When can faster environmental change help a spread-out population? An Evidence Press briefing. Picture a population living in several patches of habitat. Individuals move between patches at fixed rates, while the growth rate in each patch rises and falls with the seasons. Ecologists have long asked whether speeding up those environmental swings always lowers the population's long-run growth. For symmetric movement the answer was known to be yes. But a 2025 example with three patches in a one-way loop showed that an intermediate speed can sometimes be best. This paper finds the exact dividing line. Faster periodic change can never raise long-run growth exactly when migration satisfies a condition called detailed balance, meaning there is no net circulation of movement around any loop of patches. Every two-patch system qualifies. If movement does circulate, then some gentle environment, varying just two patches a quarter of a cycle apart, makes an intermediate speed best. A simple certificate computed from the migration rates alone says which two patches to choose and in which order. For balanced migration the same holds when the environment switches at random: faster switching strictly lowers growth, unless switching cannot matter at all. This proves a 2025 conjecture by Monmarché, Schreiber and Strickler. The paper also treats environments that simply alternate between two states, and continuous habitats. The proofs are written out in full, and a script checks every exact constant. The gains from circulation are small for gentle environments, and the result says that a helpful environment exists, not how a particular one behaves. This is an anonymous, AI-assisted, unrefereed candidate, not peer reviewed or independently reproduced. Published on the third of November twenty twenty-six, its paper and evidence are linked from the Evidence Press release page. This briefing uses an AI-generated voice and is not additional scientific evidence.