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Theoritical Inbreeding at Selectively Neutral Loci in Unparental Mass Selection and Recurrent Selection with Polycrossing of Selected Plants

Dep. of Agronomy, Univ. of Wisconsin-Madison, 1575 Linden Dr., Madison, WI 53706-1597, and Dep. of Statistics, Univ. of Wisconsin-Madison, 1210 West Dayton St., Madison, WI 53706-1685,
Dep. of Agronomy, Univ. of Wisconsin-Madison, 1575 Linden Dr., Madison, WI 53706-1597.

^* Corresponding author (mdcasler{at}facstaff.wisc.edu).

Inbreeding depression is of great concern to breeders of crosspollinated plant species, especially if the breeders intend to release synthetics or open-pollinated cultivars. Estimation of inbreeding coefficients of cycles from recurrent selection helps planning a recurrent selection program or utilizing a population derived from recurrent selection. In this paper, we derived the formulas to estimate the inbreeding coefficient of any cycle at one locus for uniparental mass selection and for recurrent selection with polycrossing of selected plants, under the assumption that the locus is selectively neutral. For uniparental mass selection, the inbreeding coefficient of Cycle i is determined mainly by the number of plants selected in Cycle i - 2, while the total number of plants in Cycles i - 1 and i - 2 and the number of seeds contributed to the seed bag by each selected plant in Cycle i - 2 also have some effects. For recurrent selection with polycrossing of selected plants, the inbreeding coefficient of Cycle i is determined mainly by the number of plants selected in Cycle i - 1 while the number of plants selected in Cycle i - 2 and the number of seeds contributed to the seed bag by each selected plant in Cycle i - 2 also have some effects. To make an inference regarding the use of cycles from uniparental mass selecting or to compare the efficacy of uniparental mass selection with recurrent selection that includes intercrossing or polycrossing of selected plants or lines, one should use the seed derived from one generation of open pollination in isolation for uniparental mass selection.

Received for publication July 26, 1998.

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