When a pattern of spatial or temporal environmental variation changes, it takes time for populations to reach their new stationary distributions, and during this time, the competitive landscape is also in flux. As a first step toward understanding community responses to altered variational regimes, I investigate the convergence of an annual–perennial plant system to its stationary spatiotemporal distribution following a change in environmental variation. I find that, to good approximation, convergence is the sum of two separate processes: global convergence, which governs changes in the total population, and local convergence, which governs population redistribution. While the slower process (global or local) eventually governs convergence, the faster process may initially dominate if it starts further from its stationary distribution, so that the populations converge quickly at first, then slow down. That is, when disturbances are spatially heterogeneous, a system may be initially more resilient under some initial conditions than others.