In the logistic differential equation dP/dt = kP(1 - P/L), the carrying capacity is:

In the logistic differential equation dP/dt = kP(1 - P/L), the carrying capacity is:

• A. The initial population
• B. The maximum sustainable population
• C. The current population
• D. The carrying capacity has no biological meaning

Answer: (B)

In this logistic model, the parameter L sets the scale for how large the population can get. The carrying capacity is the population size at which growth stops because resources limit further increase. When the population P reaches L, the growth rate dP/dt becomes zero, so the population remains steady. If P is below L, the term (1 − P/L) is positive and the population grows toward L; if P is above L, it becomes negative and the population decreases toward L. So L is the maximum sustainable population given the available resources. It’s not the initial population, nor the current population at a given moment, and it has a clear biological meaning as the long-term limit.

In this logistic model, the parameter L sets the scale for how large the population can get. The carrying capacity is the population size at which growth stops because resources limit further increase. When the population P reaches L, the growth rate dP/dt becomes zero, so the population remains steady. If P is below L, the term (1 − P/L) is positive and the population grows toward L; if P is above L, it becomes negative and the population decreases toward L. So L is the maximum sustainable population given the available resources. It’s not the initial population, nor the current population at a given moment, and it has a clear biological meaning as the long-term limit.