Long Answer
Medium difficulty • Structured explanation
Question 1
Long FormCompare exponential and logistic population growth models with respect to resource conditions, mathematical equations, and the shape of growth curves. Why is logistic growth biologically more significant?
- Exponential growth occurs under unlimited resource conditions; the equation is dN/dt = rN, and the curve is J-shaped, showing continuous unrestricted increase.
- Logistic growth occurs when resources are limiting; described by the Verhulst-Pearl equation dN/dt = rN[(K–N)/K], the curve is sigmoid (S-shaped), levelling off at carrying capacity K.
- In logistic growth, the population passes through a lag phase, then acceleration and deceleration phases, before reaching an asymptote at K.
- Since resources in nature are finite and become limiting sooner or later, logistic growth is considered a more realistic and biologically significant model.
- The intrinsic rate of natural increase (r) is common to both models and measures the population's inherent growth potential, but in logistic growth it is modified by the factor [(K–N)/K] reflecting resource limitation.