1. 10 11 PHLOX POPULATION GROWTH RATE dN = f (B, D, I, E) dt

2. POPULATION GROWTH TRENDS

3. Figs. 11.3, 11. 6 in Molles 2008 Geometric GrowthExponential Growth I) STEADILY INCREASING POPULATIONS 1) Pulsed Reproduction 2) Non-Overlapping Generations 3) Geometric Rate of Increase ( 1) Continuous Reproduction 2) Overlapping Generations 3) Per Capita Rate of Increase (r) λ)

4. UNLIMITED POPULATION GROWTH A: (Geometric Growth) Fig. 11.3 in Molles 2008 Pulsed Reproduction Non-Overlapping Generations

5. UNLIMITED POPULATION GROWTH A: (Geometric Growth: Ratio of Successive Population Size) Fig. 11.3 in Molles 2008 N7N7 = ___ N6N6 N8N8 = N7N7

6. Geometric Growth: Calculation of Geometric Rate of Increase (λ) λ = N t+1 ______________ N t

7. Phlox drummondii 8 N 0 = 996 N 1 = 2,408 λ = Calculating Geometric Rate of Increase (λ)

8. Geometric Growth: Projecting Population Numbers N 0 = 996 Phlox drummondii 8 λ = 2.42 N 2 = N 1 = 2,408 N 5 =

9. Problem A: The initial population of an annual plant is 500. If, after one round of seed production, the population increases to 1,200 plants, what is the value of λ?

10. Problem B. For the plant population described in Problem A, if the initial population is 500, how large will be population be after six consecutive rounds of seed production?

11. Problem C: For the plant population described above, if the initial population is 500 plants, after how many generations will the population double?

12. STEADILY INCREASING POPULATIONS (Geometric Growth: Rate of Population Growth) Fig. 11.3 in Molles 2008 N t = N o λ t

13. UNLIMITED POPULATION GROWTH B: (Exponential Growth) Fig. 11.7 in Molles 2008 Continuous Reproduction Overlapping Generations

14. dN dT dN ___ dT = Rate UNLIMITED POPULATION GROWTH B Exponential Growth (Rate of Population Growth)

15. Fig. 11.6 in Molles 2006 EXPONENTIAL POPULATION GROWTH: Rate of Population Growth dN ___ dT dN ___ dT dN ___ dT

16. dN ___ dT N Graph of dN/dT versus N (Exponential Growth) 1 0.5 rise run rise run r max = rise run (= intrinsic rate of increase)

17. dN __ dT = r max N EXPONENTIAL POPULATION GROWTH: Rate of Population Growth Intrinsic Rate of Increase Population Size Rate of Population Growth

18. r max = b - d Meaning of Intrinsic Rate of Increase (r max ) r max = individuals per individual per day b = per capita birth rate (= births per individual per day) d = per capita death rate (= deaths per individual per day) = intrinsic rate of increase (r) during exponential growth

19. EXPONENTIAL POPULATION GROWTH: Predicting Population Size dN __ dT = r max N N t =N o e r max t (e = 2.718)

20. Problem D. Suppose that the Silver City population of Eurasian Collared Doves, with initial population of 22 birds, is increasing exponentially with r max =.20 individuals per individual per year. How large will the population be after 10 years? After 100 years?

21. Problem E. How many years will it take the Eurasian Collared Dove population described above to reach 1000 birds? LN(AB) = LN(A) + LN(B)LN(A/B) = LN(A) – LN(B) LN(A B ) = B LN(A)LN(e) = 1 -----------------------------------------------------------------------------------------------------------

22. Problem F. “Doubling Time” is the time it takes an increasing population to double. What is the doubling time for the Eurasian Collared Dove population described above?

23. Problem E. Refer to the Eurasian Collared Dove population described earlier. How fast is the population increasing when the population is 100 birds? How fast is the population increasing once the population reaches 500 birds?

24. Problem F. How large is the Eurasian Collared Dove population when the rate of population change (dN/dt) is 5 birds per year? When the rate of population change (dN/dt) is 20 birds per year?

25. LOGISTIC GROWTH: Rate of Population Change Fig. 11.11 in Molles 2006

26. N T Carrying Capacity (K): Sigmoid Curve: 82 LOGISTIC GROWTH: Carrying Capacity

27. Figs. 11.11 in Molles 2006. (Logistic Population Growth) LOGISTIC GROWTH: Rate of Population Change dN ___ dT

28. dN ___ dT N Graph of dN/dT versus N (Logistic Growth) rise run rise run rise run rise run

29. LOGISTIC GROWTH: Rate of Population Change dN ____ dT r max N = ( ) 1 - N K “Brake” Term

30. LOGISTIC GROWTH: Predicting Population Size

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