A sudden shift in environment or cellular context necessitates rapid adaptation. A dramatic example is genome duplication, which leads to polyploidy. In such situations, the waiting time for new mutations might be prohibitive; theoretical and empirical studies suggest that rapid adaptation will largely rely on standing variation already present in source populations. Here, we investigate the evolution of meiosis proteins in Arabidopsis arenosa, some of which were previously implicated in adaptation to polyploidy, and in a diploid, habitat. A striking and unexplained feature of prior results was the large number of amino acid changes in multiple interacting proteins, especially in the relatively young tetraploid. Here, we investigate whether selection on meiosis genes is found in other lineages, how the polyploid may have accumulated so many differences, and whether derived variants were selected from standing variation. We use a range-wide sample of 145 resequenced genomes of diploid and tetraploid A. arenosa, with new genome assemblies. We confirmed signals of positive selection in the polyploid and diploid lineages they were previously reported in and find additional meiosis genes with evidence of selection. We show that the polyploid lineage stands out both qualitatively and quantitatively. Compared with diploids, meiosis proteins in the polyploid have more amino acid changes and a higher proportion affecting more strongly conserved sites. We find evidence that in tetraploids, positive selection may have commonly acted on de novo mutations. Several tests provide hints that coevolution, and in some cases, multinucleotide mutations, might contribute to rapid accumulation of changes in meiotic proteins.