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Selection with Partial Selfing. II. Family Selection¹

The expected immediate and permanent responses to various types of family or individual selection on the basis of progeny tests were formulated for a population whose members have a common fixed probability of self-fertilization(s). These results were derived using covariances of relatives and their component quadratic genetic functions for a model with arbitrary additive and dominance effects. The families considered were outcrossed full- and half-sibs(F and H), progenies from self-pollination (S), and those from natural pollination (M), and pair matings without exclusion of natural selfing (C). Methods for the prediction of both immediate and permanent selection responses are given. Numerical analysis of various models with two alleles at each of a number of loci showed the proportion of the immediately observable response that is permanent gain retained by the distant descendants of the selections to be greater for progeny testing than for family selection. Both were greater than that for mass selections studied earlier(Wright and Cockerham 1985). The range of heritability values in which family selection gives greater permanent gains than mass selection following reproduction is greatest whens is low. However, the comparison of progeny testing to mass selection prior to reproduction is less dependent on s. The S families were the preferred type for all models and s values, and the values of M and C familiese exceeded that of their counterparts under strict outcrossing (H and F), particularly for high s values and when environmental variation was large.

Key Words: Additive and dominance effects • Genetic variances and covariances • Multiple alleles • Progeny testing • Single seed descent

² Visiting associate professor, and professor of statistics and genetics, Dep. of Statistics, North Carolina State Univ., Raleigh, NC 27695-8203.

Received for publication March 28, 1985.