Comparing genetic diversity, genetic differentiation, and performance between native and nonnative populations has advanced our knowledge of contemporary evolution and its ecological consequences. However, such between‐range comparisons can be complicated by high among‐population variation within native and nonnative ranges. For example, native vs. nonnative comparisons between small and non‐representative subsets of populations for species with very large distributions have the potential to mislead because they may not sufficiently account for within‐range adaptation to climatic conditions, and demographic history that may lead to non‐adaptive evolution. We used the cosmopolitan weed Conyza canadensis to study the interplay of adaptive and demographic processes across, to our knowledge, the broadest climatic gradient yet investigated in this context. To examine the distribution of genetic diversity, we genotyped 26 native and 26 nonnative populations at 12 microsatellite loci. Furthermore, we recorded performance traits for 12 native and 13 nonnative populations in the field and in the common garden. To analyze how performance was related to range and/or climate, we fit pedigree mixed‐effects models. These models weighed the population random effect for co‐ancestry to account for the influence of demographic history on phenotypic among‐population differentiation. Genetic diversity was very low, selfing rates were very high, and both were comparable between native and nonnative ranges. Nonnative populations out‐performed native populations in the field. However, our most salient result was that both neutral genetic differentiation and common garden performance were far more correlated with the climatic conditions from which populations originated than native vs. nonnative range affiliation. Including co‐ancestry of our populations in our models greatly increased explained variance and our ability to detect significant main effects for among‐population variation in performance. High propagule pressure and high selfing rates, in concert with the ability to adapt rapidly to climatic gradients, may have facilitated the global success of this weed. Neither native nor nonnative populations were homogeneous groups but responded comparably to similar environments in each range. We suggest that studies of contemporary evolution should consider widely distributed and genotyped populations to disentangle native vs. nonnative range effects from varying adaptive processes within ranges and from potentially confounding effects of demographic history.