## Estimating Heritability from Genetically Inferred Relationships: Treelets Probe Genetic Dark Matter

#### Kathryn RoederCarnegie-Mellon University

For more than a hundred years statisticians have been fascinated by the question of genetic inheritance. What fraction of the variability is due to nature versus nurture? i.e., what is the heritability? Recently, technological advances, coupled with large sample sets for genome-wide association studies have uncovered some factors underlying the genetic basis of traits and the predisposition to complex disease; however these findings account for only a small fraction of the heritability of these traits. This has inspired questions about the nature of the genetic dark matter'' that constitutes this missing heritability. Millions of dollars have been spent on genome-wide association studies of a myriad of diseases. Yet the findings have not measured up to expectation. Recently Yang et al. (2010) presented a novel analysis technique that they claim sheds light on the genetic dark matter. Their approach requires an estimate of a large noisy matrix of relationships. We use innovative smoothing techniques (treelets) to provide a much better estimate of this matrix, which greatly enhances the estimate of heritability. In the process we further illuminate questions about what we can learn about genetic dark matter using this approach. We illustrate our method with a large genome-wide association study and estimate the heritability of body mass index quite accurately. Finally, while our methods have been developed for this application, they have much broader potential application.

This work is joint with Andrew Crossett, Ann Lee, Lambertus Klei, and Bernie Devlin.

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