Rucete ✏ Campbell Biology In a Nutshell
Unit 8 ECOLOGY — Concept 53.3 The Logistic Model Describes How a Population Grows More Slowly as It Nears Its Carrying Capacity
In reality, populations rarely grow indefinitely. The logistic growth model incorporates environmental limits by slowing growth as the population approaches the habitat’s carrying capacity (K). It predicts an S-shaped growth curve that helps ecologists estimate sustainable population sizes and growth rates.
1. From Exponential to Logistic Growth
- Exponential growth: assumes unlimited resources and constant per capita rate (r)
- In nature, resources become limited as population size (N) increases
- Carrying capacity (K): maximum population the environment can sustain
- As N nears K, growth slows due to lower birth rates or higher death rates
2. The Logistic Growth Equation
- Modified equation: dN/dt = rN × (K − N)/K
- When N is small → growth is nearly exponential
- When N approaches K → growth slows and eventually stops
- Produces an S-shaped (sigmoid) curve
3. Growth Dynamics
- Fastest growth at N = K/2: many individuals + available resources
- Overshoot can occur if reproduction continues despite declining resources
- Example: Daphnia overshoots K, crashes, then stabilizes
4. Comparing Logistic and Exponential Models
- Exponential: constant r, growth accelerates with increasing N
- Logistic: growth slows as N nears K due to environmental limits
- Logistic model is useful for:
- Predicting population rebound
- Setting conservation thresholds
- Calculating sustainable harvest levels
5. Real-World Observations
- Some lab populations (e.g., Paramecium) follow logistic curves closely
- Others (e.g., Daphnia) overshoot or fluctuate due to feedback delays
- The model's assumptions (instant response, constant environment) are idealized but helpful
6. Conservation Applications
- Helps estimate minimum viable population sizes (e.g., white rhinos)
- Guides limits for avoiding extinction or overexploitation
- Supports wildlife management and habitat restoration planning
In a Nutshell
The logistic growth model improves on the exponential model by incorporating environmental limits. It shows how growth slows as resources become scarce and predicts a stable population size at carrying capacity. While not perfect, the logistic model remains a foundational tool in ecology and conservation biology.