Supplementary Material for A rapid marker ordering approach for high-density genetic linkage maps in experimental autotetraploid populations using multidimensional scaling

A rapid marker ordering approach for high-density genetic linkage maps in experimental autotetraploid populations using multidimensional scaling

Theoretical and Applied Genetics

K.F. Preedy* and C. A. Hackett

Biomathematics and Statistics Scotland, Invergowrie, Dundee DD2 5DA

*corresponding author:

Email:

Table S1 Median rank correlations of the ordering of Simulation set 1 with the true order for chromosomes IV-XII, for four stress criteria based on Haldane’s map distance with LOD, LOD2 and LOD0.5 weightings and recombination fraction with LOD weighting. The first column gives the number of markers for each chromosome. cMDS is the constrained MDS method. PC2 and PC3 are from the Principal Curves method applied to two2- and three3-dimensional unconstrained MDS respectively.

Chromosome
(No. Markers) / Median Rank Correlation
LOD weights / LOD2 weights / LOD0.5 weights / Recombination Fraction
cMDS / PC2 / PC3 / cMDS / PC2 / PC3 / cMDS / PC2 / PC3 / cMDS / PC2 / PC3
IV (152) / 0.994 / 0.992 / 0.993 / 0.995 / 0.996 / 0.996 / 0.990 / 0.990 / 0.990 / 0.995 / 0.995 / 0.995
V (119) / 0.990 / 0.990 / 0.990 / 0.993 / 0.994 / 0.994 / 0.985 / 0.983 / 0.985 / 0.993 / 0.994 / 0.995
VI (122) / 0.995 / 0.994 / 0.995 / 0.996 / 0.996 / 0.996 / 0.992 / 0.990 / 0.992 / 0.996 / 0.994 / 0.995
VII (89) / 0.994 / 0.993 / 0.993 / 0.995 / 0.996 / 0.996 / 0.990 / 0.989 / 0.988 / 0.996 / 0.995 / 0.995
VIII (85) / 0.989 / 0.987 / 0.986 / 0.990 / 0.990 / 0.990 / 0.984 / 0.980 / 0.981 / 0.987 / 0.987 / 0.990
IX (91) / 0.991 / 0.991 / 0.991 / 0.993 / 0.994 / 0.995 / 0.988 / 0.985 / 0.987 / 0.988 / 0.988 / 0.991
X (104) / 0.988 / 0.988 / 0.990 / 0.991 / 0.993 / 0.993 / 0.986 / 0.984 / 0.985 / 0.990 / 0.987 / 0.991
XI (85) / 0.988 / 0.992 / 0.992 / 0.991 / 0.993 / 0.994 / 0.980 / 0.984 / 0.987 / 0.927 / 0.994 / 0.993
XII (119) / 0.994 / 0.994 / 0.994 / 0.996 / 0.996 / 0.996 / 0.991 / 0.991 / 0.991 / 0.996 / 0.995 / 0.995

Table S2 Mean and standard deviation of lengths from simulation set 1 with LOD, LOD2 and LOD0.5 weightings and recombination fraction with LOD weighting. The first two columns give the number of markers and the length of the map from which the data was simulated. cMDS is the constrained MDS method. PC2 and PC3 are from the Principal Curves method applied to two2- and three3-dimensional unconstrained MDS respectively. sd is the standard deviation of the estimated lengths over the 10 simulated populations of each chromosome.

Chromosome
(No. Markers) / Map Length (cM) / Mean length (sd)
LOD weights / LOD2 weights / LOD0.5 weights / Recombination fraction
cMDS / PC2 / PC3 / cMDS / PC2 / PC3 / cMDS / PC2 / PC3 / cMDS / PC2 / PC3
IV (152) / 95.77 / 94.27 (8.42) / 89.61 (8.55) / 90.09 (8.51) / 87.19 (7.65) / 84.34 (8.22) / 84.06 (8.77) / 101.31 (10.55) / 98.51 (9.90) / 98.52 (9.81) / 75.33 (4.46) / 68.00 (5.11) / 65.92 (4.75)
V (119) / 73.1 / 69.50 (6.59) / 67.72 (5.81) / 67.93 (5.97) / 63.36 (5.45) / 64.04 (4.20) / 63.70 (4.71) / 75.13 (6.53) / 73.64 (6.50) / 74.36 (6.67) / 57.53 (5.49) / 53.34 (4.44) / 52.58 (4.36)
VI (122) / 90.79 / 86.34 (9.06) / 85.95 (10.80) / 87.36 (9.78) / 79.94 (10.68) / 79.43 (7.75) / 81.31 (8.46) / 95.93 (11.47) / 93.59 (11.53) / 96.65 (11.57) / 68.47 (5.37) / 63.20 (5.45) / 64.46 (6.98)
VII (89) / 89.99 / 88.25 (4.84) / 87.45 (5.42) / 87.14 (5.37) / 83.59 (4.96) / 82.03 (4.65) / 81.63 (4.76) / 94.96 (5.80) / 95.88 (6.58) / 96.05 (5.97) / 72.68 (5.07) / 65.71 (3.64) / 65.72 (4.09)
VIII (85) / 62.32 / 64.89 (3.99) / 66.16 (5.28) / 65.38 (4.28) / 58.09 (3.84) / 60.12 (3.28) / 60.19 (2.80) / 69.52 (6.27) / 71.75 (6.69) / 72.18 (6.55) / 60.72 (12.73) / 52.25 (4.16) / 52.07 (3.83)
IX (91) / 121.61 / 112.79 (10.09) / 106.24 (9.50) / 107.75 (9.26) / 103.49 (8.17) / 98.14 (7.98) / 99.32 (6.46) / 120.86 (15.93) / 118.99 (13.85) / 118.96 (14.86) / 85.50 (6.58) / 79.07 (6.52) / 74.91 (5.49)
X (104) / 71.89 / 73.45 (3.86) / 71.49 (4.72) / 71.6 (4.46) / 64.29 (3.81) / 64.87 (2.99) / 64.83 (2.74) / 81.79 (4.39) / 80.70 (6.31) / 81.04 (5.68) / 58.63 (3.20) / 54.14 (2.76) / 55.54 (2.77)
XI (85) / 96.19 / 90.44 (13.04) / 89.88 (10.82) / 89.74 (10.84) / 83.40 (11.42) / 85.73 (7.36) / 85.50 (6.95) / 97.88 (13.79) / 97.01 (10.53) / 99.19 (9.96) / 74.76 (4.81) / 68.00 (6.09) / 68.08 (6.04)
XII (119) / 87.12 / 87.63 (4.65) / 85.98 (4.36) / 86.36 (4.46) / 79.92 (3.45) / 79.04 (3.14) / 79.01 (2.65) / 94.43 (7.14) / 94.95 (6.08) / 94.92 (6.49) / 69.92 (2.75) / 64.59 (2.99) / 63.59 (2.78)

Table S3 Mean and standard deviation (sd) of the NNfit measure from Simulation set 1, chromosomes IV-XII, with LOD, LOD2 and LOD0.5 weightings and recombination fraction with LOD weighting. cMDS is the constrained MDS method. PC2 and PC3 are from the Principal Curves method applied to two2- and three3-dimensional unconstrained MDS respectively. sd is the standard deviation of the NNfit over the 10 simulated populations of each chromosome.

Chromo – some / Mean NNfit (sd)
(No. Markers) / LOD weights / LOD2 weights / LOD0.5 weights / Recombination fraction
cMDS / PC2 / PC3 / cMDS / PC2 / PC3 / cMDS / PC2 / PC3 / cMDS / PC / PC3
IV / 1.49 (0.16) / 1.42 (0.16) / 1.43 (0.17) / 1.39 (0.14) / 1.33 (0.14) / 1.32 (0.15) / 1.62 (0.21) / 1.53 (0.19) / 1.54 (0.18) / 1.20 (0.11) / 1.08 (0.1) / 1.05 (0.08)
V / 1.41 (0.16) / 1.35 (0.13) / 1.35 (0.12) / 1.28 (0.12) / 1.30 (0.11) / 1.27 (0.11) / 1.49 (0.16) / 1.47 (0.13) / 1.49 (0.13) / 1.17 (0.12) / 1.07 (0.11) / 1.05 (0.10)
VI / 1.58 (0.19) / 1.6 (0.19) / 1.58 (0.18) / 1.45 (0.19) / 1.43 (0.13) / 1.46 (0.15) / 1.76 (0.23) / 1.73 (0.23) / 1.77 (0.22) / 1.29 (0.13) / 1.18 (0.11) / 1.18 (0.12)
VII / 2.61 (0.16) / 2.54 (0.14) / 2.54 (0.17) / 2.44 (0.19) / 2.40 (0.16) / 2.40 (0.17) / 2.83 (0.19) / 2.79 (0.20) / 2.78 (0.19) / 2.17 (0.22) / 1.92 (0.11) / 1.90 (0.09)
VIII / 1.82 (0.10) / 1.77 (0.14) / 1.72 (0.13) / 1.62 (0.12) / 1.66 (0.1) / 1.66 (0.09) / 1.95 (0.13) / 1.85 (0.16) / 1.86 (0.17) / 1.75 (0.50) / 1.42 (0.09) / 1.40 (0.12)
IX / 2.81 (0.26) / 2.63 (0.31) / 2.62 (0.31) / 2.56 (0.21) / 2.41 (0.27) / 2.43 (0.25) / 3.01 (0.41) / 2.96 (0.38) / 2.89 (0.36) / 2.21 (0.27) / 2.01 (0.26) / 1.85 (0.16)
X / 1.76 (0.12) / 1.72 (0.11) / 1.71 (0.11) / 1.52 (0.11) / 1.55 (0.14) / 1.54 (0.13) / 1.90 (0.12) / 1.90 (0.17) / 1.91 (0.16) / 1.40 (0.10) / 1.29 (0.07) / 1.31 (0.10)
XI / 2.54 (0.27) / 2.53 (0.29) / 2.52 (0.26) / 2.37 (0.27) / 2.42 (0.19) / 2.41 (0.2) / 2.80 (0.45) / 2.75 (0.26) / 2.74 (0.20) / 2.11 (0.12) / 1.95 (0.16) / 1.95 (0.14)
XII / 1.85 (0.10) / 1.78 (0.10) / 1.79 (0.09) / 1.69 (0.08) / 1.66 (0.08) / 1.67 (0.07) / 1.96 (0.15) / 1.94 (0.16) / 1.93 (0.17) / 1.50 (0.06) / 1.36 (0.08) / 1.32 (0.08)

Table S4 For one simulation of each scenario, a HMM is used to reconstruct the underlying chromosome configuration and the total number of recombinations that can be eliminated by omitting each marker in turn is calculated. HMM_mean shows the mean of this measure for all the markers, and max shows the maximum over all the markers.

Chrom. / Sim / No. markers / TRUE / LOD, PC2 / LOD, PC3 / LOD2, PC2 / LOD2, PC3
HMM_mean / HMM_mean / max / HMM_mean / max / HMM_mean / max / HMM_mean / max
I / 1 / 142 / 0.007 / 0.401 / 6 / 0.394 / 6 / 0.225 / 3 / 0.169 / 3
II / 1 / 120 / 0.008 / 0.433 / 9 / 0.492 / 7 / 0.383 / 6 / 0.208 / 4
III / 1 / 74 / 0.000 / 0.432 / 6 / 0.284 / 6 / 0.338 / 8 / 0.338 / 4
IV / 1 / 152 / 0.007 / 0.487 / 9 / 0.507 / 11 / 0.362 / 8 / 0.362 / 3
V / 1 / 119 / 0.017 / 0.639 / 6 / 0.647 / 5 / 0.361 / 7 / 0.387 / 7
VI / 1 / 122 / 0.016 / 0.262 / 5 / 0.352 / 5 / 0.213 / 6 / 0.189 / 5
VII / 1 / 89 / 0.022 / 0.281 / 3 / 0.281 / 4 / 0.292 / 3 / 0.247 / 3
VIII / 1 / 85 / 0.000 / 0.412 / 9 / 0.329 / 5 / 0.318 / 6 / 0.306 / 6
IX / 1 / 91 / 0.011 / 0.868 / 26 / 0.429 / 5 / 0.582 / 8 / 0.374 / 4
X / 1 / 104 / 0.000 / 0.471 / 7 / 0.452 / 6 / 0.385 / 6 / 0.269 / 4
XI / 1 / 85 / 0.012 / 0.200 / 3 / 0.141 / 3 / 0.118 / 2 / 0.118 / 3
XII / 1 / 120 / 0.033 / 0.675 / 12 / 0.500 / 6 / 0.442 / 8 / 0.442 / 5
I / 20% miss / 142 / 0.000 / 0.606 / 13 / 0.535 / 5 / 0.415 / 7 / 0.282 / 5
II / 20% miss / 120 / 0.008 / 0.375 / 6 / 0.292 / 5 / 0.317 / 5 / 0.225 / 2
III / 20% miss / 74 / 0.000 / 0.257 / 3 / 0.176 / 3 / 0.338 / 4 / 0.297 / 3
I / 5% error / 142 / 3.028 / 3.415 / 21 / 3.169 / 19 / 3.528 / 18 / 3.500 / 17
II / 5% error / 120 / 3.817 / 4.683 / 40 / 3.883 / 23 / 3.983 / 27 / 4.567 / 28
III / 5% error / 74 / 2.622 / 3.716 / 24 / 4.081 / 26 / 3.257 / 17 / 3.297 / 16


Table S5 This compares the maps of chromosome I. The column Number gives the identifier for each marker in the MDS analysis, MDS_Position is the position from the MDS map with the lowest NNfit (from the PC3 methods with LOD2 weighting), JM_Position is the position from mapping with JoinMap, H2013_Position is the map from Hackett et al. (2013). DM4.03 Chromosome and DM_position are the chromosome and position from the potato reference genome version 4.03 (Potato Genome Sequencing Consortium 2011; Sharma et al. 2013). (This can be downloaded as an excel file in supplementary table 5)