Most catchments plot close to the empirical Budyko curve, which allows for estimating the long-term mean annual evaporation and runoff. We found that a model that optimizes vegetation properties in response to changes in precipitation leads it to converge to a single curve. In contrast, models that assume no changes in vegetation start to deviate from a single curve. This implies that vegetation has a stabilizing role, bringing catchments back to equilibrium after changes in climate.