Many species are expected to shift their geographic distribution as climates change, and yet climate change is only one of a suite of stressors that species face. Species that might, in theory, be able to shift rapidly enough to keep up with climate velocity (the rate and direction that isotherms move across the landscape) may not in actuality be able to do so when facing the cumulative impacts of multiple stressors. Despite empirical reports of substantial interactions between climate change

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... d other stressors, we often lack a mechanistic understanding of these interactions. Here, we developed and analyzed a spatial population dynamics model to explore the cumulative impacts of climate with another dominant stressor in the ocean and on land: harvest. We found that critical rates of climate velocity and harvest depend on the growth rate and dispersal kernel of the population, as well as the magnitude of the other stressor. This allowed us to identify conditions under which harvesting and climate velocity can together drive populations extinct even when neither stressor would do so in isolation. Except in these extreme cases, we also found that the interaction between the declines in biomass caused by climate velocity and harvest is approximately additive. Finally, we have shown that threshold harvest rules can be effective management tools to mitigate the interaction between the two stressors, while protected areas can either help or hinder,depending on how harvesters reallocate their effort. We also have parameterized the model for black rockfish (Sebastes melanops) to demonstrate the model's broad applicability.