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

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

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) Time Number K

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

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

10. Geometric increase TimeNdN/dtdN/dt/N 020 123 227 331 436 542 649 757 866 977

11. Geometric increase TimeNdN/dtdN/dt/N 02023-20 = 33/20 = 0.15 12327-23 = 44/23=0.17 227 331 436 542 649 757 866 977

12. Geometric increase TimeNdN/dtdN/dt/N 02023-20 = 33/20 = 0.15 12327-23 = 44/23=0.17 22744/27=0.15 33155/31=0.16 4366 5427 6498 7579 8661111/66=0.17 977

13. Geometric increase TimeNdN/dtdN/dt/N 02023-20 = 33/20 = 0.15 12327-23 = 44/23=0.17 22744/27=0.15 33155/31=0.16 4366 5427 6498 7579 8661111/66=0.17 977 Accelerating population increase Constant per capita increase

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

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

16. Logistic TimeNdN/dtdN/dt/N 05 18 212 318 427 538 650 762 873 982

17. Logistic TimeNdN/dtdN/dt/N 058-5=33/5=0.6 1812-8=44/8=0.5 212 318 427 538 650 762 873 982

18. Logistic TimeNdN/dtdN/dt/N 058-5=33/5=0.6 1812-8=44/8=0.5 21266/12=0.5 31899/18=0.5 4271111/27=0.4 5381212/38=0.32 6501212/50=0.24 762110.18 87390.12 98260.07

19. Logistic TimeNdN/dtdN/dt/N 058-5=33/5=0.6 1812-8=44/8=0.5 21266/12=0.5 31899/18=0.5 4271111/27=0.4 5381212/38=0.32 6501212/50=0.24 762110.18 87390.12 98260.07 Highest population increase at intermediate densities Declining per capita contribution

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