1. University at Buffalo Engineering for Ecosystem Restoration Summer Workshop Series 25 June 2010 David Blersch Dept. of Civil, Structural and Environmental Engineering University at Buffalo

2. Elemental Structures of (Eco)systems Energy sources Unlimited flow source Renewable flow-limited source Non-renewable source Elements in Parallel Competitive exclusion Competitive interaction Mutual cooperation Elements in Series Predator-Prey 2-body model Oscillator 3-body model Chaotic 4-body model

3. Energy Sources Unlimited Flow Source: Constant Force/Pressure (e.g., large reservoir) Flow-limited Source: Constant flow (rate per unit time) (e.g., sunlight) Non-renewable Source: A limited energy storage (e.g., nutrient source)

4. Unlimited Flow Source E: Unlimited Flow source Q: Stored Quantity J1: Production J2: Feedback J3: Losses Model EXPO

5. Renewable Flow-Limited Source Or… Model RENEW Logistic curve

6. Non-renewable Energy Source Model NONRENEW

7. Elements in Parallel: Competitive Exclusion k 5 > k 6 Model EXCLUS

8. Elements in Parallel: Competitive Interaction k 2 > k 1 rr/K r = specific growth rate K = carrying capacity Model INTERACT

9. Elements in Parallel: Competitive Cooperation k 5 > k 6 Model COOP

10. Elements in Series: Predator-Prey model Lotka-Volterra predator-prey models Production Consumption Death Model PREYPRED

11. Elements in Series: An Oscillator Model OSCILLAT

12. Elements in Series: Chaotic System System of equations is deterministic (not random), yet prediction from past and current states is impossible.

13. CHAOS in STELLA Model CHAOS

14. CHAOS Results

15. Putting it all together: LAKE model Phytoplankton Zebra mussels SAV Herbivore ZooplanktonSmall fishLarge fish

16. The Equations

17. LAKE in STELLA Model LAKE

18. Results: Lake (Z introduced at t=50)

19. How do we model this? Abrams, P. et al (1996) Step by Step!

20. Cladophora model Higgins et al (2005)

21. Systems Diagram

22. Stella Model CDM Stella

24. Results

26. References Abrams, P., B.A. Menge, G.G. Mittelbach, D. Spiller, and P. Yodzis. 1996. The role of indirect effects in food webs. Pp. 371-395. In: Food Webs: Integration of Patterns and Dynamics. G.A. Polis and K.O. Winemiller (eds.). Chapman & Hall, New York. Adey, W.H., and K. Loveland. 2007. Dynamic Aquaria: Building and Restoring Living Ecosystems (3 rd Edition). Academic Press, San Diego, California. Gerardin, L. 1968. Bionics. McGraw-Hill, New York. Jorgensen, S.E., and G. Bendoricchio. 2001. Fundamentals of Ecological Modelling (3 rd Edition). Elsevier Science, New York. Kangas, P.C. 2004. Ecological Engineering: Principles and Practice. Lewis Publishers, Boca Raton, Florida. Odum, H.T. 1994. Ecological and General Systems: An Introduction to Systems Ecology. University Press of Colorado, Niwot, Colorado. Odum, H.T., and E.C. Odum. 2000. Modeling for All Scales: An Introduction to System Simulation. Academic Press, San Diego, California.