m Struct Inference of population m Struct Structure

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m. Struct: Inference of population m. Struct: Structure under structure in the presence of

m. Struct: Inference of population m. Struct: Structure under structure in the presence of genetic mutations admixing and allele mutations Suyash Shringarpure and Eric Xing Carnegie Mellon University

Significance 2

Significance 2

Genetic Population Structure • Structure (Pritchard et al, 2000) Ancestral proportion Africa Europe Mid-East

Genetic Population Structure • Structure (Pritchard et al, 2000) Ancestral proportion Africa Europe Mid-East Cent. /S. Asia East Asia Oceania Genetic structure of Human Populations (Rosenberg et al. 2002) 3

Generative model- Structure All the alleles observed at this locus α (for the dataset)

Generative model- Structure All the alleles observed at this locus α (for the dataset) 0. 8 0. 2 0. 3 0. 7

Modeling allele similarity • Microsatellite – Repeats of a small DNA unit, say Allele

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 • m. Struct – Structure under mutations

Hypothesis • Individual genomes in modern populations are a result of – Admixture of

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- m. Struct All the alleles observed at this locus α (for the

Generative model- m. Struct All the alleles observed at this locus α (for the dataset) 0. 8 0. 2 0. 8 0. 3 0. 2 0. 7 δ 1 δ 2

Mutation models • How to derive descendant alleles from ancestral alleles? • Distribution based

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,

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

Comparing population structure maps

Phylogenetic Trees from the Structural Maps 11

Phylogenetic Trees from the Structural Maps 11

Phylogenetic Trees from the Structural Maps m. Structure 12

Phylogenetic Trees from the Structural Maps m. Structure 12

HGDP SNP results

HGDP SNP results

Implications of Inconsistency • • Simplistic mutation model SNP mutations harder to discover from

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

Contour of Empirical Mutation

Conclusion • Generative model for population structure • Modeling mutations from ancestral alleles •

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 m. Struct

Graphical model representations Structure m. Struct

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