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Whether species are capable of adapting to rapid shifts in climate raises considerable interest. Analyses based on niche models often assume niche conservatism and equilibrium with climate, implying that species will persist only in regions where future climatic conditions match their current conditions and that they will colonize these regions promptly. However, species may adapt to changing climate and persist where future climates differ from their current optimum. Here, we provide a first macroecological generalization to the approach of evolutionary rescue, by comparing the expected shift in mean temperature within the geographic range of 7193 species of amphibians worldwide, under alternative warming scenarios. Expected evolutionary change is expressed in units of standard deviations of mean temperature, per generation (Haldanes) and compared with theoretical models defining the maximum sustainable evolutionary rates (MSER) for each species. For the pessimistic emission scenario RCP8.5, shifts in mean temperature vary between near-zero and 6°C within the geographic ranges for most species, with a median equal to 3.75°C. The probability of evolutionary rescue in temperature peaks is higher than 0.05 for about 55% of the species and higher than 0.95 for only 12% of the species. Therefore, the predicted shift in mean temperature would be too extreme to deal with for almost half of the species. When evolutionary plasticity is incorporated, this scenario becomes more optimistic, with about 44% of the species being likely to shift their thermal peaks tracking future warming. These figures are not random in geographical space: evolutionary rescue would be unlikely in the tropics, especially in South America (Amazonia), parts of Africa, Indonesia, and in the Mediterranean region. Given the uncertainty in demographic and genetic parameters for species’ responses to climate change, we caution that it remains difficult to assess the realism of the macroecological generalization. In any case, it may be precautionary to assume that our results are not liberal, showing low probability of adaptation for most of the species and thus that the persistence of populations by evolutionary rescue may, in general, be unlikely in the long term.

Despite the widespread use of ecological niche models (ENMs) for predicting the responses of species to climate change, these models do not explicitly incorporate any population‐level mechanism. On the other hand, mechanistic models adding population processes (e.g. biotic interactions, dispersal and adaptive potential to abiotic conditions) are much more complex and difficult to parameterize, especially if the goal is to predict range shifts for many species simultaneously. In particular, the adaptive potential (based on genetic adaptations, phenotypic plasticity and behavioral adjustments for physiological responses) of local populations has been a less studied mechanism affecting species' responses to climatic change so far. Here, we discuss and apply an alternative macroecological framework to evaluate the potential role of evolutionary rescue under climate change based on ENMs. We begin by reviewing eco‐evolutionary models that evaluate the maximum sustainable evolutionary rate under a scenario of environmental change, showing how they can be used to understand the impact of temperature change on a Neotropical anuran species, the Schneider's toad Rhinella diptycha. Then we show how to evaluate spatial patterns of species' geographic range shift using such models, by estimating evolutionary rates at the trailing edge of species distribution estimated by ENMs and by recalculating the relative amount of total range loss under climate change. We show how different models can reduce the expected range loss predicted for the studied species by potential ecophysiological adaptations in some regions of the trailing edge predicted by ENMs. For general applications, we believe that parameters for large numbers of species and populations can be obtained from macroecological generalizations (e.g. allometric equations and ecogeographical rules), so our framework coupling ENMs with eco‐evolutionary models can be applied to achieve a more accurate picture of potential impacts from climate change and other threats to biodiversity. [ABSTRACT FROM AUTHOR]