A two-stage variable-stringency semiparametric method for mapping quantitative-trait loci with the use of genomewide-scan data on sib pairs

Abstract

Genomewide scans for mapping loci have proved to be extremely powerful and popular. We present a semiparametric method of mapping a quantitative-trait locus (QTL) or QTLs with the use of sib-pair data generated from a two-stage genomic scan. In a two-stage genomic scan, either the entire genome or a large portion of the genome is saturated with low-density markers at the first stage. At the second stage, the intervals that are identified as probable locations of the trait loci, by means of analysis of data from the first stage, are then saturated with higher-density markers. These data are then analyzed for fine mapping of the loci. Our statistical strategy for analysis of data from the first stage is a low-stringency method based on the rank correlation of squared trait-difference values of the sib pairs and the estimated identity-by-descent scores at the marker loci. We suggest the use of a low-stringency method at the first stage, to save on computational time and to avoid missing any marker interval that may contain the trait loci. For analysis of data from the second stage, we have developed a high-stringency nonparametric-regression approach, using the kernel-smoothing technique. Through extensive simulations, we show that this approach is more powerful than is a currently used method for mapping QTLs by use of sib pairs, particularly in the presence of dominance and epistatic effects at the trait loci.

Figure 1

Mean rank correlation, based on 1,000 replications, between squared difference of trait values of a sib pair and estimated i.b.d. scores at 100 ordered markers, with the use of simulation parameter values α=5, σ²=1, p=.7, ρ=.6, and (a) β=0, (b) β=2, and (c) β=4, on the basis of data from 100 sib pairs.

Figure 2

Mean rank correlation, based on 1,000 replications, between squared difference of trait values of a sib pair and estimated i.b.d. scores at 100 ordered markers, with the use of simulation parameter values α=3, σ²=1, p=.7, ρ=.6, and (a) β=0, (b) β=1, and (c) β=2, on the basis of data from 100 sib pairs.

Figure 3

Both the mean rank correlation (unbroken line), based on 1,000 replications, between squared difference of trait values of a sib pair and estimated i.b.d. scores at markers around the true QTL location, and the empirical 95% confidence band (dotted lines) for simulation parameter values α=5, β=0, σ²=1, p=.7, and ρ=.6.

Figure 4

Mean rank correlation, based on 1,000 replications, between squared difference of trait values of a sib pair and estimated i.b.d. scores at 100 ordered markers (all of which were unlinked to the QTL), with the use of simulation parameter values α=5, σ²=1, p=.7, ρ=.6, and (a) β=0, (b) β=2, and (c) β=4, on the basis of data from 100 sib pairs.

Figure 5

Mean rank correlation, based on 1, 000 replications, between squared difference of trait values of a sib pair and estimated i.b.d. scores at 100 ordered markers, with the use of simulation parameter values α=5, σ²=1, p=.7, ρ=.6, and (a) β=0, (b) β=2, and (c) β=4, on the basis of data from 50 sib pairs.

Figure 6

Mean rank correlation, based on 1,000 replications, between squared difference of trait values of a sib pair and estimated i.b.d. scores at 100 ordered markers, with the use of simulation parameter values α=5, σ²=1, p=.7, ρ=.6, and (a) β=0, (b) β=2, and (c) β=4, on the basis of data from 25 sib pairs.

Figure 7

Mean rank correlation, based on 1,000 replications, between squared difference of trait values of a sib pair and estimated i.b.d. scores at 100 ordered markers. Panels a and b pertain to the first and second loci, respectively, when the first locus, without dominance, explains 80% of the variation in trait values; panels c and d pertain to the first and second loci, respectively, when the first locus, with dominance, explains 60% of the variation in trait values.

Figure 8

Mean rank correlation, based on 1,000 replications, between squared difference of trait values of a sib pair and estimated i.b.d. scores at 100 ordered markers. Panels a and b pertain to the first and second loci, respectively, when the first locus, without dominance but with epistatic interaction with the second locus, explains 80% of the variation in trait values; panels c and d pertain to the first and second loci, respectively, when the first locus, with dominance and with epistatic interaction with the second locus, explains 60% of the variation in trait values.