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PHLOX

POPULATION GROWTH RATE. PHLOX. 10. 11. dN = f (B, D, I, E) dt. POPULATION GROWTH TRENDS. I) STEADILY INCREASING POPULATIONS. Geometric Growth. Exponential Growth. 1) Pulsed Reproduction 2) Non-Overlapping Generations 3) Geometric Rate of Increase (. 1) Continuous Reproduction

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PHLOX

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

  2. POPULATION GROWTH TRENDS

  3. I) STEADILY INCREASING POPULATIONS Geometric Growth Exponential Growth 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 ) Figs. 11.3, 11. 6 in Molles 2008

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

  5. UNLIMITED POPULATION GROWTH A: (Geometric Growth: Ratio of Successive Population Size) N7 ___ = N6 N8 ___ = N7 Fig. 11.3 in Molles 2008

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

  7. Calculating Geometric Rate of Increase (λ) N0 = 996 8 N 1 = 2,408 Phlox drummondii λ =

  8. Geometric Growth: Projecting Population Numbers N0 = 996 N 1 = 2,408 8 λ = 2.42 N2 = Phlox drummondii N5 =

  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) Nt = Noλt Fig. 11.3 in Molles 2008

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

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

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

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

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

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

  19. EXPONENTIAL POPULATION GROWTH: Predicting Population Size dN __ rmax N = dT r t Nt = No e max (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 rmax = .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) = B LN(A) LN(e) = 1 LN(AB) = LN(A) + LN(B) LN(A/B) = LN(A) – LN(B)

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

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

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

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

  30. LOGISTIC GROWTH: Predicting Population Size

  31. 1 http://www.wpclipart.com/animals/S/sheep/Dall_Sheep.png 2 http://www.bigantlers.com/dall15c.jpg 3 http://www.oilcrash.com/images/d_price3.gif 4 http://www.akcenter.org/images/programs/oceans/beluga/ Raw-Count-Graph.gif 5 http://csiwhalesalive.org/csi04404b.jpg 6 http://www.behav.org/00gallery/ecol/carni_isle_royal_graph_1.gif 7 http://mall.ballparks.com/images/AV75.jpg 8 http://www.sbs.utexas.edu/bio406d/images/pics/plm/Phlox% 20drummondii%20flws4.jpg 9 http://www.photobirder.com/Bird_Photos/whooping_crane_2.jpg

  32. 10 http://www.learner.org/jnorth/images/graphics/c/crane_Sp04_020.jpg 11 http://www.em.ca/garden/phlox_drummondii1.JPG 12 http://newsimg.bbc.co.uk/media/images/42096000/jpg/_42096628_ crowd_416_ap.jpg

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