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Understanding Population Growth: Models and Dynamics

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37 diapositives · 481 Views · Sep 07, 2014

This piece explores the mathematical models and dynamics of population growth, focusing on two primary types: exponential and logistic growth. The equations for non-overlapping and overlapping populations are discussed, illustrating how intrinsic growth rates and carrying capacities influence population size. Key terms such as birth rates, death rates, and reproductive rates provide a framework for understanding population changes over time. Various figures illustrate concepts, including J-shaped and S-shaped growth patterns, equipping readers with foundational knowledge of population dynamics.

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  1. Populations

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

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

  4. Time: 0Cells: 1

  5. Time: 0 1Cells: 1 2

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

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

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

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

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

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

  12. Time: 0 1 2 3 4 5 6 7Cells: 1 2 4 8 16 32 64 128 “J” shaped or exponential growth

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

  14. Nt = N0RtR = 2, N0 = 1, t = 5Nt = 1 * 25 = 32

  15. Nt = N0RtR = 2, N0 = 1, t = 5Nt = 1 * 25 = 32 Mathematical model for non-overlapping (discrete) populations

  16. dN/dt = rNr = intrinsic rate of increaser = birth rate (b) – death rate (d) Mathematical model for overlapping populations

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

  18. Fig. 52.8 The exponential model for population growth

  19. Fig 52.9

  20. Fig 52.20

  21. Fig 52.16

  22. Cod in north Atlantic

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

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

  25. What do I need to know about these models? ExponentialLogistic Pattern: J-shaped S-shaped Equation*: dN/dt = rN dN/dt = rN[(K-N)/K] Assumptions: -growth rate constant growth 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.

  26. Sometimes population growth is independent of density

  27. Fig 52.18

  28. Larch budmoth

  29. Fig. 52.3

  30. Fig. 52.22

  31. A Life Table Number Probability of #Offspring born Age aged x survival to x to females aged x 0 600 1.0 0 1 300 0.5 0 2 240 0.4 2 3 60 0.1 3 4 30 0.05 5

  32. Age group (x) Nx bx lx 0 600 0 1 1 300 0 .5 2 240 2 .4 3 60 3 .1 4 30 5 .05 lxbx 0 0 .8 .3 .25 Lifetime offspring per individual female Σ lxbx = 1.35