Power and sample sizes for linkage with extreme sampling under an oligogenic model for quantitative traits

Extreme sampling of sibling pairs has been shown to be efficient in terms of statistical power and sample sizes (in number of sibling pairs needed to genotype) to detect a quantitative trait locus (QTL) when the residual distribution is normal. In the present study, the efficiency of extreme sampling strategies to detect each locus under an oligogenic model is analytically explored with a test statistic based on identical-by-descent (IBD) statuses of independent sibling pairs. In the oligogenic model, the joint effect of oligogenes is the sum of the effects of each locus. Under this model, detecting each single locus will depend, in part, on the allele frequencies and magnitudes of effect of the other loci. Effects of two QTLs with different magnitudes of displacement and acting nonepistatically are considered. Three types of extreme sampling-that is, extreme concordant high (ECH), extreme concordant low (ECL), and extreme discordant (ED)-are primarily considered herein. Among these, ED sampling under the oligogenic model is shown to be most efficient in most situations considered here in terms of allele frequency and mode of inheritance. Differences in results between ECH and ECL sampling are purely arbitrary, brought up mostly by the directions of displacement effects. However, power to detect a locus with the lesser (in magnitude) displacement effect does not necessarily increase with extremity of sampling. Combinations of extreme discordant and extreme concordant sibling pairs are briefly discussed.