mStruct: Structure under mutations

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

2. Significance

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

4. Generative model- Structure All the alleles observed at this locus α(for the dataset) 0.8 0.2 0.8 0.2 0.3 0.7

5. 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

6. 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

7. Generative model- mStruct All the alleles observed at this locus α(for the dataset) δ1 0.8 0.2 0.8 0.2 δ2 0.3 0.7

8. Mutation models • How to derive descendant alleles from ancestral alleles? • Distribution based on the single step model • P(b|a) αδabs(b-a) ,δ < 1 • Computationally “easy” • NOT conventional mutation rate.

9. 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

10. Comparing population structure maps

11. Phylogenetic Trees from the Structural Maps

12. Phylogenetic Trees from the Structural Maps mStruct Structure

13. HGDP SNP results

14. 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

15. Contour of Empirical Mutation

16. 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.

17. Graphical model representations Structure mStruct