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Populations: Regulation

Populations: Regulation. Ruesink Lecture 5 Biology 356. Three basic forms of population dynamics. Density independent Continuous reproduction: Exponential equation Discrete reproduction: Geometric equation Density dependent Logistic equation. Figure 14.5. Exponential.

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Populations: Regulation

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  1. Populations:Regulation Ruesink Lecture 5 Biology 356

  2. Three basic forms of population dynamics • Density independent • Continuous reproduction: Exponential equation • Discrete reproduction: Geometric equation • Density dependent • Logistic equation

  3. Figure 14.5 Exponential

  4. Geometric and exponential equations are roughly interchangeable because r = ln(l) Figure 14.6

  5. Exponential or geometric population growth • Density-independent (l does not change with population size) • Resources (light, prey, enemy-free space) not limiting Number Time

  6. Figure 14.17

  7. Logistic population growth • Density-dependent (population growth depends on population size) • Resources (light, prey, enemy-free space) are limiting, regulating population around K (carrying capacity) K Number Time

  8. Logistic population growth • dN/dt = r N (1 – N/K) • Slow growth at low N • Slow growth near K K Number Time

  9. Simple dynamics of DI and DD populations • Time series • Number of individuals (N) at each time t • Population rate of change • dN/dt = Nt+1-Nt • Per capita rate of change • dN/dt/N = (Nt+1-Nt)/Nt

  10. Geometric increase

  11. Geometric increase

  12. Geometric increase

  13. Geometric increase Accelerating population increase Constant per capita increase

  14. Population abundance (N) Time dN/dt Density (N) dN/dt/N Density (N)

  15. Population abundance (N) Time dN/dt Density (N) dN/dt/N Density (N)

  16. Logistic

  17. Logistic

  18. Logistic

  19. Logistic Highest population increase at intermediate densities Declining per capita contribution

  20. Population abundance (N) Time dN/dt Density (N) dN/dt/N Density (N)

  21. How to recognize density dependence • Manipulate density of an organism • Record individual performance across a range of densities

  22. Figure 14.19

  23. Figure 14.20b, c Density dependence in sparrows

  24. In class assignment • Work in groups of ~4 • Fill out separate workseets • Use the definitions and equations on your handout • Link demography, life tables, geometric and logistic population growth, population projection, and conservation

  25. In class assignment • r = exponential rate of population growth • R0 = net reproductive rate • ra = exponential rate of population growth estimated from life tables • r0 = intrinsic rate, can be modified by DD

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