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A population (X) in an ecosystem follows logistic growth curve. If the carrying capacity of the system is K, the growth realisation factor is

  • A.\(\dfrac{K - X}{X}\)
  • B.\(\dfrac{K - X}{K}\)
  • C.\(\dfrac{K - X}{K^{2}}\)
  • D.\((K - X)\)

Answer: B

The growth realisation factor is (K - X)/K.

In the logistic equation the growth rate is the product of the intrinsic rate, the population size and the fraction of the carrying capacity that is still unused.

\[ \dfrac{dX}{dt} = rX\left(\dfrac{K - X}{K}\right) \]

That bracketed fraction is the realisation factor, which falls to zero when X reaches K. The option with X in the denominator would grow without limit as X falls, K squared is not part of the equation, and (K - X) alone lacks the scaling by K.

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