The genetics of selfing with concurrent backcrossing in breeding hybrid sugar beet (Beta vulgaris altissima L.)
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Sugar beet hybrids are produced by crossing a cytoplasmic male-sterile (CMS) line with a pollinator. New CMS lines are produced by crossing a fertile plant to an existing CMS line. The fertile plant is also selfed. In the following generation, one of the selfed, fertile progeny is paired and isolated with one of the crossed, CMS progeny, to give a second generation of selfing and crossing. Over a series of such crosses and selfs, a new fertile inbred line and its corresponding, near-isogenic CMS partner are produced. Selection among lines takes place at one or more stages of the backcrossing programme. A method is presented here for calculating the genetic variances and covariances within and between lines and generations based on a derivation of additive genetic relationships modified from an approach widely employed in animal breeding. The genetic variances and covariances are used to predict response to selection from varying strategies, from which optimum schemes can be determined. Results suggest that selection should generally take place after three generations of backcrossing when the fertile plant used to initiate the backcrossing process is not inbred, but can take place after generation two when the fertile plant is inbred. Doubled haploid production is unlikely to provide an extra advantage that would be worthwhile in such a system. The method developed here can be used to explore a wide range of more complex breeding systems.
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