Ploidy-variable species allow direct inference of the effects of chromosome copy number on fundamental evolutionary processes. While an abundance of theoretical work suggests polyploidy should leave distinct population genomic signatures, empirical data remains sparse. We sequenced ~300 individuals from 39 populations of Arabidopsis arenosa, a naturally diploid-autotetraploid species. We find that the impacts of polyploidy on population genomic processes are subtle yet pervasive, such as reduced efficiency of purifying selection, differences in linked selection and rampant gene flow from diploids. Initial masking of deleterious mutations, faster rates of nucleotide substitution and interploidy introgression likely conspire to shape the evolutionary potential of polyploids.