If climate change outpaces the rate of adaptive evolution within a site, populations previously well adapted to local conditions may decline or disappear, and banked seeds from those populations will be unsuitable for restoring them. However, if such adaptational lag has occurred, immigrants from historically warmer climates will outperform natives and may provide genetic potential for evolutionary rescue. We tested for lagging adaptation to warming climate using banked seeds of the annual weed Arabidopsis thaliana in common garden experiments in four sites across the species' native European range: Valencia, Spain; Norwich, United Kingdom; Halle, Germany; and Oulu, Finland. Genotypes originating from geographic regions near the planting site had high relative fitness in each site, direct evidence for broad-scale geographic adaptation in this model species. However, genotypes originating in sites historically warmer than the planting site had higher average relative fitness than local genotypes in every site, especially at the northern range limit in Finland. This result suggests that local adaptive optima have shifted rapidly with recent warming across the species' native range. Climatic optima also differed among seasonal germination cohorts within the Norwich site, suggesting that populations occurring where summer germination is common may have greater evolutionary potential to persist under future warming. If adaptational lag has occurred over just a few decades in banked seeds of an annual species, it may be an important consideration for managing longer-lived species, as well as for attempts to conserve threatened populations through ex situ preservation.cliimate adaptation | adaptation lag | local adaptation | provenance test R apid climate change has already caused species range shifts and local extinctions (1) and is predicted to have greater future impacts (2). As the suitable climate space for a species shifts poleward (3), populations previously well adapted to the historical climate in a particular region may experience strong selection to adapt to rapidly warming local temperatures (4-10). Rapid evolutionary response to climate change has already been observed (11, 12), but it remains unclear whether evolutionary response can keep pace with rapidly changing local adaptive optima (6,8,(13)(14)(15). If local adaptation is slower than the rate of climate change, the average fitness of local populations may decline over time (7,14,16,17), possibly resulting in local extinctions and range collapse at the warmer margin. Where such lag exists, we expect that local seeds banked for conservation may no longer be well adapted to their sites of origin (18). However, such adaptational lag may be mitigated by migration or gene flow from populations in historically warmer sites if those populations are better adapted to current conditions in a site than local populations (8,13,19,20). Although adaptational lag has been predicted (4-6, 8, 14, 15, 19, 21, 22), the distinctive signature of mismatch between local p...