ON ESTIMATING THE LINKAGE OF MARKER GENES TO VIABILITY GENES-CONTROLLING INBREEDING DEPRESSION

Statistical properties and extensions of Hedrick and Muona's method fo r mapping viability alleles causing inbreeding depression are discusse d in this paper. Their method uses the segregation ratios among selfed progeny of a marker-locus heterozygote to estimate the viability redu ction, ''s'', of an allele and its recombination fraction, ''c'', with the marker. Explicit estimators are derived for c and s, including ex pressions for their variances. The degree of estimation bias is examin ed for cases when (1) the viability allele is partially recessive and (2) the marker locus is linked to two viability loci. If linkage or vi ability 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 reduc ed because alleles causing viability reduction often occur at low freq uency at specific loci in a population. To increase power, we present a statistical model for the joint analysis of several selfed progeny a rrays selected at random from a population. Assuming a fixed total num ber of progeny, we determine the optimal number of progeny arrays vers us number of progeny per array under this model. We also examine the i ncrease of information provided by a second, flanking marker. Two flan king markers provide vastly superior estimation properties, reducing s ample sizes by approximately 95% from those required by a single marke r.