Presentation on theme: "Ch. 53 Exponential and Logistic Growth"— Presentation transcript:
1Ch. 53 Exponential and Logistic Growth Objective:SWBAT explain how competition for resources limits exponential growth and can be described by the logistic growth model.
2Exponential GrowthUnrealistic! 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.
3Exponential Growth Equation Change inpopulationsizeBirthsImmigrantsenteringDeathsEmigrantsleavingNtrNPer capita (individual)B bND mNPer capita growth rater b mdNdtrmaxNUnder ideal conditions, growth rate is at its max
4Exponential Graph Exponential growth results in a J curve. Number of generationsPopulation size (N)510152,0001,5001,000500dN dt= 1.0N= 0.5N
5Real Life Examples Can occur when: Populations move to a new area. YearElephant population8,0006,0004,0002,00019001910192019301940195019601970Can occur when:Populations move to a new area.Rebounding after catastrophic event (Cambrian explosion)
6Logistic 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.).
8Logistic Graph ( ) Logistic growth results in an S-shaped curve Number of generationsPopulation growth begins slowing here.Exponential growthLogistic growthPopulation size (N)515102,0001,5001,000500K = 1,500dNdt= 1.0N1,500 – N()Logistic growth results in an S-shaped curve
9Real Life Examples Note overshoot Time (days) (a) A Paramecium population in the lab(b) A Daphnia population in the labNumber of Paramecium/mLNumber of Daphnia/50 mL1,00080060040020051020151604060801001201401801509030Note overshoot