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The simplest model for an empire’s growth curve is simple logistic (drawn-out S), leading to a steady maximum area. During this steady state, the share of coordinators in the population increases at the expense of producers. Collapse follows sooner or later, even in the absence of other inbuilt defects. Actual growth–decline curves at times deviate widely from the simple model. While the size of top empires has increased, empire duration has not over five millennia. They have tended to last for 180 years at half their maximum size. When including lesser but still major states, duration drops to 100 years. Slow growth tends to lead to more durable states. The median ratio of duration and rise times is 2.5 (as compared to five for individual rats and humans), but variation is huge.
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