On estimating the linkage of marker genes to viability genes controlling inbreeding depression.

Statistical properties and extensions of Hedrick and Muona's method for mapping viability alleles causing inbreeding depression are discussed in this paper. Their method uses the segregation ratios among selfed progeny of a marker-locus heterozygote to estimate the viability reduction, "s", of an allele and its recombination fraction, "c", with the marker. Explicit estimators are derived for c and s, including expressions for their variances. The degree of estimation bias is examined for cases when (1) the viability allele is partially recessive and (2) the marker locus is linked to two viability loci. If linkage or viability reduction is moderate, very large sample sizes are required to obtain reliable estimates of c and s, in part because these estimates show a statistical correlation close to unity. Power is further reduced because alleles causing viability reduction often occur at low frequency at specific loci in a population. To increase power, we present a statistical model for the joint analysis of several selfed progeny arrays selected at random from a population. Assuming a fixed total number of progeny, we determine the optimal number of progeny arrays versus number of progeny per array under this model. We also examine the increase of information provided by a second, flanking marker. Two flanking markers provide vastly superior estimation properties, reducing sample sizes by approximately 95% from those required by a single marker.