2. Populations

7. Population growth Nt + 1 = Nt + B – D + I – E

8. Population growth Nt + 1 = Nt + B – D + I – E Nt + 1 = Nt + B – D (assume no I and E)

9. Time: 0 Cells: 1

10. Time: 0 1 Cells: 1 2

11. Time: 0 1 2 Cells: 1 2 4

12. Time: 0 1 2 3 Cells: 1 2 4 8

13. Time: 0 1 2 3 4 Cells: 1 2 4 8 16

14. Time: 0 1 2 3 4 5 Cells: 1 2 4 8 16 32

15. Time: 0 1 2 3 4 5 6 Cells: 1 2 4 8 16 32 64

16. Time: 0 1 2 3 4 5 6 7 Cells: 1 2 4 8 16 32 64 128

17. “J” shaped or exponential growth

18. Exponential growth: # increase by constant factor (R or reproductive rate) each time interval

19. N t = N 0 R t R = 2, N 0 = 1, t = 5 N t = 1 * 2 5 = 32

20. Mathematical model for non- overlapping (discrete) populations

21. dN/dt = rN r = intrinsic rate of increase r = birth rate (b) – death rate (d) Mathematical model for overlapping populations

22. r > 0population will grow r = 0population won’t change r < 0population will shrink dN/dt = rN

23. Fig. 52.8 The exponential model for population growth

24. Fig 52.9

25. Fig 52.20

26. Fig 52.16

27. Cod in north Atlantic

28. Fig. 52.11 The patterns of exponential and logistic population growth

29. For: r=0.1K=100 if N = 10dN/dt =.1 (10) [(100 - 10)/100] =.1 (10) (.9) =.9 if N = 99dN/dt =.1 (99) [(100 - 99)/100] =.1 (99) (.01) =.099 dN/dt = r N [(K - N)/K]

30. What do I need to know about these models? ExponentialLogistic Pattern:J-shapedS-shaped Equation*:dN/dt = rN dN/dt = rN[(K-N)/K] Assumptions:-growth rate constantgrowth rate decreases with pop size -unlimited env.carrying capacity * Know what each term means and how changes in the terms affect the pattern of population growth.

31. Sometimes population growth is independent of density

32. Fig 52.18

33. Larch budmoth

34. Fig. 52.3

35. Fig. 52.22

36. A Life Table Number Probability of#Offspring born Ageaged xsurvival to xto females aged x 06001.00 13000.50 22400.42 3 600.13 4 300.055

37. Age group (x) NxNx bxbx lxlx 060001 13000.5 22402.4 3603.1 4305.05 lxbxlxbx Σ l x b x = 1.35 0 0.8.3.25 Lifetime offspring per individual female