1. Ch. 53 Exponential and Logistic Growth
Objective:
SWBAT explain how competition for resources limits exponential growth and can be described by the logistic growth model.

2. Exponential Growth
Unrealistic! Does not take into account limiting factors (resources and competition).
However, a good model for showing upper limits of growth and conditions that would facilitate growth.

3. Exponential Growth Equation
Change in
population
size
Births
Immigrants
entering
Deaths
Emigrants
leaving    N t  rN
Per capita (individual)
B  bN
D  mN
Per capita growth rate
r  b  m dN dt 
rmaxN
Under ideal conditions, growth rate is at its max

4. Exponential Graph Exponential growth results in a J curve.
Number of generations
Population size (N) 5 10 15
2,000
1,500
1,000
500
dN dt
= 1.0N
= 0.5N

5. Real Life Examples Can occur when: Populations move to a new area.
Year
Elephant population
8,000
6,000
4,000
2,000
1900
1910
1920
1930
1940
1950
1960
1970
Can occur when:
Populations move to a new area.
Rebounding after catastrophic event (Cambrian explosion)

6. Logistic Growth Takes into account limiting factors. More realistic.
Population size increases until a carrying capacity (K) is reached (then growth decreases as pop. size increases).
point at which resources and population size are in equilibrium.
K can change over time (seasons, pred/prey movements, catastrophes, etc.).

7. Logistic Growth EquationdN dt 
(K  N) K
rmax N

8. Logistic Graph ( ) Logistic growth results in an S-shaped curve
Number of generations
Population growth begins slowing here.
Exponential growth
Logistic growth
Population size (N) 5 15 10
2,000
1,500
1,000
500
K = 1,500 dN dt
= 1.0N
1,500 – N ( )
Logistic growth results in an S-shaped curve

9. Real Life Examples Note overshoot Time (days)
(a) A Paramecium population in the lab
(b) A Daphnia population in the lab
Number of Paramecium/mL
Number of Daphnia/50 mL
1,000
800
600
400
200 5 10 20 15
160 40 60 80
100
120
140
180
150 90 30
Note overshoot