In logistic growth, if the population size N exceeds the carrying capacity K, what happens?

• A. Growth rate remains constant regardless of N.
• B. The carrying capacity K has no effect on growth.
• C. If N is greater than K, the population will shrink.
• D. The population will grow without bound.

Answer: (C)

Carrying capacity and crowding effects shape how growth responds to population size. In logistic growth, the growth rate slows as the population nears K. If the population size exceeds K, resources are limited and the balance shifts so that deaths outpace births, making the per capita growth rate negative. In mathematical terms, dN/dt = rN(1 − N/K) becomes negative when N > K, so the total population declines toward K. So the population will shrink when N is greater than K. The other statements ignore this density-dependent response: growth isn’t constant, K does affect growth, and the population doesn’t grow without bound.