Ch. 53 Exponential and Logistic Growth

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

3. 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

4. 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

5. 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

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. (K  N) dN  rmax N dt K Logistic Growth Equation

8. 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

9. 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