High resolution QTL mapping in genotypically selected samples from experimental crosses Selective mapping (Fig. 1) is an experimental design strategy for genome-wide, high-density linkage mapping of molecular markers in experimental crosses that optimizes the map resolution obtained for a given amount of genotyping effort [1]. It is especially suited to permanent mapping populations (e.g. recombinant inbred lines). Introduction Simulation A base population of diploid F2 recombinant inbred lines (RIL) was simulated. From this population, n individuals were selected either at random or using selective sampling to minimize the sum of squares of the bin lengths (as implemented in the software MapPop [1]). We varied  the sample fraction (the proportion of the base population in the selected sample)  the spacing of markers on the map  genome length QTLs were added at either fixed or random positions. For simulations where additive effects were considered to be random variables, they were sampled from a gamma (1,2) distribution. QTL analysis was performed using either marker regression or simple interval mapping with QTL Cartographer [3]. References [1] Vision TJ, Brown DG, Shmoys DB (2000) Genetics 15, [2] Beavis WD (1998) pp in Paterson AH (ed) Molecular Analysis of Complex Traits. CRC Press. [3] Basten CJ, Weir BS, Zeng ZB (2002) QTL Cartographer v 1.16 Conclusions Selective sampling increases the recombination frequency between a marker and a QTL due to both  crossover enrichment and  pseudointerference. As a result  QTL detection power is reduced when markers are sparse  QTL map resolution is substantially increased with little loss of detection power if markers are sufficiently dense. Selective sampling can help maximize map resolution when  there are logistical constraints on mapping population size  marker density is at least 1 per 5-10 cM. 1 Zongli Xu, 2 Fei Zou, 1 Todd J. Vision Departments of 1 Biology and 2 Biostatistics, University of North Carolina at Chapel Hill correspondence: This work has been supported by NSF grant DBI to TJV. QTL Detection Power Crossover Enrichment QTL Mapping Resolution Pseudointerference Pseudointerference refers to the non-independence of crossover sites within a selected sample. We hypothesized that pseudointerference could be contributing to the reduced power and increased resolution of selected samples relative to CE-adjusted random samples. We found that selected samples had proportionally fewer short within-individual intercrossover intervals. Interestingly, the mode of the distribution of interval lengths was at the same cM distance as the marker spacing used for selection (Figure 6A). The altered distribution above lead to fewer close double- crossovers, and thus more observable recombinations in selected samples relative to CE-adjusted random samples (Figure 6B). The total number of crossovers in the selected sample relative to that expected in a random sample of the same size is referred to as the crossover enrichment (CE). We found that CE was inversely related to the sample fraction, marker spacing and map length (Figure 2). We found that CE could be very closely predicted by the following empirical formula: where L is map length in cM, f is the sample fraction, and A is a constant that is determined by the type of base population. For an F2 RIL population, A=500. For backcross RIL and doubled haploid populations, A=750 and 1200, respectively. The fit of this equation to the observed values of CE was quite good. Within the realistic parameter range that we explored, we obtained R 2 values of , and for F2 RIL, backcross RIL, and DH populations, respectively. In order to determine whether CE alone is responsible for the differences in QTL detection power between selected and random samples, we compared selected samples to CE-adjusted random samples in which crossover sites were independently assigned but at the same frequency as in a given selected sample. Figure 6. (A) The distribution of intercrossover interval lengths within individuals for selected samples at three marker intervals versus a random sample. Map length was 100 cM, base population size was 500, and sample fraction was 0.1. Each point represents the average of 10,000 individuals. The spike at 100 cM in the random sample consists of chromosomes without crossovers. (B) The number of recombinations per individual in selected (dashed line) and CE-adjusted random (solid line) samples along a 100 cM chromosome. Marker intervals were 5 cM (  ), 10 cM (  ) or 20 cM (  ). Each value was obtained from 1,000 replicates with a sample size of 100. Figure 3. Detection power for a single QTL (additive effect 0.5, heritability 0.2) located equidistant from the two centermost markers. Samples of size 100. Series correspond to marker intervals of 1 ( ◊ ), 5 (  ), 10 (  ) and 20 cM (  ). QTL analysis was done using marker regression. (A) Populations differing by CE alone. Map length was 1000 cM. (B) Selected (dotted) and CE-adjusted random (solid) samples. Map length was 100 cM. Figure 5. 1-LOD confidence intervals for QTLs in random and selected samples. (A) One QTL at a fixed position with h 2 =0.2. Key to legend: sampling strategy/map length/marker interval. Sampling strategy (color) was either random, selected (Sel) or CE-adjusted (CE). Symbols denote map length. (B) Five QTL with random positions (at least 100 cM apart) and effects; combined h 2 =0.5. Selection increased QTL mapping resolution in both single and multiple QTL simulations, as determined by the width of the 1-LOD confidence intervals (Figure 5). The effect was greatest with dense markers and a short map. The confidence intervals of CE-adjusted random samples were slightly larger than those of selected samples. Detection power was calculated by simulation. For the single- QTL simulations, a QTL was counted as detected if any marker on the map exceeded the significance threshold. Power was inversely related to CE but the relationship was nearly flat when the marker-QTL distance was less than 2.5 cM (Figure 3A). Interestingly, the power in the selected samples was still less than that in CE-adjusted random samples (Figure 3B). Sensitivity (Sn) and Specificity (Sp), were calculated as where true positives (TP), false positives (FP) and false negatives (FN) were determined based upon the overlap between the position of true QTLs and the likelihood ratio peaks surpassing a predetermined significance threshold. Specificity was greater, and sensitivity lower, in selected samples in both single and multiple-QTL simulations. The difference was most pronounced when markers were sparse (Figure 4) and heritability was low (not shown). Figure 4. Sensitivity and specificity in random and selected samples. (A) One QTL at a random position with heritability of 0.2. (B) Five QTL with random positions and effect sizes having an overall heritability of 0.5. Map length was 1000 cM, base population size was 100, and sample fraction was 0.2. QTL positions were always over 100 cM from each other in the five QTL simulations. Analysis was performed using marker regression. Sensitivity and Specificity In principle, a similar selection strategy could be used in quantitative trait locus (QTL) mapping population with the aim of maximizing the resolution obtained when only a limited number of permanent lines can be propagated or phenotyped. Though large mapping populations are invariably desirable for QTL mapping [2], practical constraints on population size are commonplace. We refer to the choice of individuals for phenotyping on the basis of their genotypes, namely the inferred positions of crossovers, as selective sampling. Here we describe our results on the statistical consequences of using such a selected sample for QTL mapping, particularly with regard to detection power and resolution. Figure 1. Samples are selected from larger mapping populations to optimize the distribution of bin lengths, where a bin is the shortest interval between two crossovers in a sample. Of the four possible selected samples of size 3 from the pool of gametes shown on the left, the one shown on the right would be chosen because it minimizes the sum of the squares of the bin lengths. Figure 2. CE after selection of RILs with varied framework marker intervals (A) and genome lengths (B). Base population size is 500. Genome length is 1000 cM in A. Marker interval is 10 cM in B. Each point is obtained from 10,000 individuals. A B