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Fig. 3. Under a stringent set of conditions, which can probably only be approximated in nature, a) population size grows over time to its carrying capacity, which is when the rates of births and deaths exist in a dynamic equilibrium and the population grows no further. b) As a population grows, its rate of change in size increases, but at a decelerating rate. When the population size is half as large as the carrying capacity, the population's rate of change is at its maximum and declines thereafter, reaching zero when the population reaches carrying capacity. In theory, such a population could be continuously harvested to one-half of its carrying capacity, thereby producing a perpetual, maximum yield without compromising the ability of the population to be replenished. This is the kernel of the maximum sustained yield theory.