We consider population dynamics on a network of habitats each of which has the same local dynamics, but with different carrying capacities. It is reasonable, and often assumed, that if the habitats are coupled by very fast migration the whole system will always look like one super-system with a large effective carrying capacity. This is called the "well-mixed" case.
This common belief is false. New global dynamics can emerge as a result of complete mixing. We give an example of emergent dynamics, and a general condition which must be satisfied for well-mixed systems to have the same dynamics as the constituent habitats.