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Ecology & Biodiversity
Population Dynamics
Exponential vs logistic growth, carrying capacity and the growth-rate curve.
PART 1
Topic Breakdown & Traps
The Engineering Principle
With unlimited resources a population grows exponentially (-curve). Real environments impose a carrying capacity (K), producing logistic (-shaped) growth: the rate rises, peaks at , then falls to zero at . The logistic model captures density-dependent limitation through the term.
The Core Formula Matrix
Exponential growth:
Logistic growth:
Maximum growth rate occurs at .
Intrinsic rate: (birth rate − death rate).
Logistic growth:
Maximum growth rate occurs at .
Intrinsic rate: (birth rate − death rate).
The ‘IIT Traps’
- ⚠Maximum growth rate is at K/2, not at K (where it is zero).
- ⚠**The factor** makes growth density-dependent.
- ⚠At N = K the population is stable (dN/dt = 0), not declining.
📚 Standard references
- Fundamentals of Ecology — Eugene P. Odum · Population Ecology
PART 2
Progressive 3-Tier Question Suite
Q1MEDIUM2 Marks · NAT
For logistic growth with carrying capacity K = 1000, the population size at which the growth rate dN/dt is maximum is _____.
Q2BASIC1 Mark · MCQ
The S-shaped curve characteristic of population growth with a finite carrying capacity is the:
Q3HARD2 Marks · MCQ
In the logistic equation, the term represents: