The overall population growth rate and the per capita growth rate decreases as the size of the population increases because of the carrying capacity, K, of the species. It is the maximum number of individuals of a species that an environment can sustain for an indefinite period of time if all the necessary resources are available. When a population reaches its carrying capacity, the growth rates starts to decrease as the new individuals will not be supported in the environment. Moreover, the death rate increases that leads to a decrease in the per capita growth rate.
If the resources in the environment are limited, the per capita share of the resources will decrease as the population increases in size. Moreover, competition might be introduced within the population.
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