1. Alexander Kozik and Richard Michelmore, UC Davis Genome Center
Suite of Python MadMapper scripts for quality control of genetic markers, group analysis and inference of linear order of markers on linkage groups
Visualization and validation of genetic maps using two-dimensional CheckMatrix heat-plots
Alexander Kozik and Richard Michelmore, UC Davis Genome Center 1

2. Mapping using Recombinant Inbred Lines
Genetic Cross
Genotyping
Raw Marker Scores ;
; | | | |
GM01 A A A A A A A A A A A A A A A A B B B B B B B B B
GM02 A A A A A A A A A A A A A A A B B B B B B B B B B
GM03 A A A A A A A A A A A A A B B B B B B B B B B B B
GM04 A A A A A A A A A A A B B B B B B B B B B B B B B
GM05 A A A A A A A A A A B B B B B B B B B B B B B B B
GM06 A A A A A A A A A B B B B B B B B B B B B B B B B
GM07 A A A A A A A A A B B B B B B B B B B B B B B A A
GM08 A A A A A A A A A B B B B B B B B B B B B B A A A
GM09 A A A A A A A A A B B B B B B B B B B B A A A A A
GM10 B A A A A A A A A A B B B B B B B B B A A A A A A
GM11 B B A A A A A A A A B B B B B B B B A A A A A A A
GM12 B B B A A A A A A A B B B B B B B A A A A A A A A
Locus file
Mapping – Inference of Linear Order of Markers 2

3. CheckMatrix (py_matrix_2D_V248_RECBIT.py ) –
MadMapper and CheckMatrix are Python scripts and can be used on any computer platform: UNIX, Windows, Mac OS-X. Grouping can be done on a set of ~2,000 markers; map construction works in reasonable timeframe with up to ~500 markers
MadMapper_RECBIT –
- quality control of genetic markers and group analysis
MadMapper_XDELTA –
- inference of linear order of markers on linkage groups
CheckMatrix (py_matrix_2D_V248_RECBIT.py ) –
- visualization and validation of genetic maps using two-dimensional heat-plots and graphical genotyping 3

4. 82 output files Group Info Summary: file [ *.x_tree_clust ]
MadMapper_RECBIT input and output files
Recombination
Distance Scores:
[ *.pairs_all ]
GM01 GM
GM01 GM
GM01 GM
GM01 GM
GM01 GM
GM01 GM
GM02 GM
GM02 GM
GM02 GM
GM02 GM
GM02 GM
GM02 GM
Trio Analysis:
[ *.z_trio_good ]
[ *.z_trio_best ]
[ *.z_trios_bad ]
analysis of all trios (triplets) for
non-redundant set of markers
one input file - locus file
with raw marker scores
82 output files
LOG file:
( *.x_log_file )
information about run parameters ;
; | | | |
GM01 A A A A A A A A A A A A A A A A B B B B B B B B B
GM02 A A A A A A A A A A A A A A A B B B B B B B B B B
GM03 A A A A A A A A A A A A A B B B B B B B B B B B B
GM04 A A A A A A A A A A A B B B B B B B B B B B B B B
GM05 A A A A A A A A A A B B B B B B B B B B B B B B B
GM06 A A A A A A A A A B B B B B B B B B B B B B B B B
GM07 A A A A A A A A A B B B B B B B B B B B B B B A A
GM08 A A A A A A A A A B B B B B B B B B B B B B A A A
GM09 A A A A A A A A A B B B B B B B B B B B A A A A A
GM10 B A A A A A A A A A B B B B B B B B B A A A A A A
GM11 B B A A A A A A A A B B B B B B B B A A A A A A A
GM12 B B B A A A A A A A B B B B B B B A A A A A A A A
INPUT: Locus file
Python_MadMapper_V248_RECBIT_012.py
Marker Scores Info:
[ *.x_scores_stat ]
detailed information about scores and linkage
Group Info:
[ *.group_info ]
one file per iteration
16 iterations with different cutoff values
Marker summary:
[ *.z_marker_sum ]
for each marker ‘quality class’ is assigned -
- useful for selection of ‘core’ markers
Adjacency List:
[ *.adj_list ]
one file per iteration
16 iterations with different cutoff values
Group Info Summary:
file [ *.x_tree_clust ]
Summary for clustering results for all 16 iterations
Distinct linkage groups can be inferred by analysis of this clustering / grouping information
Non-Redundant Marker Scores:
[ *.z_nr_scores.loc ]
locus file with
non-redundant raw marker scores 4

5. MadMapper BIT scoring system
#################################################################
# GENOTYPES: #
# | BIT | A – 1st; B – 2nd #
# SCORING SYSTEM: | | C - NOT A ( H or B ) #
# | REC | D - NOT B ( H or A ) #
# H - A and B #
# #
# #
# | | | | | | | #
# | A | B | C | D | H | | #
# | | | | | | | #
# * #
# | | | | | | | | #
# | A | | | | | | | #
# | | | | | | | | #
# * #
# | | | | | | | | #
# | B | | | | | | | #
# | | | | | | | | #
# * #
# | | | | | | | | #
# | C | | | | | | | #
# | | | | | | | | #
# * #
# | | | | | | | | #
# | D | | | | | | | #
# | | | | | | | | #
# * #
# | | | | | | | | #
# | H | | | | | | | #
# | | | | | | | | #
# * #
# | | | | | | | | #
# | | | | | | | | #
# *. #
#################################################################
# #
# EXAMPLES OF SCORING: #
# POSITIVE LINKAGE: #
# AAAAAAAAAAAAAAAAAAAA BIT SCORE = 6*20 = #
# AAAAAAAAAAAAAAAAAAAA REC SCORE = 0 (0.0) #
# #
# AAAAAAAAAAAAAAAAAAAA BIT SCORE = 6*18 - 6*2 = #
# AAAAAAAAAAAAAAAAAABB REC SCORE = 2 (2/20 = 0.1) #
# AAAAAAAAAABBBBBBBBBB BIT SCORE = 6*10 + 6*10 = #
# AAAAAAAAAABBBBBBBBBB REC SCORE = 0 (0.0) #
# #
# AAAAAAAAABABBBBBBBBB BIT SCORE = 6*18 - 6*2 = #
# AAAAAAAAAABBBBBBBBBB REC SCORE = 2 (2/20 = 0.1) #
# NO LINKAGE: #
# #
# AAAAAAAAAAAAAAAAAAAA BIT SCORE = 6*10 - 6*10 = #
# AAAAAAAAAABBBBBBBBBB REC SCORE = 10 (10/20 = 0.5) #
# #
# BBBAABBAAAAAAABAABBB BIT SCORE = 6*10 - 6*10 = #
# BABBAABBABABABBBAABA REC SCORE = 10 (10/20 = 0.5) #
# NEGATIVE LINKAGE: #
# #
# AAAAAAAAAAAAAAAAAAAA BIT SCORE = 6*2 - 6*18 = #
# AABBBBBBBBBBBBBBBBBB REC SCORE = 18 (18/20 = 0.9) #
# ABABABABABABABABABAB BIT SCORE = 6*2 - 6*18 = #
# ABBABABABABABABABABA REC SCORE = 18 (18/20 = 0.9) # 5

6. Arabidopsis Genetic Map: Comparison of Different Scoring Systems
JoinMap LOD scores
JoinMap REC scores
MadMapper BIT scores
MadMapper REC scores 6

7. MadMapper_RECBIT Clustering: Group Info Summary [ *.x_tree_clust file ]7

8. MadMapper_RECBIT BIN Analysis
M_1 A A A B B B A A A A B B B B A A - A A B B B B A B B A A B A A A B B B B
M_2 A A A B B B A - A A B B B B A A A A A B B B B A B B A A B A A A B B B B
M_3 A A A B B B A A A A B B - B A A A A A B B B B A B B A A B A A A B B B B
M_4 A A A B B B A A A A B B A B A A A A A B B - B A B B A A B A A A B B B B
M_2
M_1
M_3
Linked
Group
Diluted
Node
Saturated
Node
Example of
Complete Graph:
all nodes are
‘saturated’
M_4 8

9. MadMapper_RECBIT Marker Summary [ *.z_marker_sum file ]9

10. MadMapper_RECBIT Trio (Triplet) Analysis
M_1 A A A B B B A A A A B B B B A A - A A B B B B A B B A A B A A A B B B B
X X X X
M_M A A A B A B A - A A B B B B A B A A A B B A B A B B A A B A A A B B A B
M_2 A A A B B B A A A A B B - B A A A A A B B B B A B B A A B A A A B B B B
flanking marker 1
‘middle’ marker
flanking marker 2
MARKER_Flank_1
REC1
BIT1
D_FR1
MARKER_Middle
REC2
BIT2
D_FR2
MARKER_Flank_2
REC_Flank
BIT_F
D_FR_F
D_REC
D_REC_Flank
COR47
0.1
336
0.6931
CAT3
0.0857
348
G2395
***
0.0253
450
0.7822 5 +
LK141
0.1522
192
0.4554
GUT15
0.193
210
0.5644
MI238
0.1231
294
0.6436 4
MI204
0.051
528
0.9703
MI51
0.0806
312
0.6139
SGCSNP41
0.0161
360
M336
0.0494
438
0.802
COR15
0.0385
432
0.7723
VE018
0.0879
0.901
ARR7
0.0115
510
0.8614
282
0.4653
F15571
0.0179
324
0.5545
PAP3
0.0227
504
0.8713
COR78
0.0577
276
0.5149
PDC2
0.0588
270
0.505
Bad Trios
Number of double crossovers is high for bad trios
Good Trios
Number of double crossovers should be low for good trios 10

11. CheckMatrix Usage: three input files are required
LG GM
LG GM
LG GM
LG GM
LG GM
LG GM
LG GM
LG GM
LG GM
LG GM
LG GM
LG GM
Map file
GM01 GM
GM01 GM
GM01 GM
GM01 GM
GM01 GM
GM01 GM
GM02 GM
GM02 GM
GM02 GM
GM02 GM
GM02 GM
GM02 GM
Matrix file ;
; | | | |
GM01 A A A A A A A A A A A A A A A A B B B B B B B B B
GM02 A A A A A A A A A A A A A A A B B B B B B B B B B
GM03 A A A A A A A A A A A A A B B B B B B B B B B B B
GM04 A A A A A A A A A A A B B B B B B B B B B B B B B
GM05 A A A A A A A A A A B B B B B B B B B B B B B B B
GM06 A A A A A A A A A B B B B B B B B B B B B B B B B
GM07 A A A A A A A A A B B B B B B B B B B B B B B A A
GM08 A A A A A A A A A B B B B B B B B B B B B B A A A
GM09 A A A A A A A A A B B B B B B B B B B B A A A A A
GM10 B A A A A A A A A A B B B B B B B B B A A A A A A
GM11 B B A A A A A A A A B B B B B B B B A A A A A A A
GM12 B B B A A A A A A A B B B B B B B A A A A A A A A
Locus file
CheckMatrix (py_matrix_2D_V248_RECBIT.py )
upon program execution three output files will be generated:
HEAT PLOT – it assists to validate the quality of constructed genetic map and identify markers with wrong position
GRAPHICAL GENOTYPING: visualization of haplotypes per recombinant line (suspicious double crossovers are highlighted)
CIRCULAR GRAPH – it assists to validate genetic map and identify markers with spurious linkage 11

12. Genetic Map Visualization using CheckMatrix
[ good map ] 12

13. Genetic Map Visualization using CheckMatrix
[ wrong map ] 13

14. Genetic Map Visualization using CheckMatrix
[ disordered markers ] 14

15. Minimum Entropy Approach to Infer Linear Order
Using MadMapper_XDELTA program
CheckMatrix 2D plot:
random
order
high
‘entropy’
MadMapper_XDELTA analyzes two-dimensional matrices of all pairwise scores and finds best map that has minimal total sum of differences between adjacent cells (map with lowest ‘entropy’).
partially
wrong
order
right
order
low
‘entropy’
Visualization of
numerical data
using ChekMatrix 15

16. MINIMUM ENTROPY APPROACH TO INFER LINEAR ORDER OF MARKERS:
CheckMatrix Color Scheme
Two-dimensional matrix of
recombination pairwise scores
adjacent cells
(values)
Visualization of
numerical data
using CheckMatrix
Numerical data
generated
by MadMapper 16

17. optionally: unlimited list of ‘frame’ markers with fixed order
MadMapper_XDELTA Usage:
MadMapper_XDELTA takes as input three files:
Matrix (pairwise distances between markers)
List of ‘frame’ markers
List of markers to map
First step: finding of the best map for ‘frame’ markers by checking all possible combinations
(up to 10 markers)
optionally: unlimited list of ‘frame’ markers with fixed order
Best-Fit extension
Take one marker from the list of markers to map and insert it into 2-dimensional matrix of the current best map. Check for all possible positions. Calculate ‘delta’ and find the map with lowest ‘delta’ value (lowest ‘entropy’)
Move to the next marker to map until all markers are mapped. Optional shuffling (ripple) after several steps 17

18. map calculated by checking of all possible combinations
Example of Best-Fit Extension:
=============================================
MATRIX (ALL PAIRS) : madmapper_test_small.out.pairs_all
MARKERS TO MAP : madmapper_test_small.list
FRAME MARKERS LIST : madmapper_test_small.frame
OUTPUT MAP FILE : madmapper_test_small.xdelta
MAX FRAME LENGTH : 12
FIXED FRAME ORDER : FALSE
LINKAGE GROUP ID : LG
DUMMY DEBUG : TRUE
=======
GM02 GM06 GM10 *** *** *** 1
GM02 GM10 GM06 *** *** *** 2
GM06 GM02 GM10 *** *** *** 3
GM03 GM02 GM06 GM10 *** *** *** 1
GM02 GM03 GM06 GM10 *** *** *** 2
GM02 GM06 GM03 GM10 *** *** *** 3
GM02 GM06 GM10 GM03 *** *** *** 4
GM08 GM02 GM03 GM06 GM10 *** *** *** 1
GM02 GM08 GM03 GM06 GM10 *** *** *** 2
GM02 GM03 GM08 GM06 GM10 *** *** *** 3
GM02 GM03 GM06 GM08 GM10 *** *** *** 4
GM02 GM03 GM06 GM10 GM08 *** *** *** 5
GM09 GM02 GM03 GM06 GM08 GM10 *** *** *** 1
GM02 GM09 GM03 GM06 GM08 GM10 *** *** *** 2
GM02 GM03 GM09 GM06 GM08 GM10 *** *** *** 3
GM02 GM03 GM06 GM09 GM08 GM10 *** *** *** 4
GM02 GM03 GM06 GM08 GM09 GM10 *** *** *** 5
GM02 GM03 GM06 GM08 GM10 GM09 *** *** *** 6
map calculated by checking of all possible combinations
marker GM03 was inserted
marker GM08 was inserted
marker GM09 was inserted 18

19. MadMapper_XDELTA Map Output
A – marker above
B – middle marker
Distance
[A-B]
Distance
[B-C]
Distance
[A-C]
[A-B] + [B-C]
([A-B] + [B-C]) - [A-C]
C – marker below LG
MARKER
POS
#1#
DST1
#2#
DST2
#3#
DST3
#S#
SUMM
#D#
DIFF
STATUS
CLASS 2
G4553
NNNNNN
NNNNN
M246 1
0.043
0.0213
0.0778
0.0643
GOOD
__0__
MI320
0.0211
0.0002 .. …
NGA1126 26
0.0225
0.0645
0.0702
0.087
0.0168
SGCSNP135 27
0.0842
0.129
0.0448
MI54 28
0.0968
0.0856
VE014 29
0.0532
0.0745
0.0743
M283 30
0.1803
0.1833
0.2335
0.0502
__1__
SGCSNP333 31
0.1167
0.297
0.2002
LARGE
SGCSNP210 32
0.1154
0.0013
COP1 33
0.0196
0.0263
SPL3 34
0.04
0.0339
0.0596
0.0257
C4H 35
0.0227
0.0303
0.0627
0.0324
M336 54
0.0519
0.0625
0.1144
__X__
UBIQUE 55
0.0526
0.0619
0.1151
MI79A 56
0.0781
0.1307
0.0662
ATHB7 57
0.1579
0.1698
0.236
SGCSNP214 58
0.1429
0.1667
0.3008
0.1341
SGCSNP198 59 A B C 19

20. 20

21. Physical order of markers (based on BLAST search)
Side-by-side comparison of linear order of markers on Arabidopsis genome inferred by three different approaches
(mapping programs) and comparison with physical order of markers (Col- 0 genomic sequence):
MadMapper_XDELTA (minimum entropy approach),
JoinMap (maximum likelihood) and
RECORD (minimum number of recombination events)
[Diagonal dot-plot was created using GenoPix_2D_Plotter ]
Inferred order of markers by mapping programs
MadMapper
JoinMap
RECORD 21

22. Arabidopsis Genetic Map constructed by MadMapper and visualized with CheckMatrix: 2D Heat Plot
Linkage group I
Regions with
Negative Linkage
Main Diagonal with Linked Markers
Linkage group II
Linkage group III
Regions with
Quasi Linkage
High Density of Markers
Linkage group IV
Low Density of
Markers
Allele Composition per Marker
Linkage group V
Linkage group I
Linkage group II
Linkage group III
Linkage group IV
Linkage group V 22

23. Arabidopsis Genetic Map constructed by MadMapper
Linkage group I
Linkage group II
Linkage group III
Linkage group IV
Linkage group V
Arabidopsis Genetic Map constructed by MadMapper
and visualized with CheckMatrix: Graphical Genotyping 23

24. REFERENCES AND DATA SOURCES:
1. Dean and Lister Arabidopsis Genetic Map
and Raw Data:
2. MadMapper:
3. JoinMap:
4. RECORD:
5. GenoPix_2D_Plotter
CREDITS:
This work was funded by NSF grant #
to Compositae Genome Consortium
PAG-14 POSTERS WITH EXAMPLES OF MADMAPPER USAGE:
#P751 High-Density Haplotyping With Microarray-Based Single Feature Polymorphism Markers In Arabidopsis
#P761 Gene Expression Markers: Using Transcript Levels Obtained From Microarrays To Genotype A Segregating Population
#P957 MadMapper And CheckMatrix - Python Scripts To Infer Orders Of Genetic Markers And For Visualization And Validation Of Genetic Maps And Haplotypes 24