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Course Overview
14.Apr.2015Andreas Fischlin, ETH Zurich
• Fundamentals of Systems Theory: Modeling, System Representation, Stability analysis, Simulation
• Ecosystem models from recent research: agroecosystems, climate and forests etc.
• Systems Ecology Case Studies: Motto - 1,2,3 from the simple to the complex
Insertion: Simulation tool «Easy ModelWorks»
• Introduction/Basic Terms
1 2 3
• Fundamentals of Systems Theory: Modeling, System Representation, Stability analysis, Simulation
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14.Apr.2015Andreas Fischlin, ETH Zurich
Overview 14. April 2015
Fundamentals of System Theory!
!Modeling!
System Representations
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14.Apr.2015
Fundamentals of System Theory
• Modelling!• Systems Representations!• Simulation!• Stability and Stability Analysis
Andreas Fischlin, ETH Zurich
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14.Apr.2015Andreas Fischlin, ETH Zurich
The System In the Ecosystem?
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14.Apr.2015Andreas Fischlin, ETH Zurich
What Type of System?
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14.Apr.2015Andreas Fischlin, ETH Zurich
What Type of System?
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14.Apr.2015Andreas Fischlin, ETH Zurich
What Type of System?
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14.Apr.2015Andreas Fischlin, ETH Zurich
What Type of System?
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14.Apr.2015Andreas Fischlin, ETH Zurich
What Type of System?
Massachusetts Institute of Technology, 2007. The Large Scale Network Analysis Project. web.mit.edu/networks/visualizations.html
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14.Apr.2015Andreas Fischlin, ETH Zurich
Lessons to be learned:
• Systems have common properties regardless of their nature !– Thus their accessibility => Systems Theory!
• Systems can be described in a common language (System Representations)!
• All Systems can be modeled!• Systems need to be modeled to become
understood!
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14.Apr.2015Andreas Fischlin, ETH Zurich
An Ecosystem is:• a “conventional” ecosystem
such as a forest, lake, meadow etc.!
• any ecological system(autecology .. biosphere)!
• for a systems ecologist: also a systems theoretical concept
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14.Apr.2015
1 Modelling!
!
!
• Top down vs. bottom up!
• Mathematical Derivation of Model Equations vs. «System Dynamics» Approach
Andreas Fischlin, ETH Zurich
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14.Apr.2015
„Systems“ Thinking
Andreas Fischlin, ETH Zurich
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14.Apr.2015Andreas Fischlin, ETH Zurich
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14.Apr.2015
„Systemic“ Thought
Andreas Fischlin, ETH Zurich
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14.Apr.2015
The more complex the more stable!
Andreas Fischlin, ETH Zurich
Really?
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14.Apr.2015
Lord Robert M. May !
made ecologists aware that complexity, e.g. biodiversity, does not imply stability
Andreas Fischlin, ETH Zurich
May, R.M., 1972. Will a large complex system be stable? Nature, 238: 413-414
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14.Apr.2015Andreas Fischlin, ETH Zurich
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14.Apr.2015
Top-Down vs. Bottom-Up
Andreas Fischlin, ETH Zurich
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14.Apr.2015
Top-Down vs. Bottom-Up
Andreas Fischlin, ETH Zurich
MakroskopischeSicht
MikroskopischeSicht
see also Overhead Slide
Macroscopic view
Microscopic view
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14.Apr.2015
Bottom-Up• Given starting points!
• Oriented towards discipline traditions
Andreas Fischlin, ETH Zurich
• Starts holistically!
• Stepwise refinement only as needed (economical)!
• Reaches typically the set goals (synthesis)
Top-Down
• Not economical!
• Likely to introduce incompatibilities!
• Synthesis fails often:!– Lack of resources, time!– Underestimation of
needed efforts
• Prejudices are obstacles!
• Too high aggregation
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14.Apr.2015
Holisms vs. Reductionism
The most important aspect of ecosystem theory is the recognition of holism - the consideration of whole-system phenomena and an explanation of how these phenomena arise from interactions among lower-level phenomena.!
Shugart, 1984. A theory of forest dynamics - The ecological implications of forest succession models.
Andreas Fischlin, ETH Zurich
Both can be justified, but only side by side!
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14.Apr.2015
Mathematical Derivation of Model Equations vs. «System
Dynamics» Approach
Andreas Fischlin, ETH Zurich
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14.Apr.2015Andreas Fischlin, ETH Zurich
“System Dynamics” ApproachSome steps are more prominent than others!1" Problem question"
2" Sift facts and data"
3" Verbal model"
4,5" Mathematical model - Calibration"
6,7" Simulation model"
8" Simulation experiments"
9" Interpretation of simulation results"
10" Model and parameter identification"
11" Model validation"
12" Model application"
Recipe Systems Analysis
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14.Apr.2015Andreas Fischlin, ETH Zurich
Some steps are more prominent than others!1" Problem question"
2" Sift facts and data"
3" Verbal model"
4,5" Mathematical model - Calibration"
6,7" Simulation model"
8" Simulation experiments"
9" Interpretation of simulation results"
10" Model and parameter identification"
11" Model validation"
12" Model application"
Classical Approach, e.g. Physics
Recipe Systems Analysis
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14.Apr.2015Andreas Fischlin, ETH Zurich
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14.Apr.2015
Spectrum of Systems
Andreas Fischlin, ETH Zurich
Overhead Slide
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14.Apr.2015
Spatial and temporal scales correlated
Andreas Fischlin, ETH Zurich
Holling, 1992
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14.Apr.2015
The Modeling Dilemma
Andreas Fischlin, ETH Zurich
Generality
Precision Realism
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14.Apr.2015Andreas Fischlin, ETH Zurich
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14.Apr.2015Andreas Fischlin, ETH Zurich
2 System Representations
• Qualitative Representations, e.g. Relational Graph "
• State Variable Representations
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14.Apr.2015Andreas Fischlin, ETH Zurich
Qualitative Representations, e.g. Relational Graph
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14.Apr.2015Andreas Fischlin, ETH Zurich
A Relational Graph Is
Following tuple of sets:
S = (X , R) = (XI, XD, XO, RI, RID, RD, RDO, RO, RIO)
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14.Apr.2015Andreas Fischlin, ETH Zurich
Where do you get the better overview? Judge yourself!P Population NR Natural Resources CI Capital Investment CIAF Capital Investement in Agriculture Fraction POL Pollution
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14.Apr.2015Andreas Fischlin, ETH Zurich
Where do you get the better overview? Judge yourself!
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14.Apr.2015Andreas Fischlin, ETH Zurich
Overhead Slides
Ex. ForClim and EPOVIR
Relational Graph Useful Ex Post
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14.Apr.2015Andreas Fischlin, ETH Zurich
State Variable Representations
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14.Apr.2015Andreas Fischlin, ETH Zurich
Important Model Properties• Time (continuous vs. discrete)!
• Deterministic vs. stochastic!
• Linear vs. non-linear!
• Ordinary vs. partial differential equations (concentrated vs. distributed parameters)!
• Canonical vs. non-canonical forms!
• Autonomous vs. non-autonomous system!
• Reachability, observability and controllability!
• Complexity
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14.Apr.2015Andreas Fischlin, ETH Zurich
Ordinary Difference and Differential Equation Systems
System Re-presentations
Continuous timet ∈ ℜ
Discrete timek = 0,1,2,...
Input vector
State vector
System order
Output vector
Derivative vector
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14.Apr.2015Andreas Fischlin, ETH Zurich
Model of Time
Overhead Slide
Model of Time
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14.Apr.2015Andreas Fischlin, ETH Zurich
Canonical Form of Linear Systems
Ex.: Exponential Growth:
Ex.: Proportional controller (negative feedback):
Continuous timet ∈ ℜ
Discrete timek = 0,1,2,...
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14.Apr.2015Andreas Fischlin, ETH Zurich
Canonical Form of Non-linear Systems
Overhead Slides
Canonical Form Non-linear Systems
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14.Apr.2015Andreas Fischlin, ETH Zurich
Overview 14. April 2015
Fundamentals of System Theory!
!Modeling!
System Representations