Environmental Science / Unit 4: Populations
4.2 Exponential and Logistic Growth
Notes
Populations can grow in two main patterns.
- Exponential growth produces a J-shaped curve. The population grows by a constant percentage, so it speeds up. It occurs when resources are unlimited.
- Logistic growth produces an S-shaped curve. Growth slows as the population nears its carrying capacity (K).
- Carrying capacity is the maximum population size an environment can support sustainably.
- If a population overshoots K, it may crash (a dieback).
- The growth rate as a percent: $\displaystyle r = \frac{\text{births} - \text{deaths}}{\text{population}} \times 100$.
- Rule of 70: doubling time (years) $\displaystyle = \frac{70}{\text{growth rate in percent}}$.
- Example: a population growing 2% per year doubles in $70 \div 2 = 35$ years.
Practice
A population grows at 3.5% per year. Using the rule of 70, about how long does it take to double?
$70 \div 3.5 = 20$ years.
A population of 1,000 mice has 150 births and 50 deaths in one year (no migration). What is its growth rate?
$\displaystyle \frac{150 - 50}{1000} \times 100 = 10\%$.
A graph shows a population growing quickly and then leveling off near a maximum value. This S-shaped curve is called:
Logistic growth slows as the population approaches carrying capacity.
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