Summary
The covariances of relatives arising under selfing from a general outbred base population in linkage equilibrium and without epistasis given by Cockerham (1983) are expressed in an alternative form which is an extension of the treatment by Mather and Jinks (1982) of the more restricted population descended from a single F1 family. Whereas no more than two quadratic components are required to describe any covariance in the case of F1, descendants, this more general case calls for a total of four, three of which are needed for any particular covariance. The estimation of covariances and their use for the prediction of selection response is described for breeding programs initiated by one or more cycles of intermating among a number of parental lines, as advocated by Hansel (1964) and Jensen (1970). It is pointed out that the homozygous lines descended from such a population will have up to twice as much variance as those from an F1 between a randomly chosen pair from the same population of parents. The selection method is especially recommended for undeveloped species in which the parental lines are not well characterized and large selection responses are needed.
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References
Baker RJ (1968) Extent of intermating in self-pollinated species necessary to counteract the effect of random drift. Crop Sci 8:547–550
Bos I (1977) More arguments against intermating F2 plants of a self-fertilizing crop. Euphytica 26:33–46
Cockerham CC (1983) Covariances of relatives from self-fertilization. Crop Sci 23:1177–1180
Gallais A (1974) Covariances between arbitrary relatives with linkage and epistasis in the case of linkage disequilibrium. Biometrics 30:429–446
Gates CE (1954) The constitution of genetic variances and covariances in self-fertilized crops assuming linkage. Unpublished PhD Thesis, DH Hill Library, North Carolina State University, Raleigh
Gates CE, Comstock RE, Robinson HF (1957) Generalized genetic variance and covariance formulae for self-fertilized crops assuming linkage. Genetics 42:749–763
Hansel H (1964) Der Kreuzungsverband (Gedanken zu einer neuen Zuchtmethode bei Weizen). In: Ber Arbeitstagung 1964, Arbeitsgemeinschaft Saatzuchtleiter. Bundesversuchs-anstalt für alpenländische Landwirtschaft, Gumpenstein bei Irdning, Austria, pp 74–95
Hanson WD (1959) The breakup of initial linkage blocks under selected mating systems. Genetics 44:857–868
Horner TW (1952) Non-allelic gene interaction and the interpretation of quantitative genetic data. Unpublished PhD Thesis, DH Hill Library, North Carolina State University, Raleigh
Horner TW, Weber CR (1956) Theoretical and experimental study of self fertilized populations. Biometrics 12:404–414
Jensen NF (1970) A diallel selective scheme for cereal breeding. Crop Sci 10:629–635
Jinks JL, Perkins JM (1972) Predicting the range of inbred lines. Heredity 28:399–403
Jinks JL, Pooni HS (1976) Predicting the properties of recombinant inbred lines derived by single seed descent. Heredity 36:253–266
Jinks JL, Pooni HS (1982) Predicting the properties of pure breeding lines extractable from a cross in the presence of linkage. Heredity 49:265–270
Kempthorne O (1957) Introduction to genetic statistics. Iowa State University Press, Ames, Iowa
Mather K, Jinks JL (1982) Biometrical genetics. Chapman and Hall, London
Pederson DG (1974) Arguments against intermating before selection in a self-fertilizing species. Theor Appl Genet 45: 157–162
Snape JW, Riggs TJ (1975) Genetical consequences of single seed descent in the breeding of self-pollinating crops. Heredity 35:211–219
Weir BS, Cockerham CC (1977) Two-locus theory in quantitative genetics. In: Proc Int Conf Quant Genet. Iowa State University Press, Ames, Iowa, pp 247–269
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Communicated by A. Robertson
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Wright, A.J., Cockerham, C.C. Covariances of relatives and selection response in generations of selfing from an outcrossed base population. Theoret. Appl. Genetics 72, 689–694 (1986). https://doi.org/10.1007/BF00289010
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DOI: https://doi.org/10.1007/BF00289010