Question Explanation

Correct Answer: (B) The per capita rate of increase approaches zero as the population nears the carrying capacity.

Logistic Growth Equation

Logistic growth follows the equation:

dN/dt = rN(1 − N/K),

where N is population size, r is the intrinsic growth rate, and K is the carrying capacity.

Option Analysis

• (A) Incorrect: Individuals do not reproduce at full physiological capacity throughout;
  density-dependent factors like resource limits reduce reproduction as N approaches K.
• (B) Correct: The per capita growth rate
  (1/N)(dN/dt) = r(1 − N/K)
  drops to zero at N = K due to balancing births and deaths.
• (C) Incorrect: Near K, deaths can equal or exceed births, stabilizing population;
  births exceed deaths only when N < K.
• (D) Incorrect: The birth-to-death ratio (net growth) directly depends on K
  via density dependence in the model.

Introduction

The logistic growth model describes realistic population dynamics under resource limitations,
unlike the unlimited exponential growth model. In this CSIR NET-style question, option (B) highlights
how the per capita rate of increase approaches zero as the population nears
its carrying capacity (K), forming the well-known S-shaped curve central to ecology.

Core Equation and Interpretation

Population change follows the formula
dN/dt = rN(1 − N/K).
Early growth is exponential (N ≪ K), later slowing due to competition and eventually halting at
N = K. The per capita rate r(1 − N/K) confirms zero growth at equilibrium.

Growth Phases

1. Initial phase: Low density allows maximum r; births greatly exceed deaths.
2. Acceleration: Rapid increase continues with ample resources.
3. Deceleration: Density-dependent factors limit resources; reproduction slows near K.
4. Equilibrium: At N = K, births equal deaths and net growth equals zero.

CSIR NET Relevance

For Life Sciences aspirants, mastering the distinction between density-dependent logistic growth
and density-independent exponential growth is crucial. CSIR NET questions often test understanding
of the logistic equation and the S-shaped population curve.