On the Complete Life Career of Populations in Environments with a Finite Carrying Capacity

If a general branching process evolves in a habitat with a finite carrying capacity, i. e. a number such that reproduction turns subcritical as soon as population size exceeds that number, then the population may either die out quickly, or else grow up to arround the carrying capacity, where it will linger for a long time, until it starts decaying exponentially to extinction