Carrying capacity (K) is the maximum population size that an environment can sustain indefinitely given available resources like food, water, habitat, and other necessities. When a population exceeds K, resource depletion causes increased death rates and decreased birth rates, pushing the population back down. Below K, abundant resources allow rapid growth. The logistic growth model describes this density-dependent regulation mathematically.

The logistic equation dN/dt = rN(1 - N/K) captures this dynamic: when N (population) is small relative to K, the term (1-N/K) ≈ 1, giving approximately exponential growth. As N approaches K, (1-N/K) approaches zero, slowing growth. At N = K, growth stops entirely (equilibrium). The fastest growth occurs at N = K/2, where the product N(1-N/K) is maximized—this is why fisheries target harvest at K/2 for maximum sustainable yield.

Carrying capacity varies with environmental conditions and isn't fixed. Droughts reduce K, abundant rainfall increases it. Human activities dramatically alter K—deforestation reduces wildlife carrying capacity, while agriculture increases human carrying capacity. Exceeding K causes overshoot and crash cycles seen in many populations: rapid growth depletes resources, population crashes, resources recover, cycle repeats. Understanding K is critical for conservation, wildlife management, agriculture, and predicting human population dynamics.