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NEETZoologyOrganisms and Populations

In a population exhibiting Verhulst-Pearl logistic growth, what is the outcome when the population density ( N ) exactly reaches the carrying capacity ( K ) of the habitat?

Options

  1. AThe growth rate ( dN dt ) becomes zero and the population reaches an asymptote.
  2. BThe growth rate ( dN dt ) becomes maximum and the population enters the log phase.
  3. CThe growth rate ( dN dt ) becomes negative and the population curve crashes.
  4. DThe growth rate ( dN dt ) equals r and the population enters the acceleration phase.

Correct answer

A. The growth rate ( dN dt ) becomes zero and the population reaches an asymptote.

Step-by-step solution

The Verhulst-Pearl logistic growth is described by the equation dN dt = rN ( K-N K ) . When the population density ( N ) reaches the carrying capacity ( K ), we substitute N = K into the equation. The environmental resistance term ( K-N K ) becomes ( K-K K ) = 0 . Multiplying by zero makes the overall growth rate dN dt = 0 . Biologically, this means the population size stabilizes and stops increasing, which corresponds to the asymptote phase of the sigmoid growth curve. Answer: The growth rate ( dN dt ) becomes zer

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