A NOVEL SPECTRAL METHOD FOR INFERRING GENERAL SELECTION FROM TIME SERIES GENETIC DATA By Matthias Steinrücken∗,†,‡

Recently there has been growing interest in using time series ge-netic variation data, either from experimental evolution studies or an-cient DNA samples, to make inference about evolutionary processes. While such temporal data can facilitate identifying genomic regions under selective pressure and estimating associated fitness parameters, it is a challenging problem to compute the likelihood of the underlying selection model given DNA samples obtained at several time points. Here, we develop an efficient algorithm to tackle this challenge. The key methodological advance in our work is the development of a novel spectral method to analytically and efficiently integrate over all tra-jectories of the population allele frequency between consecutive time points. This advance circumvents the limitations of existing methods which require fine-tuning the discretization of the allele frequency space to approximate certain integrals using numerical schemes. Fur-thermore, our method is flexible enough to handle general diploid models of selection where the heterozygote and homozygote fitness parameters can take any values, while previous methods focused on only a few restricted models of selection. We demonstrate the utility of our method on simulated data and apply the method to analyze time series ancient DNA data from genetic loci (ASIP and MC1R) associated with coat coloration in horses. In contrast to the conclu-sions of previous studies which considered only a few special selection schemes, our exploration of the full fitness parameter space reveals that balancing selection (in the form of heterozygote advantage) may have been acting on these loci. 1. Introduction. Natura