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Abstract Rapid evolution of increased dispersal at the edge of a range expansion can accelerate invasions. However, populations expanding across environmental gradients often face challenging environments that reduce fitness of dispersing individuals. We used an eco‐evolutionary model to explore how environmental gradients influence dispersal evolution and, in turn, modulate the speed and predictability of invasion. Environmental gradients opposed evolution of increased dispersal during invasion, even leading to evolution of reduced dispersal along steeper gradients. Counterintuitively, reduced dispersal could allow for faster expansion by minimizing maladaptive gene flow and facilitating adaptation. While dispersal evolution across homogenous landscapes increased both the mean and variance of expansion speed, these increases were greatly dampened by environmental gradients. We illustrate our model's potential application to prediction and management of invasions by parameterizing it with data from a recent invertebrate range expansion. Overall, we find that environmental gradients strongly modulate the effect of dispersal evolution on invasion trajectories. 

Populations often vary in their evolutionary responses to a shared environmental perturbation. A key hurdle in building more predictive models of rapid evolution is understanding this variation—why do some populations and traits evolve while others do not? We combined long-term demographic and environmental data, estimates of quantitative genetic variance components, a resurrection experiment and individual-based evolutionary simulations to gain mechanistic insights into contrasting evolutionary responses to a severe multi-year drought. We examined five traits in two populations of a native California plant, Clarkia xantiana , at three time points over 7 years. Earlier flowering phenology evolved in only one of the two populations, though both populations experienced similar drought severity and demographic declines and were estimated to have considerable additive genetic variance for flowering phenology. Pairing demographic and experimental data with evolutionary simulations suggested that while seed banks in both populations likely constrained evolutionary responses, a stronger seed bank in the non-evolving population resulted in evolutionary stasis. Gene flow through time via germ banks may be an important, underappreciated control on rapid evolution in response to extreme environmental perturbations. 

Spatial patterns of adaptation provide important insights into agents of selection and expected responses of populations to climate change. Robust inference into the spatial scale of adaptation can be gained through reciprocal transplant experiments that combine multiple source populations and common gardens. Here, we examine the spatial scale of local adaptation of the North American annual plant common ragweed, Ambrosia artemisiifolia, using data from four common gardens with 22 source populations sampled from across a ∼1200 km latitudinal gradient within the native range. We found evidence of local adaptation at the northernmost common garden, but maladaptation at the two southern gardens, where more southern source populations outperformed local populations. Overall, the spatial scale of adaptation was large—at the three gardens where distance between source populations and gardens explained variation in fitness, it took an average of 820 km for fitness to decline to 50% of its predicted maximum. Taken together, these results suggest that climate change has already caused maladaptation, especially across the southern portion of the range, and may result in northward range contraction over time. 

What prevents populations of a species from adapting to the novel environments outside the species' geographic distribution? Previous models highlighted how gene flow across spatial environmental gradients determines species expansion versus extinction and the location of species range limits. However, space is only one of two axes of environmental variation—environments also vary in time, and we know temporal environmental variation has important consequences for population demography and evolution. We used analytical and individual-based evolutionary models to explore how temporal variation in environmental conditions influences the spread of populations across a spatial environmental gradient. We find that temporal variation greatly alters our predictions for range dynamics compared to temporally static environments. When temporal variance is equal across the landscape, the fate of species (expansion versus extinction) is determined by the interaction between the degree of temporal autocorrelation in environmental fluctuations and the steepness of the spatial environmental gradient. When the magnitude of temporal variance changes across the landscape, stable range limits form where this variance increases maladaptation sufficiently to prevent local persistence. These results illustrate the pivotal influence of temporal variation on the likelihood of populations colonizing novel habitats and the location of species range limits.