Rucete ✏ Campbell Biology In a Nutshell
Unit 8 ECOLOGY — Concept 53.2 The Exponential Model Describes Population Growth in an Idealized, Unlimited Environment
In an ideal environment with unlimited resources, populations grow rapidly and continuously. The exponential growth model illustrates how a constant per capita growth rate leads to a J-shaped population curve, useful for understanding population potential before limiting factors set in.
1. Change in Population Size
- Births (B) and Deaths (D) determine population growth
- Formula: ΔN/Δt = B − D
- Let R = B − D: net change in individuals
- Per capita growth: ΔN/Δt = rΔt × N, where rΔt = per capita rate of change
2. Instantaneous Growth Rate
- For very short intervals, use calculus: dN/dt = r × N
- r = intrinsic rate of increase (per capita rate at an instant)
- As N increases, more individuals are added even if r stays the same
3. Exponential Growth
- Occurs when:
- Resources are abundant
- Individuals reproduce at max capacity
- Creates a J-shaped curve
- Growth accelerates as population size (N) increases
4. Example: Bacteria and Elephants
- A bacterium doubling every 20 minutes could cover Earth in 36 hours (theoretically)
- In nature, exponential growth is temporary:
- Colonizing new habitats
- Rebounding from population crashes
- Elephants in Kruger National Park grew exponentially for decades post-hunting ban
- Eventually managed by birth control and relocation
5. Population Growth Curve Comparison
- Different r-values produce different curves:
- r = 0.5 → slower growth
- r = 1.0 → faster, steeper growth
- Larger N always adds more individuals per unit time, even if r is constant
In a Nutshell
The exponential growth model shows how populations can increase rapidly when resources are unlimited. Growth depends on both the intrinsic rate of increase and the current population size. While useful for understanding biological potential, exponential growth rarely lasts long in natural systems due to environmental constraints.