Project Summary The Wei Lab develops accurate and scalable inference methods in population genetics and statistical genetics. In the next few years, we will focus on understanding the evolution and genetic basis of complex traits. Large biobank datasets with hundreds of thousands of human genomes and tens of thousands of phenotypic measurements provide unprecedented opportunities to understand complex phenotypes. At the same time, these massive data sets demand more scalable and unbiased computational methods. My lab recently developed new algorithms and data structures to improve the scalability of standard computations involving genotype matrices, including the calculation of heritability components and linkage disequilibrium scores. Our RSHE method runs 10-100x faster than the current state-of-the-art method to allow heritability analysis on biobank-size whole-genome sequencing data. Further methodological improvements will require new conceptualizations of the genotype-phenotype relationships. Conventional statistical genetics uses genotype matrices directly, ignoring that genetic polymorphisms are organized by gene genealogy into an interpretable graph structure. Whole-genome genealogies can now be readily inferred using ancestral recombination graph (ARG) inference software. Studying genealogy-phenotype relationships on ARGs could pinpoint causal mutations, reduce multiple testing, promote algorithm efficiency, and integrate evolutionarily meaningful models. We are developing a scalable algorithm for ARG-wide association studies and will demonstrate its advantages even in the face of uncertainty in ARG reconstruction. We will also develop fine-mapping methods on ARGs to study homogeneous and admixed populations. Leveraging our RSHE code, we will implement a scalable method for estimating heritability from ARGs and will apply this new method to the UK biobank to understand why heritability estimated in unrelated individuals is lower than that from pedigree analyses. Building upon this, we will implement a novel model parameterization to study complex trait evolution using ARGs. Current polygenic adaptation papers all inevitably assume that GWAS significant SNPs can be treated as causal variants and that different polygenicity levels across phenotypes can be ignored. Our proposed method will provide the first rigorous framework that takes these factors into account. In summary, this proposal will develop methods to fully integrate ARGs into statistical genetics to better understand and conceptualize phenotype-genealogy relationships. It will provide more scalable computational tools for the field in response to the rapidly growing biomedical data and enable novel and more calibrated discoveries for human disease genetics and phenotypic evolution.