vg: the variation graph toolkit
Eric Dawson October 2016@erictdawson
1
Variation graphs
"Variation graphs provide a succinct encoding of the sequences of many genomes. A variation graph (in particular as implemented in vg) is composed of: • nodes, which are labeled by sequences and ids • edges, which connect two nodes via either of their respective ends • paths, describe genomes, sequence alignments, and annotations (such as gene
models and transcripts) as walks through nodes connected by edges"*
*From the vg wiki
Variation graphs allow us to map directly against known (or proposed) variation.
2
Variation graphs
GRCh38 alts in B-3106 from human MHC (@erikgarrison)
3
Variation graphs are pangenomes
“Computational Pan-Genomics: Status, Promises and Challenges.” Computational Pan-Genomics Consortium. Briefings in Bioinformatics (2016) in press
Pangenomes should fulfill a number of basic functions.
Erik Garrison, A toolkit for practical pangenomics, ECCB 20164
Variation graphs are pangenomes
We've implemented most of these operations in vg.
github.com/vgteam/vgErik Garrison, A toolkit for practical pangenomics, ECCB 2016
5
Constructing graphs
construct - build graphs from paired FASTA/VCF files.
msga - use progressive assembly to generate a graph from input sequences.
an example of a graph made with MSGA @erikgarrison
6
Graph modification
mod - prune and normalize graphs, shorten nodes, and much more.
circularize - circularize paths in the graph.
ids - coordinate the ID spaces of multiple subgraphs.
Circular HPV variation graph @erictdawson & Sarah Wagner (NCI)7
Indexing variation graphs
The core, mutable VG data structures support graph manipulation, queries, and alignment, but they are not scalable. Thus...
XG - immutable bidirectional graph index
gPBWT - graph-generalized positional BWT (Adam Novak)
GCSA2 - path index queries for variation and de Bruijn graphs (Jouni Sirén)
8
Indexing variation graphs
The core, mutable VG data structures support graph manipulation, queries, and alignment, but they are not scalable. Thus...
XG - immutable bidirectional graph index
gPBWT - graph-generalized positional BWT (Adam Novak)
GCSA2 - path index queries for variation and de Bruijn graphs (Jouni Sirén)
These structures enable mapping at whole-genome scale.
9
Mapping to a variation graph
vg can operate on arbitrary sequence graphs. All other graph-based resequencing implementations (GRAL, BWBBLE, vBWT, GCSAv1) require a DAG.
Local alignment to cyclic graphs is provided by unrolling:
10
Exact-match guided alignment in vg
@erikgarrison
Obtain MEMs from GCSA2, cluster MEMs with xg's positional index, then fully resolve alignment for non-matching portions using dynamic programming.
11
Obtain MEMs from GCSA2, cluster MEMs with xg's positional index, then fully resolve alignment for non-matching portions using dynamic programming.
Exact-match guided alignment in vg
@erikgarrison12
Mapping to a variation graph
1 billion reads / 32 vCPUs / 30 hours
13
Small variant calling in vg
call - bubble informed pileup-based caller
genotype - FreeBayes style genotyping using graph augmentation and superbubble detection
14
Genotyping
Genotyping and MSGA produce identical results (as expected).
15
Interchange with other programs
vectorize - export Alignments as Vowpal-Wabbit vectors for ML
view - GFA/JSON/DOT for many graph entities
1.0 1 ref_1A | ref 1 1 0 1 0 1 0 1
16
Other functions
locify(beta) - extract relevant info for external phasing.
deconstruct(beta) - extract an input VCF from the graph.
sim - simulate reads and exact alignments from the graph.
stats - print relevant graph properties.
surject- push graph alignments to BAM space.
sift/scrub(beta) - filter / select alignments by mapping properties.
translate - lift graph coordinates between graphs.
17
Structural variation in variation graphs
1:CAAATAAG
9:GC
11:TTGGAAATT
20:TTCTGGA
27:GTT30:CTAT
34:TATATTCCAACTCTCTG
18
Structural variation
Loosely defined as changes to the genomic sequence >50bp in length.
1. Balanced events1. Inversions 2. Translocations
2. Unbalanced events 1. Insertions 2. Deletions 3. Duplications
3. "Complex" - not shown - Multiple events occurring in tandem, specific time series of events, etc.
19
Why are we talking about SVs?
1. Evidence for structural variation in the NCI Chernobyl study.
• Matched tumor/normal samples from >400 individuals exposed to 131I post-Chernobyl who subsequently developed papillary thyroid carcinoma.
2. Variation graphs provide novel ways to locate and score SV calls.
• Graphs are mutable - candidate variation can be inserted, mapped against, and refined.
20
*From Stephen Chanock, IARC 2016
*
Evidence of SV in Chernobyl data
21
*From Stephen Chanock, IARC 2016
*
Evidence of SV in Chernobyl data
22
Evidence of SV in Chernobyl data
Median and (Total) Lumpy Calls DEL INV Other
(excl. BND)
Tumor (12) 9074 (187,150) 3925 (53,643) 2185 (25,182)Normal (11*) 5059 (60,508) 378 (9,494) 1234 (13,682)Blood (12) 6634 (88,985) 98 (1,195) 1247 (14,181)
Median and total call numbers (as well as analysis by others) indicate we might expect a high burden of deletions and inversions in tumours from our dataset (relative to normals) after normalization and QC.
*No A90N normal tissue sample; A90G metastasis sequenced instead23
Representing SVs in variation graphs
1:CAAATAAG
9:GC
11:TTGGAAATT
20:TTCTGGA
27:GTT30:CTAT
34:TATATTCCAACTCTCTG
Chr22 (hg38) + all well-defined DEL in COSMIC
DEL DEL INV
1
135016
37808148
1589543
43182096
1630246
31721015
1971760
32113305
3486016
49466765
4591816
35142677
5258415
46082172
6554688
37491158
7482235
46541861
7490801
43912917
7645222
17645868
9107072
39119258
9211653
39211948
15863014
41334872
1667571116715410
16749787 16749860 17453803
1968856317607658
33362615
17680825
24547235
17833893
49444261
17953345
31769296
18105753
24462449
1919805920266331
20401803
20559555
20418416
22667693
20428509
38498905
20449686
20460773
20495146
26946532
20556428 20556507
20629345
25505622
20858930 20859045
20998041
21014964
20998896
34786948
21976209
23275184
22809182
47694849
2289030422890578
22892052
36354893
22968473
40005367
2299524323044783
23217730
28778854
23707469 23707517 24005396 24005489 24022830
46351709
24050976
28312522
24313858 25287170
24689711
25039224
2478610824786184
2493484224938933
24961953 25024208
25384267
25598221
25522003 25532761
25811512
40712721
2589621325896729
26007969
49049131
26040431
2617316426059464 26059807
26696284
30291397
2682049327059846
27066476
30207912
2716066127549882
2719753729290220
27625140 29304612
27697764
29329477
27723918 287111822786550127976839
28089859 2809217228092133
28092647 28441765
28443407 28933298
29222962
2899748529041055
29054732
29200621
29154954
2960411929300024
29622689 29662131
29695589 29767547
29769677 29794897
29794976 30059328
30063522
30230653
42218395
30510557
30594775
30800489
39670615
3082108630821499
31549373
48238901
31688192
31906023
3243903933452164
33169872
46714959
33196648
40656081
33414421 33866535
33544907
37528980
33759250
33838398
3432455434328838
3537874835431175
35399553 35498355
3543994835440200
35469079
3546977735645167
35646141
35674584
49531956
35695221
35701287 3601894636073495
36065230 36065282
3612388236592640
36322496
36377678
36352462
38740869
3666036736662632
36769878
39423761
37677432 3767956137679553
3776830438118504
38247610
38130719 3815115138338892 38339933
3850128138505951
38681924 38684723
38923921
46828240
39045134 39133961
39244496
47134951
39508497
39508544
39538021 40358236
40184398
41353196
40758854
40866405
41809105
41893706
4225580242257371
42392911
42645638
42445335
48239211
4257825542580869
4261055442705775
42619175
42621044
4284981543002419
43018793
43018838
44167678
44167725
44251524
44328879
44995265
50697686
45995523
47719786
46073976
46075080
46190553 46824926
47230884 47296874
47759517
4810624148441597
48441643 48669037
48669921
48779783 4886426548858429
48939664
49801006
50464635
50276308
50278914
50276746 50277060
24 github.com/edawson/lasso
Why use a variation graphs and not [your favorite SV caller here] ?
25
Read alignment is Bayesian
Our best alignment gets the highest posterior score
The reference genome
The read from the sequencer
26@erikgarrison
Detecting SVs with vg
graph
mapq soft clipping mate orientation
reads
fragment length path divergence unmapped reads
sample
We're stuck with our reads, but with variation graphs we can sample from possible reference priors to maximize:
P( reference | reads)
We can also refine our breakpoints using this approach.
Informative for SV typeUninformative
27
Detecting deletions with vg
1000 simulated reads w/ 1kb deletion mapped to an 8kb flat HPV genome graph.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80
36
35
31
32
1 2
6
5
72
71
70
66
67
68
69
72
71
4
5
9
8
28
29
33
32
37
36
32
33
49
50
55
54
22
23
27
26
25
77
76
72
73
74
58
57
53
54
74
75
78
77
55
54
50
51
40
41
45
44
68
69
72
71
23
22
8
9
10
27
26
23
24
27
28
32
31
52
5146
47
72
73
77
76
79
78
74
75
40
41 46
4524
25
26
29
28
8
7
3
4
5
25
26
30
29
8
7
3
4
6
7
10
9
77
76
71
72
3
4
9
8
7
59
60
63
62
52
53
56
55
66
65
61
62
72
73
74
77
76
76
75
71
72
35
3430
31
51
50
46
47
22
21
7
8
55
54
50
51
41
42
46
45
7
6
2
3
4
35
3430
31
42
43
46
45
2
3
7
6
8
7
6
2
3
4
74
75
79
78
45
44
40
41
39
40
44
43
59
58
54
55 65
64
60
61
48
47
44
45
71
72
76
75
48
49
53
52
70
71
74
73
47
46
42
43
54
53
48
49
33
34
35
38
37
75
74
70
71
72
73
77
76
34
35
39
38
53
5247
48
63
64
69
68
67
72
73
77
76
67
6665
60
61
44
45
49
48
36
35
32
333
4
8
7
34
33
29
30
52
53
57
56
58
57
54
55
5
6
9
8
68
67
63
64
65
32
31
30
26
27
54
53
49
50
57
58
62
61
71
70
66
67
38
37
34
35
51
50
46
47
28
27
23
24
34
33
28
29
30
75
74
70
71
7269
68
64
65
22
21
8
9
56
55
51
52
42
43
48
47
41
40
37
38
72
71
67
68
47
46
42
43
44
8
9
10
24
23
67
66
61
62
63
73
72
68
69
65
66
70
69
60
61
65
64
41
42
43
46
45
66
65
61
62
78
77
73
74
42
43
44
47
46
43
44
49
48
8
7
4
5
60
61
65
64
51
52 56
55
63
62
58
59
24
25
29
28
53
52
47
48
49
42
41
37
38
31
30
29
25
26
27
62
61
57
58
35
34
30
31 48
47
44
45
54
5349
50
51
24
25
29
28
73
74
78
77
8
9
10
24
23
22
67
68
72
71
71
72
76
75
57
58 61
60
64
65
69
68
42
41
37
38
29
30
34
33
33
34
38
37
3
4
7
6
79
78
74
75
36
37
41
40
62
61
57
58
29
30
31
34
33
64
63
60
61
73
74
79
78
77
39
40
44
43
35
36
41
40
38
37
33
34
56
55
51
52
25
26
31
30
29
41
42
46
45
54
55
56
59
58
63
64
69
68
40
39
36
37
8
7
3
4
32
31
27
28
61
62
66
65
66
65
64
61
62
56
57
60
59
40
41
45
44
43
36
35
32
33
53
54
55
59
58
72
73
76
75
23
22
8
9
47
48
51
50
52
53
57
56
34
33
29
30
76
75
71
72
73
58
57
54
55
79
78
74
75
57
56
55
51
52
32
33
34
37
36
8
7
3
4
51
50
46
47
22
23
27
26
61
60
57
58
70
71
75
74
58
57
53
54 69
68
64
65
66
45
46
49
48
38
39
43
42
60
59
55
56 63
62
58
59
30
29
28
25
26
65
66
67
70
69
47
46
43
44
27
26
21
22
5
6
10
9
8
68
69
74
73
67
66
61
62
3
4
7
6
73
72
68
69
40
41
45
44
35
36
40
39
69
70
75
74
73
60
59
56
57
21
22
26
25
7
8
22
21
31
32
36
35
61
60
56
57
1 2
6
5
4
45
46
50
49
48
71
70
66
67
34
33
32
28
29
77
76
72
73
7431
30
25
26
71
72
75
74
64
63
58
59
30
29
28
25
26
76
75
74
70
71
37
36
32
33
34
67
66
62
63
32
33
37
36
35
53
5247
48
46
45
42
43
26
25
24
21
22
53
54
59
58
76
75
71
72
73
52
53
57
56
28
2722
23
46
45
41
42
43
44
48
47
73
72
68
69
23
24
29
28
31
32
36
35
59
60
61
65
64
24
23
22
9
10 22
21
7
8
33
32
28
29
30
59
60
63
62
63
64
65
68
67
62
61
58
59
21
22
27
26
25
63
64
68
67
75
74
70
71
34
33
29
30
25
26
27 31
30
23
22
8
9
78
77
72
73
74
27
28
33
32
52
51
47
48
47
48
52
51
58
59
62
61
53
52
51
48
49
39
40
44
43
48
49
54
53
54
53
49
50
34
35
39
38
46
47
52
51
42
43
47
46
52
53
58
57
64
63
60
61
52
51
47
48
33
34
38
37
33
32
29
30
72
71
66
67
36
37
41
40
29
30
33
32
30
31
32
35
34
28
27
23
24
26
27 31
30
74
73
69
70
55
56
57
60
59
36
37
38
41
40
3
4
7
6
38
37
33
34
35
10
9
5
6
72
73
77
76
70
69
64
65
53
5248
49
55
56
57
60
59
58
59
64
63
62
51
52
57
56
55
43
44
47
46
35
36 40
39
33
34
38
37
53
52
51
48
49
54
55
59
58
27
28
32
31
58
57
56
53
54
52
53
54
57
56
58
59
63
62
61
30
29
26
27
72
71
67
68
60
59
56
57
26
25
21
22
47
48
53
52
51
26
25
21
22
55
56
60
59
34
33
29
30
61
62
66
65
28
27
26
22
23
54
53
49
50
51
74
75
79
78
77
61
60
55
56
33
34
38
37
79
78
74
75
71
72
77
76
51
52
55
54
39
40
44
43
4
5
9
8
7
67
68
73
72
45
46
47 50
49
67
68
69 72
71
70
60
61
66
65
64
68
69 72
71
10
9
5
6
10
9
6 7
8
21
22
26
25
24
25 28
27
1 2
5
4
40
39
35
36
37
9
8
4
5
6
4
5
9
865
66
67
71
70
69
45
44
40
41
42
51
52
56
55
58
59
63
62
51
52
56
55
38
39
40
43
42
52
51
47
48
9
10
24
23
29
30
34
33
9
10
24
23
22
31
30
26
27
28
36
35
31
32
29
28
25
26
53
54
55
58
57
59
60
61
64
63
54
55
56
59
58
79
78
77
74
75
44
45
49
48
52
51
47
48
58
57
52
53
53
54
59
58
57
56
57
61
60
61
60
55
56
57
56
57
60
59
22
23
26
25
55
54
53
49
50
51
54
55
59
58
61
62
63
66
65
51
50
47
48
35
36
39
38
8
9
23
22
36
35
34
31
32
62
61
60
56
57
58
40
39
36
37
6
7
10
9
27
26
25
21
22
31
30
29
25
26
27
63
62
58
59
60
68
69
73
72
52
53
57
56
55
8
9
23
22
35
34
30
31
56
55
50
51
52
61
62
67
66
65
33
34
37
36
74
73
69
70
64
65
68
67
25
26
30
29
10
9
5
6
32
31
27
28
76
75
71
72
73
38
37
36
33
34
78
77
76
72
73
67
68
72
7136
37
41
40
69
70
71
75
74
33
34
38
37
24
23
8
9
36
35
30
31
32
33
32
28
29
7
8
9
22
21
28
29
30
33
32
56
57
61
60
72
71
67
68
29
30
35
34
32
33
37
36
71
70
66
6759
58
54
55
31
32
36
35
55
56
57 60
59
35
34
31
32
9
8
7
4
5
66
67
71
70
69
4
5
9
8
28
27
23
24
61
60
56
57
58 66
65
61
62
32
3128
29
77
76
72
73
74
42
41
40
37
38
1 2
6
5
4
43
42
37
38
38
37
36
32
3327
26
22
23
29
30
34
33
73
74
75
79
78
37
38
42
41
42
41
37
38
8
9
23
22
33
32
28
29
74
75
79
78
62
63
67
66
66
67
71
70
79
78
74
75
40
41
44
43
24
25
29
28
40
41
42
46
45
47
48
51
50
3
4
8
7
64
63
60
61
46
45
41
42
43 45
44
43
39
40
47
46
45
41
42
43
5
6
7
10
9
32
33 37
36
35
33
32
28
29
30
21
6
7
25
24
21
66
67
70
69
66
67
71
70
28
29
32
31
41
42
43
47
46
71
72
73
77
76
75
42
41
37
38
49
48
47
44
45
26
27
31
30
3
4
8
7
67
68
72
7155
56
60
59
77
76
73
74
58
59 63
62
53
52
48
49
30
29
26
27
33
34
39
38
37
62
63
67
66
22
23
26
25
47
46
45
41
42
35
34
30
31
34
33
29
30
53
52
48
49
50
76
75
71
72
38
39
43
42
79
78
74
75
64
65
69
68
8
9
24
23
39
40
45
44
43
29
30
33
32
61
60
56
57
33
34
38
37
29
30
34
33
32
79
78
73
74
75
73
74
78
77
76
70
69
65
6658
57
53
54
36
35
30
31
32
7
8
22
21
39
40
44
43
29
28
24
25
49
50
54
53
33
34
38
37
58
59
62
61
76
75
71
72
30
31
36
35
34
45
44
41
42
58
57
54
55
29
28
24
25
26
21
26
25
24
23
9
10
5
6
21
26
25
21
22
26
25
24
21
22
10
24
23
44
45
48
47
23
24
25
29
28
9
8
4
5
34
33
32
29
30
66
65
64
62
63
48
47
41
42
43
21
22
26
25
71
70
67
68
32
31
30
27
28
63
62
59
60
62
61
60
56
57
7
8
23
22
21
33
34
35
39
38
4
5
10
9
8
24
25 28
27
42
41
38
39
79
78
74
75
48
49 52
51
35
36 40
39
38
30
29
25
26 55
54
53
49
50
7
8
9
22
21
38
39
42
41
55
56
59
58
23
24
28
27
4
5
9
8
75
74
73
70
71
26
27
30
29
26
27
30
29
31
32
36
35
77
76
72
73
75
74
70
71
53
54
59
58
57
25
26
30
29
62
61
57
58
62
63
67
66
56
55
50
51
53
54
58
57
43
44 48
47
52
53
56
55
41
42
46
45
47
46
42
43
75
76
79
78
73
74
78
77
10
25
24
6
7
22
21
6
7
8
21
3
4
8
7
38
39
42
41
28
29
30
33
32
8
7
3
4
36
37
42
41
40
50
51 55
54
23
24
29
28
27
27
28
31
30
68
69
70
74
73
72
6
7
22
21
42
43
46
45
46
45
41
42
52
51
47
48
68
67
63
64
65
69
70
74
73
50
4945
46
64
63
58
59
39
38
34
35
70
71
72 75
74
9
10
24
23
34
3329
30
31
30
26
27
65
64
60
61
62
6157
58
57
56
53
54
73
74
78
77
61
62
66
65
9
8
7
3
4
5
28
27
23
24
41
42
45
44
79
78
75
76
28
29
30
34
33
48
47
43
44
29
30
35
34
53
54
58
57
37
38
43
42
54
53
49
50
72
73
74
77
76
66
67
71
70
44
45
49
48
61
62
66
65
34
35
40
39
38
73
72
68
69
53
54
58
57
63
62
58
59
40
41
45
44
78
77
74
75
21
6
7
10
24
23
10
6
7
7
8
21
21
6
7
62
63
64
68
67
66
51
52
53
56
55
61
60
59
56
57
50
49
45
46
47
69
70
73
72
64
65
69
68
50
49
48
44
45
43
44
45 49
48
33
34
35
38
37
8
9
22
21
65
66 69
68
50
51 55
54
53
47
46
42
43
33
34
38
37
57
58
61
60
30
29
24
25
40
41
45
44
43
59
58
57
54
55
32
31
27
28 34
33
29
30
71
70
67
68
47
48
52
51
26
25
21
22
6
7
10
58
59
63
62
70
71 75
74
39
40 43
42 64
65
66
70
69
67
68
72
71
70
22
23
28
27
48
49 52
51
44
43
40
41
70
69
65
66
43
44
48
47
71
72
76
75
30
29
25
26
27
32
31
28
29
79
78
7774
75
31
30
27
28
58
57
54
55
33
32
31
28
29
33
34
38
37
68
69
73
72
33
32
31
28
29
32
33
37
36
32
33
36
35
25
24
23
21
57
58
59
63
62
21
22
26
25
7
6
2
3
71
70
66
67
65
66
67
70
69
55
54
53
49
50
62
63
67
66
60
61
65
64
63
24
23
22
8
9
35
36 40
39
2
3
6
5
41
40
36
37
52
53
54 57
56
52
51
50
48
49
67
68
72
71
30
29
26
27
51
52
53
57
56
55
39
40 45
44
43
53
52
50
51
74
73
68
69
70
38
39
43
42
65
66
70
69
6
5
1 2
64
6360
61
35
36
37
41
40
39
74
75
78
77
5
6
10
9
32
33
34
37
36
7
6
1 2
66
67
70
6955
56
60
59
63
64
65
68
67
47
46
41
42
43
67
68
71
70
47
46
45
42
43
1 2
6
5
10
9
5
6
10
6
7
69
70
71
74
73
73
74
78
77
50
49
45
46
2
3
7
6
50
49
46
47
24
23
22
9
10
51
52
56
55
31
32
37
36
69
68
64
65
72
73
77
76
43
44
48
47
46
28
27
24
25
35
34
31
32
79
78
74
75
52
51
47
48
59
60 63
62
67
66
61
62
32
31
27
28
50
51
54
53
44
43
39
40
34
3328
29
77
76
72
73
44
45 49
48
35
34
33
29
30
31
23
24
28
27
8
7
3
4
40
39
35
36
37
68
69
74
73
72
60
59
55
56
25
24
21
22
43
44
47
46
41
42
43
47
46
30
31
35
34
59
58
55
56
50
49
45
46
71
72
73
76
75
66
65
62
63
68
69
73
72
77
76
72
73
22
21
7
8
9
48
49
53
529
10 24
23
39
38
34
35
21
22
23 26
25
38
37
36
33
34
25
26
30
29
3
4
7
6
22
21
7
8
9
51
50
45
46
3
4
8
7
8
9
23
22
21
22
23 26
25
10
9
8
4
5 50
49
46
47
35
34
30
31
70
71 74
73
72
53
5248
49
60
61
65
64
5
6
9
8
7
8
22
21
51
52
56
55
61
62
66
65
73
72
69
70
69
70 75
74
38
37
34
35
51
52
53
56
55
10
24
23
57
58
62
61
55
54
53
51
52
34
3329
30
31
30
29
26
27
75
74
70
71
58
57
53
54
31
32
36
35
34
43
42
38
39
61
62
66
65
27
26
25
21
22
35
36
39
38
29
28
24
25 72
71
68
69
70
69
65
66
56
57
61
60
67
68
72
71
43
42
38
39 61
60
57
58
67
66
65
62
63
58
59
60
63
62
61
60
59
56
57
58
54
53
50
51
65
66
70
69
35
34
33
30
31
67
68
69
72
71
44
45
49
48
79
78
74
75
76
46
45
41
42
6
5
1 2
33
32
31
28
29
39
40
44
43
59
58
54
55
37
36
35
31
32
7
8
21
30
31
32
36
35
44
45
49
48
47
69
68
65
66
3
4
9
8
7
24
25
29
28
7
6
5
2
3
4
21
22 27
26
25
77
76
73
74
75
43
42
41
38
39 60
59
55
56
55
56
57 60
59
61
60
57
58
4
5
8
7
35
36
40
39
38
21
22
26
25
34
35
40
39
38
37
34
35
36
37
41
40
39
73
74
78
77
8
7
3
4
69
68
67
63
64
65
59
58
55
56
30
31
32 35
34
36
35
31
32
40
41
46
45
44
38
39
42
41
24
23
22
8
9 35
34
30
31
71
72
76
75
9
10 24
23
48
49
52
51
29
30 33
32
41
40
39
35
36
26
27
33
32
8
7
3
4
27
26
22
23
51
52
56
55
46
45
41
42
33
34 38
37
7
6
5
1 2
3
30
31 36
35
28
27
26
23
24
25
63
62
58
5941
40
36
37
44
45
50
49
44
45
48
47
3
4
8
7
72
73 77
76
75
8
7
3
4 22
21
7
8 30
29
28
24
25
51
50
46
47
68
69 72
71
39
40 43
42
24
25 29
28
59
58
55
56 74
73
70
71
39
40
41 45
44
1kb
28
Detecting deletions with vg
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80
36
35
31
32
1 2
6
5
72
71
70
66
67
68
69
72
71
4
5
9
8
28
29
33
32
37
36
32
33
49
50
55
54
22
23
27
26
25
77
76
72
73
74
58
57
53
54
74
75
78
77
55
54
50
51
40
41
45
44
68
69
72
71
23
22
8
9
10
27
26
23
24
27
28
32
31
52
5146
47
72
73
77
76
79
78
74
75
40
41 46
4524
25
26
29
28
8
7
3
4
5
25
26
30
29
8
7
3
4
6
7
10
9
77
76
71
72
3
4
9
8
7
59
60
63
62
52
53
56
55
66
65
61
62
72
73
74
77
76
76
75
71
72
35
3430
31
51
50
46
47
22
21
7
8
55
54
50
51
41
42
46
45
7
6
2
3
4
35
3430
31
42
43
46
45
2
3
7
6
8
7
6
2
3
4
74
75
79
78
45
44
40
41
39
40
44
43
59
58
54
55 65
64
60
61
48
47
44
45
71
72
76
75
48
49
53
52
70
71
74
73
47
46
42
43
54
53
48
49
33
34
35
38
37
75
74
70
71
72
73
77
76
34
35
39
38
53
5247
48
63
64
69
68
67
72
73
77
76
67
6665
60
61
44
45
49
48
36
35
32
333
4
8
7
34
33
29
30
52
53
57
56
58
57
54
55
5
6
9
8
68
67
63
64
65
32
31
30
26
27
54
53
49
50
57
58
62
61
71
70
66
67
38
37
34
35
51
50
46
47
28
27
23
24
34
33
28
29
30
75
74
70
71
7269
68
64
65
22
21
8
9
56
55
51
52
42
43
48
47
41
40
37
38
72
71
67
68
47
46
42
43
44
8
9
10
24
23
67
66
61
62
63
73
72
68
69
65
66
70
69
60
61
65
64
41
42
43
46
45
66
65
61
62
78
77
73
74
42
43
44
47
46
43
44
49
48
8
7
4
5
60
61
65
64
51
52 56
55
63
62
58
59
24
25
29
28
53
52
47
48
49
42
41
37
38
31
30
29
25
26
27
62
61
57
58
35
34
30
31 48
47
44
45
54
5349
50
51
24
25
29
28
73
74
78
77
8
9
10
24
23
22
67
68
72
71
71
72
76
75
57
58 61
60
64
65
69
68
42
41
37
38
29
30
34
33
33
34
38
37
3
4
7
6
79
78
74
75
36
37
41
40
62
61
57
58
29
30
31
34
33
64
63
60
61
73
74
79
78
77
39
40
44
43
35
36
41
40
38
37
33
34
56
55
51
52
25
26
31
30
29
41
42
46
45
54
55
56
59
58
63
64
69
68
40
39
36
37
8
7
3
4
32
31
27
28
61
62
66
65
66
65
64
61
62
56
57
60
59
40
41
45
44
43
36
35
32
33
53
54
55
59
58
72
73
76
75
23
22
8
9
47
48
51
50
52
53
57
56
34
33
29
30
76
75
71
72
73
58
57
54
55
79
78
74
75
57
56
55
51
52
32
33
34
37
36
8
7
3
4
51
50
46
47
22
23
27
26
61
60
57
58
70
71
75
74
58
57
53
54 69
68
64
65
66
45
46
49
48
38
39
43
42
60
59
55
56 63
62
58
59
30
29
28
25
26
65
66
67
70
69
47
46
43
44
27
26
21
22
5
6
10
9
8
68
69
74
73
67
66
61
62
3
4
7
6
73
72
68
69
40
41
45
44
35
36
40
39
69
70
75
74
73
60
59
56
57
21
22
26
25
7
8
22
21
31
32
36
35
61
60
56
57
1 2
6
5
4
45
46
50
49
48
71
70
66
67
34
33
32
28
29
77
76
72
73
7431
30
25
26
71
72
75
74
64
63
58
59
30
29
28
25
26
76
75
74
70
71
37
36
32
33
34
67
66
62
63
32
33
37
36
35
53
5247
48
46
45
42
43
26
25
24
21
22
53
54
59
58
76
75
71
72
73
52
53
57
56
28
2722
23
46
45
41
42
43
44
48
47
73
72
68
69
23
24
29
28
31
32
36
35
59
60
61
65
64
24
23
22
9
10 22
21
7
8
33
32
28
29
30
59
60
63
62
63
64
65
68
67
62
61
58
59
21
22
27
26
25
63
64
68
67
75
74
70
71
34
33
29
30
25
26
27 31
30
23
22
8
9
78
77
72
73
74
27
28
33
32
52
51
47
48
47
48
52
51
58
59
62
61
53
52
51
48
49
39
40
44
43
48
49
54
53
54
53
49
50
34
35
39
38
46
47
52
51
42
43
47
46
52
53
58
57
64
63
60
61
52
51
47
48
33
34
38
37
33
32
29
30
72
71
66
67
36
37
41
40
29
30
33
32
30
31
32
35
34
28
27
23
24
26
27 31
30
74
73
69
70
55
56
57
60
59
36
37
38
41
40
3
4
7
6
38
37
33
34
35
10
9
5
6
72
73
77
76
70
69
64
65
53
5248
49
55
56
57
60
59
58
59
64
63
62
51
52
57
56
55
43
44
47
46
35
36 40
39
33
34
38
37
53
52
51
48
49
54
55
59
58
27
28
32
31
58
57
56
53
54
52
53
54
57
56
58
59
63
62
61
30
29
26
27
72
71
67
68
60
59
56
57
26
25
21
22
47
48
53
52
51
26
25
21
22
55
56
60
59
34
33
29
30
61
62
66
65
28
27
26
22
23
54
53
49
50
51
74
75
79
78
77
61
60
55
56
33
34
38
37
79
78
74
75
71
72
77
76
51
52
55
54
39
40
44
43
4
5
9
8
7
67
68
73
72
45
46
47 50
49
67
68
69 72
71
70
60
61
66
65
64
68
69 72
71
10
9
5
6
10
9
6 7
8
21
22
26
25
24
25 28
27
1 2
5
4
40
39
35
36
37
9
8
4
5
6
4
5
9
865
66
67
71
70
69
45
44
40
41
42
51
52
56
55
58
59
63
62
51
52
56
55
38
39
40
43
42
52
51
47
48
9
10
24
23
29
30
34
33
9
10
24
23
22
31
30
26
27
28
36
35
31
32
29
28
25
26
53
54
55
58
57
59
60
61
64
63
54
55
56
59
58
79
78
77
74
75
44
45
49
48
52
51
47
48
58
57
52
53
53
54
59
58
57
56
57
61
60
61
60
55
56
57
56
57
60
59
22
23
26
25
55
54
53
49
50
51
54
55
59
58
61
62
63
66
65
51
50
47
48
35
36
39
38
8
9
23
22
36
35
34
31
32
62
61
60
56
57
58
40
39
36
37
6
7
10
9
27
26
25
21
22
31
30
29
25
26
27
63
62
58
59
60
68
69
73
72
52
53
57
56
55
8
9
23
22
35
34
30
31
56
55
50
51
52
61
62
67
66
65
33
34
37
36
74
73
69
70
64
65
68
67
25
26
30
29
10
9
5
6
32
31
27
28
76
75
71
72
73
38
37
36
33
34
78
77
76
72
73
67
68
72
7136
37
41
40
69
70
71
75
74
33
34
38
37
24
23
8
9
36
35
30
31
32
33
32
28
29
7
8
9
22
21
28
29
30
33
32
56
57
61
60
72
71
67
68
29
30
35
34
32
33
37
36
71
70
66
6759
58
54
55
31
32
36
35
55
56
57 60
59
35
34
31
32
9
8
7
4
5
66
67
71
70
69
4
5
9
8
28
27
23
24
61
60
56
57
58 66
65
61
62
32
3128
29
77
76
72
73
74
42
41
40
37
38
1 2
6
5
4
43
42
37
38
38
37
36
32
3327
26
22
23
29
30
34
33
73
74
75
79
78
37
38
42
41
42
41
37
38
8
9
23
22
33
32
28
29
74
75
79
78
62
63
67
66
66
67
71
70
79
78
74
75
40
41
44
43
24
25
29
28
40
41
42
46
45
47
48
51
50
3
4
8
7
64
63
60
61
46
45
41
42
43 45
44
43
39
40
47
46
45
41
42
43
5
6
7
10
9
32
33 37
36
35
33
32
28
29
30
21
6
7
25
24
21
66
67
70
69
66
67
71
70
28
29
32
31
41
42
43
47
46
71
72
73
77
76
75
42
41
37
38
49
48
47
44
45
26
27
31
30
3
4
8
7
67
68
72
7155
56
60
59
77
76
73
74
58
59 63
62
53
52
48
49
30
29
26
27
33
34
39
38
37
62
63
67
66
22
23
26
25
47
46
45
41
42
35
34
30
31
34
33
29
30
53
52
48
49
50
76
75
71
72
38
39
43
42
79
78
74
75
64
65
69
68
8
9
24
23
39
40
45
44
43
29
30
33
32
61
60
56
57
33
34
38
37
29
30
34
33
32
79
78
73
74
75
73
74
78
77
76
70
69
65
6658
57
53
54
36
35
30
31
32
7
8
22
21
39
40
44
43
29
28
24
25
49
50
54
53
33
34
38
37
58
59
62
61
76
75
71
72
30
31
36
35
34
45
44
41
42
58
57
54
55
29
28
24
25
26
21
26
25
24
23
9
10
5
6
21
26
25
21
22
26
25
24
21
22
10
24
23
44
45
48
47
23
24
25
29
28
9
8
4
5
34
33
32
29
30
66
65
64
62
63
48
47
41
42
43
21
22
26
25
71
70
67
68
32
31
30
27
28
63
62
59
60
62
61
60
56
57
7
8
23
22
21
33
34
35
39
38
4
5
10
9
8
24
25 28
27
42
41
38
39
79
78
74
75
48
49 52
51
35
36 40
39
38
30
29
25
26 55
54
53
49
50
7
8
9
22
21
38
39
42
41
55
56
59
58
23
24
28
27
4
5
9
8
75
74
73
70
71
26
27
30
29
26
27
30
29
31
32
36
35
77
76
72
73
75
74
70
71
53
54
59
58
57
25
26
30
29
62
61
57
58
62
63
67
66
56
55
50
51
53
54
58
57
43
44 48
47
52
53
56
55
41
42
46
45
47
46
42
43
75
76
79
78
73
74
78
77
10
25
24
6
7
22
21
6
7
8
21
3
4
8
7
38
39
42
41
28
29
30
33
32
8
7
3
4
36
37
42
41
40
50
51 55
54
23
24
29
28
27
27
28
31
30
68
69
70
74
73
72
6
7
22
21
42
43
46
45
46
45
41
42
52
51
47
48
68
67
63
64
65
69
70
74
73
50
4945
46
64
63
58
59
39
38
34
35
70
71
72 75
74
9
10
24
23
34
3329
30
31
30
26
27
65
64
60
61
62
6157
58
57
56
53
54
73
74
78
77
61
62
66
65
9
8
7
3
4
5
28
27
23
24
41
42
45
44
79
78
75
76
28
29
30
34
33
48
47
43
44
29
30
35
34
53
54
58
57
37
38
43
42
54
53
49
50
72
73
74
77
76
66
67
71
70
44
45
49
48
61
62
66
65
34
35
40
39
38
73
72
68
69
53
54
58
57
63
62
58
59
40
41
45
44
78
77
74
75
21
6
7
10
24
23
10
6
7
7
8
21
21
6
7
62
63
64
68
67
66
51
52
53
56
55
61
60
59
56
57
50
49
45
46
47
69
70
73
72
64
65
69
68
50
49
48
44
45
43
44
45 49
48
33
34
35
38
37
8
9
22
21
65
66 69
68
50
51 55
54
53
47
46
42
43
33
34
38
37
57
58
61
60
30
29
24
25
40
41
45
44
43
59
58
57
54
55
32
31
27
28 34
33
29
30
71
70
67
68
47
48
52
51
26
25
21
22
6
7
10
58
59
63
62
70
71 75
74
39
40 43
42 64
65
66
70
69
67
68
72
71
70
22
23
28
27
48
49 52
51
44
43
40
41
70
69
65
66
43
44
48
47
71
72
76
75
30
29
25
26
27
32
31
28
29
79
78
7774
75
31
30
27
28
58
57
54
55
33
32
31
28
29
33
34
38
37
68
69
73
72
33
32
31
28
29
32
33
37
36
32
33
36
35
25
24
23
21
57
58
59
63
62
21
22
26
25
7
6
2
3
71
70
66
67
65
66
67
70
69
55
54
53
49
50
62
63
67
66
60
61
65
64
63
24
23
22
8
9
35
36 40
39
2
3
6
5
41
40
36
37
52
53
54 57
56
52
51
50
48
49
67
68
72
71
30
29
26
27
51
52
53
57
56
55
39
40 45
44
43
53
52
50
51
74
73
68
69
70
38
39
43
42
65
66
70
69
6
5
1 2
64
6360
61
35
36
37
41
40
39
74
75
78
77
5
6
10
9
32
33
34
37
36
7
6
1 2
66
67
70
6955
56
60
59
63
64
65
68
67
47
46
41
42
43
67
68
71
70
47
46
45
42
43
1 2
6
5
10
9
5
6
10
6
7
69
70
71
74
73
73
74
78
77
50
49
45
46
2
3
7
6
50
49
46
47
24
23
22
9
10
51
52
56
55
31
32
37
36
69
68
64
65
72
73
77
76
43
44
48
47
46
28
27
24
25
35
34
31
32
79
78
74
75
52
51
47
48
59
60 63
62
67
66
61
62
32
31
27
28
50
51
54
53
44
43
39
40
34
3328
29
77
76
72
73
44
45 49
48
35
34
33
29
30
31
23
24
28
27
8
7
3
4
40
39
35
36
37
68
69
74
73
72
60
59
55
56
25
24
21
22
43
44
47
46
41
42
43
47
46
30
31
35
34
59
58
55
56
50
49
45
46
71
72
73
76
75
66
65
62
63
68
69
73
72
77
76
72
73
22
21
7
8
9
48
49
53
529
10 24
23
39
38
34
35
21
22
23 26
25
38
37
36
33
34
25
26
30
29
3
4
7
6
22
21
7
8
9
51
50
45
46
3
4
8
7
8
9
23
22
21
22
23 26
25
10
9
8
4
5 50
49
46
47
35
34
30
31
70
71 74
73
72
53
5248
49
60
61
65
64
5
6
9
8
7
8
22
21
51
52
56
55
61
62
66
65
73
72
69
70
69
70 75
74
38
37
34
35
51
52
53
56
55
10
24
23
57
58
62
61
55
54
53
51
52
34
3329
30
31
30
29
26
27
75
74
70
71
58
57
53
54
31
32
36
35
34
43
42
38
39
61
62
66
65
27
26
25
21
22
35
36
39
38
29
28
24
25 72
71
68
69
70
69
65
66
56
57
61
60
67
68
72
71
43
42
38
39 61
60
57
58
67
66
65
62
63
58
59
60
63
62
61
60
59
56
57
58
54
53
50
51
65
66
70
69
35
34
33
30
31
67
68
69
72
71
44
45
49
48
79
78
74
75
76
46
45
41
42
6
5
1 2
33
32
31
28
29
39
40
44
43
59
58
54
55
37
36
35
31
32
7
8
21
30
31
32
36
35
44
45
49
48
47
69
68
65
66
3
4
9
8
7
24
25
29
28
7
6
5
2
3
4
21
22 27
26
25
77
76
73
74
75
43
42
41
38
39 60
59
55
56
55
56
57 60
59
61
60
57
58
4
5
8
7
35
36
40
39
38
21
22
26
25
34
35
40
39
38
37
34
35
36
37
41
40
39
73
74
78
77
8
7
3
4
69
68
67
63
64
65
59
58
55
56
30
31
32 35
34
36
35
31
32
40
41
46
45
44
38
39
42
41
24
23
22
8
9 35
34
30
31
71
72
76
75
9
10 24
23
48
49
52
51
29
30 33
32
41
40
39
35
36
26
27
33
32
8
7
3
4
27
26
22
23
51
52
56
55
46
45
41
42
33
34 38
37
7
6
5
1 2
3
30
31 36
35
28
27
26
23
24
25
63
62
58
5941
40
36
37
44
45
50
49
44
45
48
47
3
4
8
7
72
73 77
76
75
8
7
3
4 22
21
7
8 30
29
28
24
25
51
50
46
47
68
69 72
71
39
40 43
42
24
25 29
28
59
58
55
56 74
73
70
71
39
40
41 45
44
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80
36
35
31
32
1 2
6
5
72
71
70
66
67
68
69
72
71
4
5
9
8
28
29
33
32
37
36
32
33
49
50
55
54
22
23
27
26
25
77
76
72
73
74
58
57
53
54
74
75
78
77
55
54
50
51
40
41
45
44
68
69
72
71
23
22
8
9
10
27
26
23
24
27
28
32
31
52
5146
47
72
73
77
76
79
78
74
75
40
41 46
4524
25
26
29
28
8
7
3
4
5
25
26
30
29
8
7
3
4
6
7
10
9
77
76
71
72
3
4
9
8
7
59
60
63
62
52
53
56
55
66
65
61
62
72
73
74
77
76
76
75
71
72
35
3430
31
51
50
46
47
22
21
7
8
55
54
50
51
41
42
46
45
7
6
2
3
4
35
3430
31
42
43
46
45
2
3
7
6
8
7
6
2
3
4
74
75
79
78
45
44
40
41
39
40
44
43
59
58
54
55 65
64
60
61
48
47
44
45
71
72
76
75
48
49
53
52
70
71
74
73
47
46
42
43
54
53
48
49
33
34
35
38
37
75
74
70
71
72
73
77
76
34
35
39
38
53
5247
48
63
64
69
68
67
72
73
77
76
67
6665
60
61
44
45
49
48
36
35
32
333
4
8
7
34
33
29
30
52
53
57
56
58
57
54
55
5
6
9
8
68
67
63
64
65
32
31
30
26
27
54
53
49
50
57
58
62
61
71
70
66
67
38
37
34
35
51
50
46
47
28
27
23
24
34
33
28
29
30
75
74
70
71
7269
68
64
65
22
21
8
9
56
55
51
52
42
43
48
47
41
40
37
38
72
71
67
68
47
46
42
43
44
8
9
10
24
23
67
66
61
62
63
73
72
68
69
65
66
70
69
60
61
65
64
41
42
43
46
45
66
65
61
62
78
77
73
74
42
43
44
47
46
43
44
49
48
8
7
4
5
60
61
65
64
51
52 56
55
63
62
58
59
24
25
29
28
53
52
47
48
49
42
41
37
38
31
30
29
25
26
27
62
61
57
58
35
34
30
31 48
47
44
45
54
5349
50
51
24
25
29
28
73
74
78
77
8
9
10
24
23
22
67
68
72
71
71
72
76
75
57
58 61
60
64
65
69
68
42
41
37
38
29
30
34
33
33
34
38
37
3
4
7
6
79
78
74
75
36
37
41
40
62
61
57
58
29
30
31
34
33
64
63
60
61
73
74
79
78
77
39
40
44
43
35
36
41
40
38
37
33
34
56
55
51
52
25
26
31
30
29
41
42
46
45
54
55
56
59
58
63
64
69
68
40
39
36
37
8
7
3
4
32
31
27
28
61
62
66
65
66
65
64
61
62
56
57
60
59
40
41
45
44
43
36
35
32
33
53
54
55
59
58
72
73
76
75
23
22
8
9
47
48
51
50
52
53
57
56
34
33
29
30
76
75
71
72
73
58
57
54
55
79
78
74
75
57
56
55
51
52
32
33
34
37
36
8
7
3
4
51
50
46
47
22
23
27
26
61
60
57
58
70
71
75
74
58
57
53
54 69
68
64
65
66
45
46
49
48
38
39
43
42
60
59
55
56 63
62
58
59
30
29
28
25
26
65
66
67
70
69
47
46
43
44
27
26
21
22
5
6
10
9
8
68
69
74
73
67
66
61
62
3
4
7
6
73
72
68
69
40
41
45
44
35
36
40
39
69
70
75
74
73
60
59
56
57
21
22
26
25
7
8
22
21
31
32
36
35
61
60
56
57
1 2
6
5
4
45
46
50
49
48
71
70
66
67
34
33
32
28
29
77
76
72
73
7431
30
25
26
71
72
75
74
64
63
58
59
30
29
28
25
26
76
75
74
70
71
37
36
32
33
34
67
66
62
63
32
33
37
36
35
53
5247
48
46
45
42
43
26
25
24
21
22
53
54
59
58
76
75
71
72
73
52
53
57
56
28
2722
23
46
45
41
42
43
44
48
47
73
72
68
69
23
24
29
28
31
32
36
35
59
60
61
65
64
24
23
22
9
10 22
21
7
8
33
32
28
29
30
59
60
63
62
63
64
65
68
67
62
61
58
59
21
22
27
26
25
63
64
68
67
75
74
70
71
34
33
29
30
25
26
27 31
30
23
22
8
9
78
77
72
73
74
27
28
33
32
52
51
47
48
47
48
52
51
58
59
62
61
53
52
51
48
49
39
40
44
43
48
49
54
53
54
53
49
50
34
35
39
38
46
47
52
51
42
43
47
46
52
53
58
57
64
63
60
61
52
51
47
48
33
34
38
37
33
32
29
30
72
71
66
67
36
37
41
40
29
30
33
32
30
31
32
35
34
28
27
23
24
26
27 31
30
74
73
69
70
55
56
57
60
59
36
37
38
41
40
3
4
7
6
38
37
33
34
35
10
9
5
6
72
73
77
76
70
69
64
65
53
5248
49
55
56
57
60
59
58
59
64
63
62
51
52
57
56
55
43
44
47
46
35
36 40
39
33
34
38
37
53
52
51
48
49
54
55
59
58
27
28
32
31
58
57
56
53
54
52
53
54
57
56
58
59
63
62
61
30
29
26
27
72
71
67
68
60
59
56
57
26
25
21
22
47
48
53
52
51
26
25
21
22
55
56
60
59
34
33
29
30
61
62
66
65
28
27
26
22
23
54
53
49
50
51
74
75
79
78
77
61
60
55
56
33
34
38
37
79
78
74
75
71
72
77
76
51
52
55
54
39
40
44
43
4
5
9
8
7
67
68
73
72
45
46
47 50
49
67
68
69 72
71
70
60
61
66
65
64
68
69 72
71
10
9
5
6
10
9
6 7
8
21
22
26
25
24
25 28
27
1 2
5
4
40
39
35
36
37
9
8
4
5
6
4
5
9
865
66
67
71
70
69
45
44
40
41
42
51
52
56
55
58
59
63
62
51
52
56
55
38
39
40
43
42
52
51
47
48
9
10
24
23
29
30
34
33
9
10
24
23
22
31
30
26
27
28
36
35
31
32
29
28
25
26
53
54
55
58
57
59
60
61
64
63
54
55
56
59
58
79
78
77
74
75
44
45
49
48
52
51
47
48
58
57
52
53
53
54
59
58
57
56
57
61
60
61
60
55
56
57
56
57
60
59
22
23
26
25
55
54
53
49
50
51
54
55
59
58
61
62
63
66
65
51
50
47
48
35
36
39
38
8
9
23
22
36
35
34
31
32
62
61
60
56
57
58
40
39
36
37
6
7
10
9
27
26
25
21
22
31
30
29
25
26
27
63
62
58
59
60
68
69
73
72
52
53
57
56
55
8
9
23
22
35
34
30
31
56
55
50
51
52
61
62
67
66
65
33
34
37
36
74
73
69
70
64
65
68
67
25
26
30
29
10
9
5
6
32
31
27
28
76
75
71
72
73
38
37
36
33
34
78
77
76
72
73
67
68
72
7136
37
41
40
69
70
71
75
74
33
34
38
37
24
23
8
9
36
35
30
31
32
33
32
28
29
7
8
9
22
21
28
29
30
33
32
56
57
61
60
72
71
67
68
29
30
35
34
32
33
37
36
71
70
66
6759
58
54
55
31
32
36
35
55
56
57 60
59
35
34
31
32
9
8
7
4
5
66
67
71
70
69
4
5
9
8
28
27
23
24
61
60
56
57
58 66
65
61
62
32
3128
29
77
76
72
73
74
42
41
40
37
38
1 2
6
5
4
43
42
37
38
38
37
36
32
3327
26
22
23
29
30
34
33
73
74
75
79
78
37
38
42
41
42
41
37
38
8
9
23
22
33
32
28
29
74
75
79
78
62
63
67
66
66
67
71
70
79
78
74
75
40
41
44
43
24
25
29
28
40
41
42
46
45
47
48
51
50
3
4
8
7
64
63
60
61
46
45
41
42
43 45
44
43
39
40
47
46
45
41
42
43
5
6
7
10
9
32
33 37
36
35
33
32
28
29
30
21
6
7
25
24
21
66
67
70
69
66
67
71
70
28
29
32
31
41
42
43
47
46
71
72
73
77
76
75
42
41
37
38
49
48
47
44
45
26
27
31
30
3
4
8
7
67
68
72
7155
56
60
59
77
76
73
74
58
59 63
62
53
52
48
49
30
29
26
27
33
34
39
38
37
62
63
67
66
22
23
26
25
47
46
45
41
42
35
34
30
31
34
33
29
30
53
52
48
49
50
76
75
71
72
38
39
43
42
79
78
74
75
64
65
69
68
8
9
24
23
39
40
45
44
43
29
30
33
32
61
60
56
57
33
34
38
37
29
30
34
33
32
79
78
73
74
75
73
74
78
77
76
70
69
65
6658
57
53
54
36
35
30
31
32
7
8
22
21
39
40
44
43
29
28
24
25
49
50
54
53
33
34
38
37
58
59
62
61
76
75
71
72
30
31
36
35
34
45
44
41
42
58
57
54
55
29
28
24
25
26
21
26
25
24
23
9
10
5
6
21
26
25
21
22
26
25
24
21
22
10
24
23
44
45
48
47
23
24
25
29
28
9
8
4
5
34
33
32
29
30
66
65
64
62
63
48
47
41
42
43
21
22
26
25
71
70
67
68
32
31
30
27
28
63
62
59
60
62
61
60
56
57
7
8
23
22
21
33
34
35
39
38
4
5
10
9
8
24
25 28
27
42
41
38
39
79
78
74
75
48
49 52
51
35
36 40
39
38
30
29
25
26 55
54
53
49
50
7
8
9
22
21
38
39
42
41
55
56
59
58
23
24
28
27
4
5
9
8
75
74
73
70
71
26
27
30
29
26
27
30
29
31
32
36
35
77
76
72
73
75
74
70
71
53
54
59
58
57
25
26
30
29
62
61
57
58
62
63
67
66
56
55
50
51
53
54
58
57
43
44 48
47
52
53
56
55
41
42
46
45
47
46
42
43
75
76
79
78
73
74
78
77
10
25
24
6
7
22
21
6
7
8
21
3
4
8
7
38
39
42
41
28
29
30
33
32
8
7
3
4
36
37
42
41
40
50
51 55
54
23
24
29
28
27
27
28
31
30
68
69
70
74
73
72
6
7
22
21
42
43
46
45
46
45
41
42
52
51
47
48
68
67
63
64
65
69
70
74
73
50
4945
46
64
63
58
59
39
38
34
35
70
71
72 75
74
9
10
24
23
34
3329
30
31
30
26
27
65
64
60
61
62
6157
58
57
56
53
54
73
74
78
77
61
62
66
65
9
8
7
3
4
5
28
27
23
24
41
42
45
44
79
78
75
76
28
29
30
34
33
48
47
43
44
29
30
35
34
53
54
58
57
37
38
43
42
54
53
49
50
72
73
74
77
76
66
67
71
70
44
45
49
48
61
62
66
65
34
35
40
39
38
73
72
68
69
53
54
58
57
63
62
58
59
40
41
45
44
78
77
74
75
21
6
7
10
24
23
10
6
7
7
8
21
21
6
7
62
63
64
68
67
66
51
52
53
56
55
61
60
59
56
57
50
49
45
46
47
69
70
73
72
64
65
69
68
50
49
48
44
45
43
44
45 49
48
33
34
35
38
37
8
9
22
21
65
66 69
68
50
51 55
54
53
47
46
42
43
33
34
38
37
57
58
61
60
30
29
24
25
40
41
45
44
43
59
58
57
54
55
32
31
27
28 34
33
29
30
71
70
67
68
47
48
52
51
26
25
21
22
6
7
10
58
59
63
62
70
71 75
74
39
40 43
42 64
65
66
70
69
67
68
72
71
70
22
23
28
27
48
49 52
51
44
43
40
41
70
69
65
66
43
44
48
47
71
72
76
75
30
29
25
26
27
32
31
28
29
79
78
7774
75
31
30
27
28
58
57
54
55
33
32
31
28
29
33
34
38
37
68
69
73
72
33
32
31
28
29
32
33
37
36
32
33
36
35
25
24
23
21
57
58
59
63
62
21
22
26
25
7
6
2
3
71
70
66
67
65
66
67
70
69
55
54
53
49
50
62
63
67
66
60
61
65
64
63
24
23
22
8
9
35
36 40
39
2
3
6
5
41
40
36
37
52
53
54 57
56
52
51
50
48
49
67
68
72
71
30
29
26
27
51
52
53
57
56
55
39
40 45
44
43
53
52
50
51
74
73
68
69
70
38
39
43
42
65
66
70
69
6
5
1 2
64
6360
61
35
36
37
41
40
39
74
75
78
77
5
6
10
9
32
33
34
37
36
7
6
1 2
66
67
70
6955
56
60
59
63
64
65
68
67
47
46
41
42
43
67
68
71
70
47
46
45
42
43
1 2
6
5
10
9
5
6
10
6
7
69
70
71
74
73
73
74
78
77
50
49
45
46
2
3
7
6
50
49
46
47
24
23
22
9
10
51
52
56
55
31
32
37
36
69
68
64
65
72
73
77
76
43
44
48
47
46
28
27
24
25
35
34
31
32
79
78
74
75
52
51
47
48
59
60 63
62
67
66
61
62
32
31
27
28
50
51
54
53
44
43
39
40
34
3328
29
77
76
72
73
44
45 49
48
35
34
33
29
30
31
23
24
28
27
8
7
3
4
40
39
35
36
37
68
69
74
73
72
60
59
55
56
25
24
21
22
43
44
47
46
41
42
43
47
46
30
31
35
34
59
58
55
56
50
49
45
46
71
72
73
76
75
66
65
62
63
68
69
73
72
77
76
72
73
22
21
7
8
9
48
49
53
529
10 24
23
39
38
34
35
21
22
23 26
25
38
37
36
33
34
25
26
30
29
3
4
7
6
22
21
7
8
9
51
50
45
46
3
4
8
7
8
9
23
22
21
22
23 26
25
10
9
8
4
5 50
49
46
47
35
34
30
31
70
71 74
73
72
53
5248
49
60
61
65
64
5
6
9
8
7
8
22
21
51
52
56
55
61
62
66
65
73
72
69
70
69
70 75
74
38
37
34
35
51
52
53
56
55
10
24
23
57
58
62
61
55
54
53
51
52
34
3329
30
31
30
29
26
27
75
74
70
71
58
57
53
54
31
32
36
35
34
43
42
38
39
61
62
66
65
27
26
25
21
22
35
36
39
38
29
28
24
25 72
71
68
69
70
69
65
66
56
57
61
60
67
68
72
71
43
42
38
39 61
60
57
58
67
66
65
62
63
58
59
60
63
62
61
60
59
56
57
58
54
53
50
51
65
66
70
69
35
34
33
30
31
67
68
69
72
71
44
45
49
48
79
78
74
75
76
46
45
41
42
6
5
1 2
33
32
31
28
29
39
40
44
43
59
58
54
55
37
36
35
31
32
7
8
21
30
31
32
36
35
44
45
49
48
47
69
68
65
66
3
4
9
8
7
24
25
29
28
7
6
5
2
3
4
21
22 27
26
25
77
76
73
74
75
43
42
41
38
39 60
59
55
56
55
56
57 60
59
61
60
57
58
4
5
8
7
35
36
40
39
38
21
22
26
25
34
35
40
39
38
37
34
35
36
37
41
40
39
73
74
78
77
8
7
3
4
69
68
67
63
64
65
59
58
55
56
30
31
32 35
34
36
35
31
32
40
41
46
45
44
38
39
42
41
24
23
22
8
9 35
34
30
31
71
72
76
75
9
10 24
23
48
49
52
51
29
30 33
32
41
40
39
35
36
26
27
33
32
8
7
3
4
27
26
22
23
51
52
56
55
46
45
41
42
33
34 38
37
7
6
5
1 2
3
30
31 36
35
28
27
26
23
24
25
63
62
58
5941
40
36
37
44
45
50
49
44
45
48
47
3
4
8
7
72
73 77
76
75
8
7
3
4 22
21
7
8 30
29
28
24
25
51
50
46
47
68
69 72
71
39
40 43
42
24
25 29
28
59
58
55
56 74
73
70
71
39
40
41 45
44
Stacked soft clips
Long fragment lengthLow mapping depth
1kb
29
SV realignment / calling in vg
Arbitrary genome graph
30
SV realignment / calling in vg
1. Map our reads
31
SV realignment / calling in vg
1. Map our reads
2. Collect read signatures - soft clipped reads - discordant fragment length
32
SV realignment / calling in vg
1. Map our reads
2. Collect read signatures - soft clipped reads - discordant fragment length
3. Create candidate alleles based on signatures and add them to graph
33
SV realignment / calling in vg
1. Map our reads
2. Collect read signatures - soft clipped reads - discordant fragment length
3. Create candidate alleles based on signatures and add them to graph
4. Remap our reads, score the new alignments, and repeat if necessary
34
Early results - small variants
We submitted the first whole human genome analysis using variation graph reference methods as part of the PrecisionFDA resequencing competition. (May 2016.)
We did not win... but we did get a star for:
We're now approaching 99% F-score with vg call.
Erik Garrison, A toolkit for practical pangenomics, ECCB 201635
Progress - structural variants
Pipeline still under development: • Deletions in time for the holidays. • Inversions, insertions, and duplications to follow.
36
Opportunities for improvement
• Variant calling at all scales remains unsolved. • Haplotype phasing on the graph unexplored. • Currently no local assembly functionality.
• Exploring fermi-lite, but by no means finished. • Few downstream analysis options
• Apps can easily operate on vg structures, JSON, GFA, etc. • Additional user feedback / requests would be useful.
and many more...
37
Where do I see vg making a difference in my work?*
• Viral coinfection detection / classification • Multiclonal tumors • SV breakpoint refinement • Tumor / normal specific graphs
@erictdawson38
Acknowledgements
Many thanks to: Richard Durbin Stephen Chanock
Erik Garrison Adam Novak Benedict Paten Glenn Hickey Jordan Eizinga Jerven Bolleman Maciek Smuga Mike Lin
... and many others!
Thank y'all for listening!
@erictdawson39
Top Related