinburgh Math. Soc. (2) 12 (1960), 41–53.CrossRefGoogle Scholar
(7) Gonshor, H., Contributions to genetic algebras, Proc. Edinburgh Math. Soc. (2) 17 (1971), 289–298.CrossRefGoogle Scholar
(8) Holgate, P., Genetic algebras associated with polyploidy, Proc. Edinburgh Math. Soc. (2) 15 (1966), 1–9.CrossRefGoogle Scholar
(9) Holgate, P., Sequences of powers in genetic algebras, J. London Math. Soc. 42 (1967), 489–496.CrossRefGoogle Scholar
(10) Holgate, P., The genetic algebra of k linked loci, Proc. London Math. Soc. (3) 18 (1968), 315–327.CrossRefGoogle Scholar
(11) Jordan, C., Calculus of Finite Differences, 3rd edition (Chelsea, New York, 1965).Google Scholar
(12) ReiersØl, O., Genetic algebras studied recursively and by means of differential operators, Math. Scand. 10 (1962), 25–44.CrossRefGoogle Scholar
(13) Schafer, R. D., Structure of genetic algebras, Amer. J. Math. 71 (1949), 121–135.CrossRefGoogle Scholar