Summary
Using the general principle of linear prediction for autotetraploids in the absence of epistasis, we envisage different types of individual selection with truncation: mass selection, general combining ability selection, and selection on progenies from self fertilization. General expressions for the first cycle of selection are given. With the assumption that a locus effect can be neglected relative to the total variance, response to n cycles of selection can be predicted. Because of a dominance effect, the response will be curvilinear. The consequence of relaxation of selection is also envisaged. For all three selection procedures, after several cycles of random mating without selection, the genetic advance decreases rapidly towards an asymptotic value which is dependent only on the additive variance. Results for autotetraploids without epistasis are clearly analogous to Griffing's results for diploids with epistasis restricted to pairs of loci.
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Literature
Bouffette, Jacqueline: Expression de la covariance génotypique chez les tétraploides. Thèse 3è cycle Fac. Sci. Lyon (1966)
Demarly, Y.: Génétique des tétraploides et amélioration des plantes. Thèse Fac. Sci. Paris. Ann. Amélior. Plantes 13, 307–400 (1963)
Falconer, D.S.: Introduction to quantitative genetics. London: Oliver and Boyd 1961
Gallais, A.: Moyenne des populations tétraploides. Ann. Amélior. Plantes 17, 217–228 (1967)
Gallais, A.: Covariances entre apparentés quelconques avec linkage et épistasie. I. Expression générale. Ann. Génét. Sél. Anim. 2, 281–310 (1970)
Gallais, A.: Covariances between arbitrary relatives with linkage and epistasis in the case of linkage disequilibrium and inbreeding. Biometrics 30, 429–446 (1974a)
Gallais, A.: Covariances between arbitrary relatives in autotetraploids with panmictic disequilibrium. Genetics 76, 587–600 (1974b)
Gillois, M.: La relation d'identité en génétique. Thèse Fac. Sci. Paris (1964)
Griffing, B.: Theoretical consequences of truncation selection based on the individual phenotype. Aust. J. Biol. Sci. 13, 307–343 (1960)
Griffing, B.: Consequences of truncation selection based on combinations of individual performance and gen eral combining ability. Aust. J. Biol. Sci. 15, 333–351 (1962)
Griffing, B.: Selection in reference to biological groups. II. Consequences of selection in groups of one size when evaluated in groups of a different size. Aust. J. Biol. Sci. 21, 1163–1170 (1968)
Harris, D.L.: Genotypic covariance between inbred relatives. Genetics 50, 1319–1348 (1964)
Hill, R.R., Jr.: Selection in autotetraploids. Theoret. Appl. Genet. 41, 181–186 (1971)
Kempthorne, O.: Biometrical relations between relatives and selection theory. In: Biometrical Genetics, 5. Ed. Kempthorne, O. 12–23. Oxford: Pergamon Press 1960
Kimura, M.: On the change of population fitness by natural selection. Heredity, London, 12, 145–167 (1958)
Latter, B.D.H.: The response to artificial selection due to autosomal genes of large effect. I. Changes in gene frequency at an additive locus. Aust. J. Biol. Sci. 18, 585–598 (1965)
Malécot, G.: Les mathématiques de l'hérédité. Paris: Masson et Cie. 1948
Pederson, D.G.: The prediction of selection response in a self fertilizing species. I. Individual selection. Aust. J. Biol. Sci. 22, 117–129 (1968)
Price, G.R.: Selection and covariance. Nature 227, n∘ 5257, 520–521 (1970)
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Communicated by R.C. Lewontin
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Gallais, A. Selection with truncation in autotetraploids comparison with diploids. Theoret. Appl. Genetics 46, 387–394 (1975). https://doi.org/10.1007/BF00281142
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DOI: https://doi.org/10.1007/BF00281142