Ch. 53 Exponential and Logistic Growth

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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). However, a good model for showing upper limits of growth and conditions that would facilitate growth.

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

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

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)

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 Growth Equation
dN dt (K  N) K rmax N

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

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