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Published byManuel Arundel Modified over 2 years ago

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Objective: SWBAT explain how competition for resources limits exponential growth and can be described by the logistic growth model.

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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

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Exponential Growth Equation Change in population size Births Immigrants entering population Deaths Emigrants leaving population Per capita (individual) B bN D mN Per capita growth rate r b m NN tt rN dN dt r max N Under ideal conditions, growth rate is at its max

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

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Can occur when: Populations move to a new area. Rebounding after catastrophic event (Cambrian explosion) Real Life Examples Year Elephant population 8,000 6,000 4,000 2,

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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

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Logistic Growth Equation dN dt (K N) K r max N

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

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Real Life Examples 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, Note overshoot

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