Stressors such as antibiotics, herbicides and pollutants are becoming increasingly common in the environment. The effects of stressors on populations are typically studied in homogeneous, non-spatial settings. However, most populations in nature are spatially distributed over environmentally heterogeneous landscapes with spatially-restricted dispersal. Little is known about the effects of stressors in these more realistic settings. Here, we combine laboratory experiments with novel mathematical theory to rigorously investigate how a stressor’s physiological effect and spatial distribution...