1. The centre-periphery hypothesis (CPH) predicts a decrease in population performance from the centre of the species range towards the edge, hindering further species expansion. To overcome ecological limitation, local adaptation of peripheral populations is assumed necessary to extend niche space and thus to potentially facilitate species’ range expansion. However, adaptive changes do not necessarily correspond to current ecological marginality. Instead, population history may provide a fuller context for understanding patterns of local adaptation within the species range. Here, we test whether local adaptation to current conditions or population history explains current species distribution in an annual heterocarpic species, Atriplex tatarica, in Europe. 2. The ecological marginality and population history were estimated using species distribution modelling (SDM) and 13 microsatellite markers. To test for local adaptation, we evaluated the population performance of both currently central and currently peripheral populations by examining germination and growth traits under three temperature regimes which correspond to climates within, and also beyond, the species’ current range. In addition, we compared Bayesian estimates of population differentiation in neutral genetic markers and quantitative traits to test whether phenotypic differentiation evolved by local adaptation and/or by genetic drift. 3. We found population performances were not higher under temperature regimes corresponding to their own habitats, suggesting that patterns of local adaptation in A. tatarica do not correspond to current centre-periphery gradient. In contrast, population genetic structure indicated a strong influence of population history on variation in the germination phenotype. Species distribution modelling suggested a more cold-tolerant genetic lineage was located at the species’ range periphery during the last glacial period. Meanwhile, a less cold-tolerant lineage occurred in more suitable areas of the Balkan Peninsula and southeastern Europe. Thus, the strong adaptive divergence of evolutionary lineages may reflect a past spatial arrangement of populations, suggesting evolutionary processes were ongoing before the species expansion in the Holocene. 4. Synthesis. There is continuing debate concerning the speed of trait evolution during range expansion with climate change. Our results indicate that even though organisms expand rapidly, the accompanying evolutionary changes in phenotype may be much slower.