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Population Growth Models: Geometric and Exponential Growth

Population Growth Models: Geometric and Exponential Growth. Exponential Growth. Geometric Growth. Population Growth Models: Unrestrained Growth: How realistic?. Population Growth Models: Limits to Unrestrained Growth: Carrying Capacity (K). Carrying Capacity:.

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Population Growth Models: Geometric and Exponential Growth

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  1. Population Growth Models: Geometric and Exponential Growth Exponential Growth Geometric Growth

  2. Population Growth Models: Unrestrained Growth: How realistic?

  3. Population Growth Models: Limits to Unrestrained Growth: Carrying Capacity (K) Carrying Capacity:

  4. LOGISTIC GROWTH: Rate of Population Change 11 13 Saccharomyces cervisiae (Yeast) 10 12

  5. Logistic Population Growth: Yeast K Carrying Capacity (K): Maximum Population that a Given Population can Support Fig. 11.9 in Molles 2008

  6. Logistic Population Growth: Buffalo, Barnacles and Paramecia Figs. 11.10, 11.11, 11.12, 11.26 in Molles 2008

  7. Pattern of Human Population Growth? Previous 2000 yr Previous 40 yr Fig. 11.26 in Molles 2010

  8. LOGISTIC GROWTH (= Sigmoidal Growth Curve) K: Carrying Capacity r realized: Realized Per Capita Rate of Increase rmax: Intrinsic Rate of Increase: Maximum Possible Per Capita Rate of Increase

  9. LOGISTIC GROWTH: Rate of Population Change dN ___ dt (Logistic Population Growth) Figs. 11.18 in Molles 2008

  10. Rate of Population Change (Logistic Growth) (dN/dT versus N) Rate of Population Change is Maximum dN ___ dT K 2 K N

  11. Rate of Population Change (Logistic Growth) (dN/dT versus N) r = rrealized(2) r = rrealized(3) dN ___ r = rrealized(1) dT r = rrealized(4) = 0 r = rmax N K rrealized = actual per capita rate of increase

  12. Per Capita Rate of Increase Exponential Growth Logistic Growth r max r max rrealized rrealized K N K N

  13. LOGISTIC GROWTH: Rate of Population Change dN N ) ( r max N - 1 ____ = K dt Rate of Population Growth (Exponential) “Brake” Term on rmax

  14. Realized Per Capita Rate of Increase (1 - N ) rmax * r realized = K N (1 - ) N r max r realized K _____ __________ ________ .02 .02 .02 .02 16 50 100 150 (K = 100)

  15. Problem A: Suppose a population of duckweed is growing • logistically (r max = .08 duckweed/duckweed/day) in a • styrofoam bowl with carrying capacity = 100 plants. • What is the rate of population change when N = 16? • b) What is the rate of population change when N = 50? • c) What is the rate of population change when N = 100? • d) What is the rate of population change when N = 150?

  16. LOGISTIC GROWTH: Predicting Population Size dN N ) ( r max N - 1 ____ = K dT

  17. Problem B: Suppose sixteen duckweed (rmax = .08) are growing • logistically in a styrofoam bowl with carrying capacity = • 100 duckweed. • How big will the population be in ten days? • How big will the population by in one hundred days?

  18. POPULATION REGULATION: Keeping Populations in Check

  19. Density Independent Factors: Exert effects INDEPENDENT of Population Density

  20. Density Dependent Factors: Factors Influenced by Population Density Survivorship vs.

  21. Density Dependent Factors: Factors Influenced by Population Density lx Fig. 9.14 in Cain et al. 2008

  22. Density Dependent Factors: Factors Influenced by Population Density Survivorship vs.

  23. Density Dependent Factors: Factors Influenced by Population Density lx Soybean (Glycine max) Fig. 9.14 in Cain et al. 2008

  24. Density Dependent Factors: Factors Influenced by Population Density Fecundity Population Size (N) Fig. 16-7 in Ricklefs and Miller 2000 1

  25. Density Dependent Factors: Factors Influenced by Population Density Fecundity Fig. 16-9 in Ricklefs and Miller 2000

  26. Density Independent and Density Dependent Factors (Summary) Fig. 9.13 in Cain et al. 2008

  27. Which has more impact on Population Regulation: Density Dependent or Density Independent Factors Density Dependent? Density Independent?

  28. DENSITY DEPENDENCE IS A MYTH! “The Distribution and Abundance of Animals” Andrewartha and Birch” (1954) THRIPS

  29. Population Fluctuation: Density Dependent or Density Independent Factors? Fig. 16-15 in Ricklefs and Miller 2000

  30. Andrewartha and Birch: Thrip Density Predicted on Basis of CLIMATIC Variables Effective Degree Days: Winter-Aug. 31 Rainfall: Sept. – Oct. Effective Degree Days: Sept. – Oct. Effective Degree Days: Winter-Aug. 31 (prev. year) N = F (X1, X2, X3, X4)

  31. Predictions versus Observed Fig. 9-12 in Cain et al. 2008

  32. Andrewartha and Birth: DENSITY-INDEPENDENT FACTORS Regulate Populations

  33. ECOLOGISTS COUNTER: Thrip Populations ARE Controlled by Density-Dependent Factors Fig. 16-7 in Ricklefs et al. 2000

  34. The Debate Rages On ….

  35. 1 http://www.cofc.edu/~bernardoj/Genetics%20Lab/drosophila.gif 2 http://www.unexco.com/conflour.jpg 3 http://www.caudata.org/daphnia/images/Daphnia_magna_large.jpg 4 http://www.coffeecreekwc.org/photos/birds/Song_Sparrow.jpg 5 http://www.ruhr-uni-bochum.de/boga/html/Conyza.canadensis.ja05.jpg 6 http://flogaus-faust2.de/photo/amarretr.jpg 7 http://www.ces.ncsu.edu/plymouth/graphics/ent/thriplarva1.jpg 8 http://www.ruf.rice.edu/~ecology/insects/ Thrip%20Phloeothripidae%20short%20wgs%20blk.jpg 9 http://hortipm.tamu.edu/pestprofiles/sucking/ghthrips/thripe.jpg 10 http://greenpreferred.com/wp-content/uploads/2007/11/dsc02948.JPG 11 http://sylviabass.com/foodie/wp-content/uploads/2007/11/potato-rosemary- bread-rising.jpg 12 http://www.explorewisconsin.com/CedarCreekWinery/cedarburg_winery2b.jpg

  36. 13 http://www.diwinetaste.com/html/dwt200701/images/SaccharomycesCerevisiae.jpg 14 http://student.biology.arizona.edu/honors99/group7/glycolysis.jpg 15 http://www.micro.siu.edu/micr201/images/Ethanol.gif 16 http://biology.kenyon.edu/courses/biol114/Chap08/longread_sequence.gif 17 http://www.bath.ac.uk/bio-sci/images/profiles/wheals2.gif

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