mStruct: Structure under mutations

Suyash Shringarpure and Eric XingCarnegie Mellon University

mStruct: Inference of population structure in the presence of genetic

admixing and allele mutations

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Significance

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Genetic Population Structure

• Structure (Pritchard et al, 2000)

Genetic structure of Human Populations (Rosenberg et al. 2002)

Africa Europe Mid-East Cent./S. Asia East Asia Oceania

Ancestral proportion

Generative model- Structure

0.3 0.7

0.8 0.2

α (for the dataset)

0.8 0.2

All the alleles observed at this locus

Modeling allele similarity

• Microsatellite– Repeats of a small DNA unit, say

Allele - 2

Allele - 9

Allele - 10

•Allele 9 is much more similar to allele 10 than allele 2.•Allele 10 might be a mutation of allele 9.•Mathematically encode the idea in the model•mStruct – Structure under mutations

Hypothesis

• Individual genomes in modern populations are a result of– Admixture of ancestral populations.– Mutations from ancestral alleles.

• Ancestral populations have fewer alleles– (Mostly) True for microsatellites

Generative model- mStruct

0.3 0.7

0.8 0.2

α (for the dataset)

0.8 0.2

All the alleles observed at this locus

δ1

δ2

Mutation models

• How to derive descendant alleles from ancestral alleles?

• Distribution based on the single step model

• P(b|a) α δabs(b-a) , δ < 1• Computationally “easy”• NOT conventional mutation rate.

Finding ancestral alleles

• Fit mixtures of mutation distributions

• Try using 1,2,3….. ancestral alleles

• Use information theory to decide how many ancestral alleles are appropriate

Histogram of observed alleles

Comparing population structure maps

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Phylogenetic Trees from the Structural Maps

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Phylogenetic Trees from the Structural Maps

mStruct Structure

HGDP SNP results

Implications of Inconsistency

• Simplistic mutation model• SNP mutations harder to discover from data• The model reduces to Structure• Fundamental difference– Different markers treated differently

• Structure’s treatment of alleles is almost categorical

Contour of Empirical Mutation

Conclusion

• Generative model for population structure• Modeling mutations from ancestral alleles• Gives mutational information apart from

population structure.• (in press) Genetics• Online version up now.

Graphical model representations

Structure mStruct