introduction/basic terms • systems ecology case studies: motto … · 2015-04-14 · theory is...

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


Overview 14. April 2015

Fundamentals of System Theory!

!Modeling!

System Representations

14.Apr.2015

Fundamentals of System Theory

• Modelling!• Systems Representations!• Simulation!• Stability and Stability Analysis

Andreas Fischlin, ETH Zurich


The System In the Ecosystem?


What Type of System?


What Type of System?

Massachusetts Institute of Technology, 2007. The Large Scale Network Analysis Project. web.mit.edu/networks/visualizations.html


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!


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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1 Modelling!

!

!

• Top down vs. bottom up!

• Mathematical Derivation of Model Equations vs. «System Dynamics» Approach


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„Systems“ Thinking


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„Systemic“ Thought


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The more complex the more stable!


Really?

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Lord Robert M. May !

made ecologists aware that complexity, e.g. biodiversity, does not imply stability


May, R.M., 1972. Will a large complex system be stable? Nature, 238: 413-414

14.Apr.2015

Top-Down vs. Bottom-Up


14.Apr.2015

Top-Down vs. Bottom-Up


MakroskopischeSicht

MikroskopischeSicht

see also Overhead Slide

Macroscopic view

Microscopic view

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Bottom-Up• Given starting points!

• Oriented towards discipline traditions


• 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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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.


Both can be justified, but only side by side!

14.Apr.2015

Mathematical Derivation of Model Equations vs. «System

Dynamics» Approach



“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


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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Spectrum of Systems


Overhead Slide

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Spatial and temporal scales correlated


Holling, 1992

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The Modeling Dilemma


Generality

Precision Realism


2 System Representations

• Qualitative Representations, e.g. Relational Graph "

• State Variable Representations


Qualitative Representations, e.g. Relational Graph


A Relational Graph Is

Following tuple of sets:

S = (X , R) = (XI, XD, XO, RI, RID, RD, RDO, RO, RIO)


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


Where do you get the better overview? Judge yourself!


Overhead Slides

Ex. ForClim and EPOVIR

Relational Graph Useful Ex Post


State Variable Representations


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


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


Model of Time

Overhead Slide

Model of Time


Canonical Form of Linear Systems

Ex.: Exponential Growth:

Ex.: Proportional controller (negative feedback):

Continuous timet ∈ ℜ

Discrete timek = 0,1,2,...


Canonical Form of Non-linear Systems

Overhead Slides

Canonical Form Non-linear Systems


Overview 14. April 2015

Fundamentals of System Theory!

!Modeling!

System Representations

introduction/basic terms • systems ecology case studies: motto … · 2015-04-14 · theory is...

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