In population ecology, what mathematical equation represents logistic population growth where represents carrying capacity?
Answer and explanation
Correct answer: C.
- Step 1: In finite natural habitats, population expansion is regulated by environmental resistance and resource scarcity.
- Step 2: The Verhulst-Pearl logistic growth differential equation models this density-dependent constraint: , where is the intrinsic rate of natural increase, is population size, and represents habitat carrying capacity.
- Step 3: As approaches , the term tends toward zero, generating a characteristic sigmoid (S-shaped) saturation curve.
Answer
.
Why not the others: represents unlimited exponential (J-shaped) population growth where resources are infinite; inverts the carrying capacity numerator and denominator, producing negative growth below carrying capacity; represents an arbitrary non-ecological fraction that decreases with population size without saturation kinetics.
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