Here x is the size of the population at a given time, r is the inherent per-capita growth rate, and K is the carrying capacity. However, as the population reaches its maximum (the carrying capacity), ...Here x is the size of the population at a given time, r is the inherent per-capita growth rate, and K is the carrying capacity. However, as the population reaches its maximum (the carrying capacity), intraspecific competition becomes fiercer and the per capita growth rate slows until the population reaches a stable size. At the carrying capacity, the rate of change of population density is zero because the population is as large as possible based on the resources available.
