Evaluating the relative importance of neutral and adaptive processes as determinants of population differentiation across environments is a central theme of evolutionary biology. We applied the QST-FST comparison flanked by a direct test for local adaptation to infer the role of climate-driven selection and gene flow in population differentiation of an annual grass Avena sterilis in two distinct parts of the species range, edge and interior, which represent two globally different climates, desert and Mediterranean. In a multi-year reciprocal transplant experiment the plants of desert and Mediterranean origin demonstrated home advantage, and population differentiation in several phenotypic traits related to reproduction exceeded neutral predictions, as determined by comparisons of QST values with theoretical FST distributions. Thus variation in these traits likely resulted from local adaptation to desert and Mediterranean environments. The two separate common garden experiments conducted with different experimental design revealed that two population comparisons are likely to detect population differences in virtually every trait, but many of these differences reflect effects of local rather than regional environment. We detected a general reduction in neutral (SSR) genetic variation but not in adaptive quantitative trait variation in peripheral desert as compared with Mediterranean core populations. On the other hand, the molecular data indicated intensive gene flow from the Mediterranean core towards desert periphery. Although species range position in our study (edge vs. interior) was confounded with climate (desert vs. Mediterranean), the results suggest that the gene flow from the species core does not have negative consequences for either performance of the peripheral plants or their adaptive potential.