pure parsimony

RECOMB SNPs Workshop/Jan 28, 2007

How Accurate is Pure Parsimony Haplotype Inferencing?

Sharlee ClimerDepartment of Computer Science and Engineering

Department of BiologyWashington University in Saint Louis

[email protected]

Joint work with Weixiong Zhang and Gerold Jaeger


Pure Parsimony

• Pure Parsimony Haplotype Inferencing (PPHI)– Find smallest set of unique haplotypes that can

resolve a set of genotypes

• Suggested by Earl Hubbell in 2000• Cast as an Integer Linear Program (IP) by

Dan Gusfield [CPM’03]

• Great research interest


Overview

• Biological forces

• Haplotypes with low frequency

• Define haplotype classes

• Data sets

• Characteristics of real data


Biological forces


Biological forces

• Relatively few unique haplotypes

• Subset of haplotypes with low frequency

• Problems for PPHI– Large number of optimal solutions– True biological solution might not be

parsimonious

• What are structural characteristics of optimal solutions?


Classes of haplotypes

• Set of possible haplotypes is exponentially large• Partition similar to Traveling Salesman Problem• Backbone haplotypes

– Appear in every optimal solution

• Fat haplotypes– Do not appear in any optimal solution

• Fluid haplotypes– Appear in some, but not all, optimal solutions


Backbone haplotypes

• Implicit backbones– All haplotypes that resolve unambiguous

genotypes

• Explicit backbones– Can identify by solving at most one IP for each

haplotype in solution that isn’t implicit backbone


Backbone haplotypes

h3 h7 h15 h27 h39 h50 h55 h79 h91

bb bb bb bb


Backbone graph


An optimal solution


Low frequency haplotype


Data sets

• 7 true haplotype data sets– Orzack et al.[Genetics, 2003]

• 80 genotypes

• 9 sites

• ApoE

– Andres et al. [Genet. Epi., in press]

• 6 sets of complete data

• 39 genotypes

• 5 to 47 sites

• KLK13 and KLK14


Data sets

• HapMap data [Nature 2003, 2005]

– Phase unknown– Random instance generator– 20 unique genotypes – 20 sites– Three populations

• CEU• YRI• JPT+CHB

– 22 chromosomes


Size of haplotype backbonePercentage of haplotypes that are backbones

0

0.2

0.4

0.6

0.8

1

1.2

BF

HG

BV

ceu2:

ceu5:

ceu8:

ceu11:

ceu14:

ceu17:

ceu20:

yri3:

yri6:

yri9:

yri12:

yri15:

yri18:

yri21:

jpt+

chb1:

jpt+

chb4:

jpt+

chb7:

jpt+

chb10:

jpt+

chb13:

jpt+

chb16:

jpt+

chb19:

jpt+

chb22:

Implicit backbones

hBBTotal


Number of fluid haplotypes in each solution

0

2

4

6

8

10

12

14

16

18

20

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75


Number of optimal solutions

1

10

100

1000

1 2 3 45 6 7 8910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061626364656667686970717273747576


Number of fluid haplotypes and solutions

0

2

4

6

8

10

12

14

16

18

20

12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061626364656667686970717273747576

Nu

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# fluid haplotypes # of solutions


Biological correctness

Data set

# gen. # sites # BB

hap.

#fluid hap.

# opt. sols.

Avg. distance to real

A 30 9 15 0 1 8

B 10 5 7 0 1 0

C 18 17 9 3 16 7.5

D 10 8 6 1 4 2.5

E 23 26 9 7 >1000 4.33

F 26 22 12 5 630 28.24

G 35 47 12 16 >1000 10.95



Data set Parsimony # of haplotypes

True # of haplotypes

A 15 17

B 7 7

C 12 12

D 7 7

E 16 16

F 17 18

G 28 32



• Accuracy of backbone haplotypes

• Two data sets (F and G) had errors – One parsimony backbone haplotype not in real

solution


Number of solutions vs. number of genotypes

0

2

4

6

8

10

12

14

16

18

nu

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f h

aplo

typ

es

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400

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nu

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f o

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# of haplotypes

# of solutions


Conclusions

• Biological forces tend to minimize cardinality, but also create low frequency haplotypes

• Low frequency in unique genotypes might not be low frequency in full set

• Low frequency haplotypes– Large number of optimal solutions

– True solution not necessarily parsimonious

– Combinatorial nature can lead to errors in backbones

• Parsimony combined with other biological clues

pure parsimony

Documents

possible haplotypes

low frequencyproblems

set of genotypessuggested

complete data39 genotypes

integer linear program

weixiong zhang

largepartition similar

classes of haplotypesset