Transcript Modeling in perspective

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
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
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)
Unlimited Flow Source
Model EXPO
Q: Stored
Quantity
J2: Feedback
J1: Production
E: Unlimited
Flow source
Q  k1EQ  k2 EQ  k3Q
J3: Losses
Renewable Flow-Limited Source
R  J  k0 RQ
Model RENEW
Or…
R J
1  k 0Q
Q  k3 RQ  k 4Q
k3  k1  k 2
Logistic curve
Non-renewable Energy Source
Model NONRENEW
Q
Assets
K2*E*Q
E
Energy
Reserve
K0*E*Q
K4*Q
K1*E*Q
NONRENEW
E  k0 EQ
Q  (k1  k2 ) EQ  k4Q
Elements in Parallel: Competitive Exclusion
Model EXCLUS
k5 > k 6
R I
1  k1Q1  k2Q2 
Q1  k5 RQ1  k3Q1
Q  k RQ  k Q
2
6
2
4
2
Elements in Parallel: Competitive Interaction
Model INTERACT
k2 > k 1
r
r = specific growth rate
K = carrying capacity
r/K
Q1  k1 EQ1  k3Q1Q1  k5Q1Q2
Q  k EQ  k Q Q  k Q Q
2
2
2
4
2
2
6
1
2
Elements in Parallel: Competitive Cooperation
Model COOP
k5 > k6
R I
1  k1Q1Q2  k2Q1Q2 
Q1  k5 RQ1Q2  k3Q1  k7 RQ1Q2
Q  k RQ Q  k Q  k RQ Q
2
6
1
2
4
2
8
1
2
Elements in Series: Predator-Prey model
Model PREYPRED
Production
Consumption
Death
 Lotka-Volterra predator-prey models
H  k1 EH  k 2CH  k3 H
C  k CH  k C
4
5
Elements in Series: An Oscillator
Model OSCILLAT
P  kJ  k1P  k 2 PH
H  k3 PH  k 4 H  k5 HC
C  k HC  k C
6
7
Elements in Series: Chaotic System
P  k3 EP  k7 P  k8 PQ
Q  k PQ  k Q  k QH
0
9
2
H  k1QH  k4CH  k6 H
C  k HC  k C
5
10
System of equations is deterministic
(not random), yet prediction from past
and current states is impossible.
CHAOS in STELLA
Model CHAOS
CHAOS Results
Putting it all together: LAKE model
Phytoplankton
Zebra mussels
Zooplankton
Small fish
Herbivore
SAV
Large fish
The Equations
R J
1  KP1  K ' P2 
P1  k3 P1 R  k15 ZP1  k8QP1  k7 P1
P  k P R  k BP  k P
2
11 2
16
2
12 2
Z  k13 ZP1  k14 Z
B  k BP  k B
17
2
18
Q  k0QP1  k 2 HQ  k9Q
H  k HQ  k CH  k H
1
4
C  k5CH  k10C
6
LAKE in STELLA
Model LAKE
Results: Lake (Z introduced at t=50)
How do we
model this?
Step by Step!
Abrams, P. et al (1996)
Cladophora
model
Higgins et al (2005)
Systems Diagram
Stella Model
 CDM Stella
Results
Results
References
 Abrams, P., B.A. Menge, G.G. Mittelbach, D. Spiller, and P. Yodzis. 1996. The
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role of indirect effects in food webs. Pp. 371-395. In: Food Webs:
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Adey, W.H., and K. Loveland. 2007. Dynamic Aquaria: Building and
Restoring Living Ecosystems (3rd 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 (3rd 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.