Impacts of climate change can differ substantially across species' geographic ranges, and impacts on a given population can be difficult to predict accurately. A commonly used approximation for the impacts of climate change on the population growth rate is the product of local changes in each climate variable (which may differ among populations) and the sensitivity (the derivative of the population growth rate with respect to that climate variable), summed across climate variables. However, this approximation may not be accurate for predicting changes in population growth rate across geographic ranges, because the sensitivities to climate variables or the rate of climate change may differ among populations. In addition, while this approximation assumes a linear response of population growth rate to climate, population growth rate is typically a nonlinear function of climate variables. Here, we use climate-driven integral projection models combined with projections of future climate to predict changes in population growth rate from 2008 to 2099 for an uncommon alpine plant species, Douglasia alaskana, in a rapidly warming location, southcentral Alaska USA. We dissect the causes of among-population variation in climate change impacts, including magnitude of climate change in each population and nonlinearities in population response to climate change. We show that much of the variation in climate change impacts across D. alaskana's range arises from nonlinearities in population response to climate. Our results highlight the critical role of nonlinear responses to climate change impacts, suggesting that current responses to increases in temperature or changes in precipitation may not continue indefinitely under continued changes in climate. Further, our results suggest the degree of nonlinearity in climate responses and the shape of responses (e.g., convex or concave) can differ substantially across populations, such that populations may differ dramatically in responses to future climate even when their current responses are quite similar.