Using molecular markers to estimate quantitative trait locus parameters power and genetic variances for unreplicated and replicated progeny

Many of the progeny types used to estimate quantitative trait locus (QTL) parameters can be replicated, e.g., recombinant inbred, doubled haploid, and F3 lines. These parameters are estimated using molecular markers or QTL genotypes estimated from molecular markers as independent variables. Experiment designs for replicated progeny are functions of the number of replications per line (r) and the number of replications per QTL genotype (n). The value of n is determined by the size of the progeny population (N), the progeny type, and the number of simultaneously estimated QTL parameters (q-1). Power for testing hypotheses about means of QTL genotypes is increased by increasing r and n, but the effects of these factors have not been quantified. In this paper, we describe how power is affected by r, n, and other factors. The genetic variance between lines nested in QTL genotypes (sigma 2/n:q) is the fraction of the genetic variance between lines (sigma 2/n) which is not explained by simultaneously estimated intralocus and interlocus QTL parameters (phi 2/Q); thus, sigma 2/n:q = sigma 2/n - phi 2/Q. If sigma 2/n:q is not equal to 0, then power is not efficiently increased by increasing r and is maximized by maximizing n and using r = 1; however, if sigma 2/n:q = 0, then r and n affect power equally and power is efficiently increased by increasing r and is maximized by maximizing N.r. Increasing n efficiently increases power for a wide range of values of sigma 2/n:q. sigma 2/n:q = 0 when the genetic variance between lines is fully explained by QTL parameters (sigma 2/n = phi 2/Q). This can be achieved by fitting N -1 independent QTL parameters. Significant power increases are seldom achieved by using replicated progeny unless a significant fraction of the genetic variance between lines is explained by simultaneously estimated QTL parameters. QTL parameter estimation algorithms are proposed which maximize power by minimizing sigma 2/n:q.