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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. Exponential Growth. Unrealistic! Does not take into account limiting factors (resources and competition).

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ch 53 exponential and logistic growth

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.

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

Change in

population

size

Immigrants

entering

population

Emigrants

leaving

population

Births

Deaths

dN

rmaxN

dt

N

rN

t

Exponential Growth Equation

Per capita (individual)

B bN

D  mN

Per capita growth rate

r b  m

Under ideal conditions, growth rate is at its max

exponential graph

2,000

Exponential Graph

dNdt

= 1.0N

1,500

dNdt

= 0.5N

  • Exponential growth results in a J curve.

Population size (N)

1,000

500

0

5

10

15

Number of generations

real life examples
Real Life Examples

8,000

6,000

  • Can occur when:
    • Populations move to a new area.
    • Rebounding after catastrophic event (Cambrian explosion)

Elephant population

4,000

2,000

0

1900

1910

1920

1930

1940

1950

1960

1970

Year

logistic growth
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.).
logistic graph

Exponentialgrowth

Logistic Graph

2,000

dN

dt

= 1.0N

1,500

  • Logistic growth results in an S-shaped curve

K = 1,500

Logistic growth

1,500 – N

1,500

dN

dt

(

)

Population size (N)

= 1.0N

1,000

Population growthbegins slowing here.

500

0

0

5

10

15

Number of generations

real life examples1
Real Life Examples

Note overshoot

180

1,000

150

800

120

Number of Daphnia/50 mL

Number of Paramecium/mL

600

90

400

60

200

30

0

0

0

5

10

15

0

20

40

60

80

100

120

140

160

Time (days)

Time (days)

(b) A Daphnia population in the lab

(a) A Paramecium population in the lab