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

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

3. Population Growth Models: Limits to Unrestrained Growth: Carrying Capacity (K) Carrying Capacity: The Maximum Population Size of a Population that a Particular Ecosystem can Sustain

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

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

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

7. Pattern of Human Population Growth? Fig. 11.26 in Molles 2013 Previous 2000 yrPrevious 40 yr

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

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

10. dN ___ dT N Rate of Population Change (Logistic Growth) (dN/dT versus N) K Rate of Population Change is Maximum K2K2

11. N N r realized Exponential GrowthLogistic Growth K r max Per Capita Rate of Increase r realized K

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

13. r realized r max * ( 1 - N K ) Realized Per Capita Rate of Increase N r max r realized = (K = 100) 16 50 100 150.02 ( 1 - N K ) _______________________

14. 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. a)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?

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

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

17. POPULATION REGULATION: Keeping Populations in Check

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

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

20. Density Dependent Factors: Factors Influenced by Population Density Fig. 9.14 in Cain et al. 2008 lxlx

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

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

23. Fig. 16-7 in Ricklefs and Miller 20001 Population Size (N) Fecundity Density Dependent Factors: Factors Influenced by Population Density

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

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

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

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

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

29. Andrewartha and Birch: Thrip Density Predicted on Basis of CLIMATIC Variables N = F (X 1, X 2, X 3, X 4 ) Effective Degree Days: Winter-Aug. 31 Rainfall: Sept. – Oct. Effective Degree Days: Sept. – Oct. Effective Degree Days: Winter-Aug. 31 (prev. year)

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

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

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

33. The Debate Rages On ….

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