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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.

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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.

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**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

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**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

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**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)

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**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.).

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**Logistic Growth Equation**

dN dt (K N) K rmax N

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**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

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**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

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