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The large gaps observed in the individual maps were reduced in the consensus map.
The large gaps observed in individual maps were reduced due to the increased marker density, and the final consensus integrated map had only one large gap (>10 cM) in the A2 linkage group.
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The component maps are reduced, and the negatives are cut and assembled into a mosaic on a clear sheet of plastic, the master negative of which provides guide copy for the several colour-separation plates required, which are then completed for reproduction.
In this way, the similarity between two connection probability maps is reduced as a function of their anatomical proximity.
We see in Table 2, that the size of the extracted conserved domain pair is reduced from 83 to 45%, as the size v0 of the common equatorial domain used in the simulated maps is reduced from 100to25%5%.
Thresholds for regression mapping are relaxed in only three of 47 cases (Table 7; the total number of maps is reduced from 50 because families F12, F20, and F45 had too few two biparentally segregating markers on LG 9 for map construction).
When LiDAR-AGB_50% were used, the uncertainties in the national forest AGB map were reduced by 20 40% compared to the map calibrated with all LiDAR-AGB (Figs. 11, 13, 14c, d).
The false-positive merges in our final map were reduced greatly.
Compared with the previously published map [ 16], intervals of >10 cM remaining in the tetraploid map were reduced to 16 - nine in the At subgenome, and seven in the Dt subgenome, with the largest number of gaps on chromosome D8 (4 gaps >10 cM) and the largest overall gap on chromosome A3 (between two adjacent loci) 22.2 cM (Additional file 1: Table S1).
We remark that (i) if (alpha_{i}=0) for every (i=1,2,ldots,N), then G-mapping is reduced to S-mapping; (ii) if (alpha_{i}=0) and (gamma_{i}=0) for every (i=1,2,ldots, N), then G-mapping is reduced to W-mapping; (iii) if (alpha_{i}=0) and (delta_{i}=0) for every (i=1,2,ldots, N), then G-mapping is reduced to K-mapping.
When a pair of complex conjugate eigenvalues of the Jacobian matrix cross the unit circle and satisfy the resonant condition λ04="1 or λ03= 1, the four-dimensional map is reduced to a two-dimensional one by the center manifold theorem, and the reduced map is put into its normal form by the method of normal form.
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