PROJECT SUMMARY Genome-wide association studies (GWAS) in humans have revealed that heritable variation in most traits of interest arises from genetic differences in numerous genes. Yet our ability to use GWAS to learn about trait biology and disease etiology remains limited by the fact that we still not understand how what GWAS detect— the contribution of a gene to variation in a trait—relates to the importance of the gene to the biology of the trait. The high polygenicity revealed by GWAS has a second implication, supporting the notion that adaptive changes to traits in humans and in other species will often be “polygenic”, i.e., result from changes in allele frequencies at many small effect loci. How this mode of selection is expected to behave also remains poorly understood, however, impeding our ability to search for its footprints in genomic data. Moreover, despite the expectation that polygenic adaptation should be ubiquitous, there are notable examples of large effect adaptive differences (“sweeps”) between populations and species, raising the question of the conditions under which one mode of adaptation is favored over another. Here, we plan to address these gaps in our understanding as follows: Aim 1. When should ‘important genes’ stand out in GWAS? We will combine (i) our model from the last grant period, which describes from first principles how the contribution of a locus to heritability in a focal trait depends on its effects on that trait and on others subject to stabilizing selection, with (ii) a model describing how allelic effects on traits arise from their direct (e.g., cis) and indirect (e.g., trans) effects on the activity of genes in a network. In this way, we will relate the importance of a gene to a focal trait (and to others) with its contribution to heritability in the focal trait. The modeling will also generate predictions about how the heritability attributed to a gene relates to heritable variance in its expression levels and to its level of selective constraint; these predictions will be tested for >49 quantitative traits. Aim 2. How do phenotypes and alleles respond to changing selection pressures on complex traits? We will extend our modeling of the polygenic adaptation that occurs after a complex quantitative trait experiences a sudden shift in fitness optimum to consider (i) that alleles affecting a focal trait often have deleterious, pleiotropic effects on other traits, i.e., that selection occurs in a multi-dimensional trait space, and (ii) that selection pressures on complex traits may change more rapidly than it takes for genetic variation to equilibrate after a single shift, i.e., that there may be repeated shifts in that timeframe. Aim 3. When should we expect a highly polygenic adaptive response versus one involving few changes of large effect (e.g., sweeps)? By placing these different modes of adaptation within the same modeling framework, we will characterize how the polygenicity and predictability of t...