Endelman BMC Genomics 2011, 12:407 http://www.biomedcentral.com/1471-2164/12/407 An unusual feature of both the LP and QP lineariza- tion methods is their tendency to compress map inter- vals, whereas most consensus maps are inflated relative to the original linkage maps (e.g., [7,11]). As shown in Table 1, the amount of compression increased as more linkage maps were integrated. For two linkage maps, the LP and QP consensus maps were compressed by 17% and 12% respectively, while for eight linkage maps the compression was 44% (LP) and 38% (QP). The QP con- sensus maps had consistently less compression than the LP maps. For the simple example shown in Figure 1, where both linkage maps have a total length of 3.0 cM, one can verify analytically that the QP consensus map is compressed to 2.8 cM (the LP map is 2.5 cM). By default DAGGER rescales the consensus map so that its total length equals the mean length of the component linkage maps, but the user can also request the com- pressed map. Table 1 shows that, in addition to increasing marker density, integrating more linkage maps tends to reduce the error between the consensus map and the simulated phy- sical map. This was true regardless of whether error was measured with the L1 norm (mean absolute error) or L2 norm (root-mean-squared [RMS] error). With only one linkage map the average RMS error was 4.7 (SE 0.2) cM, while with eight linkage maps the average RMS error was 2.4 (SE 0.1) cM for the QP method. Using either norm, the QP maps had consistently less error than the LP maps (contrast: RMSEQP - RMSELP = -0.3 cM < 0, p < 10-4). Validation with barley data The original impetus for developing DAGGER came from analyzing the results of Close et al. [11], who used Merge- Map [14] to integrate the information from four barley linkage maps genotyped at nearly 3000 SNP markers. These same linkage maps were used as input for DAG- GER, and no ordering conflicts were detected. The ordinal consensus graphs for the seven barley chromosomes (Figures S1-S7, Additional Files 1, 2, 3, 4, 5, 6, and 7) and the QP consensus map (Table S1, Additional File 8) pro- duced by DAGGER are available online. Figure 2 compares the ordinal consensus graph from DAGGER and the simplified consensus graph from MergeMap at the 5HS telomere. The four linkage maps for this region are reproduced in Table 2. Nine of the markers are for genes at the barley hardness locus, for which there is a physical map [21]. The physical order of these genes is hinb/hina/gsp from the distal end. None of the ordinal information in the DAGGER graph violates this physical order. The only relationships among the hinb/hina/gsp markers in the DAGGER graph are that marker 3_0984(hinb) is distal to markers 3_0975(gsp), 3_0979(hina), and 3_0977(gsp). Table 2 Page 5 of 9 shows that this information comes from the Oregon Wolfe Barley (OWB) linkage map, and that no other ordinal information for the hardness locus markers is present in the linkage maps. MergeMap also captures this ordering, but in addition there are numerous relationships that are not present in the linkage maps. This is apparent from the unphysical ordering of the hinb/hina/gsp markers. MergeMap shows the markers 3_0976(gsp), 3_0978(hina), 3_0980 (hina), and 2_0226(hina) as mapping distal to both hinb markers, and the marker 3_0975(gsp) is shown distal to 3_0979(hina). The order of these markers is indetermi- nate from the linkage maps, which is how they are por- trayed by DAGGER. The unphysical relationships in the simplified graph from MergeMap arise because of the way markers are binned. MergeMap will potentially bin markers if they are binned in at least one of the linkage maps and if their order is indeterminate [14]. To appreciate the consequences of this rule, consider the vertex with six markers at the top of the MergeMap graph. Four of these markers are from the hardness locus and were only present in the Steptoe-Morex (SM) map: 3_0976(gsp), 3_0978(hina), 3_0980(hina), and 2_0226 (hina). The other two markers in the vertex–1_0745 and 2_0894–are binned with the hardness locus markers in the SM linkage map (see Table 2). The markers 1_0745 and 2_0894 were also co-segregating in the Morex-Barke (MB) population, where they mapped distal to the hinb marker 3_0983. Because the aforementioned hina and gsp markers were binned with 1_0745 and 2_0894 in the SM linkage map, and because their relationship to 3_0983(hinb) is indeterminate from the linkage maps, MergeMap binned all six markers together. This creates the implication that the hina and gsp markers are distal to 3_0983(hinb), which is consistent with the linkage maps but not implied by them (and known to be false from the physical map [21]). As this example illustrates, the simplified graphs from MergeMap are not ordinally equivalent to the linkage maps and will potentially con- tain unphysical relationships even if the linkage maps do not. The simplified graphs from DAGGER are ordinally equivalent to the linkage maps and will not contain unphysical relationships provided the linkage maps are physically correct. Table 3 shows the number of markers, number of mar- ker bins, and amount of compression in the DAGGER consensus map (using the QP method). Because DAG- GER linearizes the unsimplified consensus graph, whereas MergeMap linearizes a simplified graph, the consensus map from DAGGER had twice the number of marker bins (1886 vs. 942). Over the entire genome the DAGGER map was compressed by 13%, while the con- sensus map from MergeMap was inflated by 46%. The