[Campbell Biology P.1249] Based on the logistic growth model, at what population size does a ... | Practice Question

Based on the logistic growth model, at what population size does a population typically experience its highest growth rate?

  • A: When the population size (N) is very small.
  • B: When N is exactly at the carrying capacity (K).
  • C: When N is at approximately half of the carrying capacity (K/2).
  • D: When N slightly exceeds K.

Explanation

In the logistic growth model, the population growth rate dN/dt = rN K-N /K is maximized when the product of N and K-N is maximized. This occurs when N is exactly half of the carrying capacity K/2 . At this point, there are enough individuals to reproduce, and still sufficient resources for growth, leading to the fastest rate of population increase.