Outline 1 The topic 2 Decision support systems 3 Modeling 3.2 - - PowerPoint PPT Presentation

Model-Based Systems & Qualitative Reasoning Group of the Technical University of Munich

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Outline

 “Classical” numerical models  Utility  and limitations 1 The topic 2 Decision support systems 3 Modeling 3.2 Numerical models

Model-Based Systems & Qualitative Reasoning Group of the Technical University of Munich

WS 14/15 EMDS 3 - 35

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Ecological Modeling and Decision Support Systems Populations and Impact on Populations

Model-Based Systems & Qualitative Reasoning Group of the Technical University of Munich

WS 14/15 EMDS 3 - 36

Evolution of a Population

 Population: set of individual organisms of one species  Species: class of organisms – Can breed together – Produce fertile descendants  Individual organism: – Clear for unitary organisms – ?? Modular organisms (herbs, fungi, coral, …)

Model-Based Systems & Qualitative Reasoning Group of the Technical University of Munich

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Influences on Population Size

 Birth  Death  Movement – Emigration – Immigration

Model-Based Systems & Qualitative Reasoning Group of the Technical University of Munich

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Life History (of Unitary Organisms)

The basic pattern: sequence  Juvenile phase (growth of individual organism)  Reproductive phase  Post-reproductive phase Reproductive output birth death Juvenile phase Reproductive phase Post- reproductive phase

Model-Based Systems & Qualitative Reasoning Group of the Technical University of Munich

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Qualitative Types of Life Histories

 Iteroparous species: repeated breeding – seasonal – continuous  Semelparous species: breeding only once Juvenile phase Reproductive phase Year 1 Year 2 Year 3 Year 4 Year 5 Death Year 1 Year 2 Year 3 Year 1 Year 2 Year 3 Death Juvenile phase Year n

Model-Based Systems & Qualitative Reasoning Group of the Technical University of Munich

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Motion of Organisms

Dispersal:  motion of individuals of a species relative to each other, in one area  E.g. seeds of a tree; male elephants w.r.t. the herd  Affects spatial distribution, not size of population  Can be density-dependent – away from high density (declining resources) – away from low density (avoid inbreeding) Migration:  directed mass movement of individuals between areas  E.g. elephant herd to water resources; eels to Sargasso Sea  Impact on population  Mainly away from declining resources

Model-Based Systems & Qualitative Reasoning Group of the Technical University of Munich

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Population Growth

t

N ObservedPopulationtrout

t

X X X X X X X X X X

 N: number of individuals in population  N(t) = ?  dN/dt = ?  New individuals not by transformation of material  Reproduction of existing individuals  r: intrisic rate of natural increase,  i.e. reproduction rate per individual

• dN/dt = r*N

 N(t) = er*t  Realistic?

?

Model-Based Systems & Qualitative Reasoning Group of the Technical University of Munich

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• 42

Ecological Modeling and Decision Support Systems Population Growth and Intraspecific Competition

Model-Based Systems & Qualitative Reasoning Group of the Technical University of Munich

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Population Growth with Intraspecific Competition

 Individual organisms compete for resources  Net rate equals r only for small population  Resources limit population size  K: maximal capacity  Assumption: linear decrease of the rate   1/N*dN/dt = r - (r/K)N   dN/dt = rN*[1 – (N/K)]  “logistic equation”

N

1/N* dN/dt

r K t

N

K

 Realistic?  Why linear decrease?  What influences the function?

Model-Based Systems & Qualitative Reasoning Group of the Technical University of Munich

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Intraspecific Competition

 Indirectly, via resource depletion: exploitation  Directly, actively, by fighting: interference competition  Effects can be density-dependent

Model-Based Systems & Qualitative Reasoning Group of the Technical University of Munich

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“Capturing the Essence of Ecological Processes”?

“ … a pattern generated by such a model … is not of interest, or important, because it is generated by the model. … Rather, the point about the pattern is that it reflects important, underlying ecological processes – and the model is useful in that it appears to capture the essence of those processes.” (Townsend et al., Essentials of Ecology)

N

1/N* dN/dt

r K t

N

K

 dN/dt = rN*[1 – (N/K)] ???  Yes, it may reflect the processes  But leaves them implicit!  Where is “birth”, “competition”, “death”, … ?

Model-Based Systems & Qualitative Reasoning Group of the Technical University of Munich

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Extracting Models from Data?

 Many ways to fit a curve …  (Unknown) limits of the model  Knowledge, i.e. the model, determines interpretation  (Numerical) proximity vs. qualitative properties ObservedPopulationtrout

t

X X X X X X X X X X

ObservedPopulationtrout

t

X X X X X X X X X X

ObservedPopulationtrout

t

X X X X X X X X X X

Model-Based Systems & Qualitative Reasoning Group of the Technical University of Munich

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• 47

Ecological Modeling and Decision Support Systems Population Growth and Interspecific Competition

Model-Based Systems & Qualitative Reasoning Group of the Technical University of Munich

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More Competition …

 Not only intraspecific competition  Competition between different species  E.g. trout and Galaxias compete for invertebrates  dN/dt = rN*[1 – (N/K)] reflects intraspecific competition

Model-Based Systems & Qualitative Reasoning Group of the Technical University of Munich

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Lotka-Volterra Model of Interspecific Competition

 Two species with size N1, N2  In dN/dt = rN*[1 – (N/K)]:  N  N1 + N2?  Competitive effect can be different!  E.g. hyena vs. vulture vs. jackal  a12 = 1/ n2 : competition coefficient  n2 individuals of species 2 have same competitive effect on species 1 as one individual

• f species 1

 N  N1 + a12*N2  dN1 /dt = r*N1 *[1 – (N1 + a12*N2)/K1)]  dN2 /dt = r*N2 *[1 – (N2 + a21*N1)/K2)]  Lotka-Volterra model

Model-Based Systems & Qualitative Reasoning Group of the Technical University of Munich

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N1 N2

Population Change from Lotka-Volterra

 dN1/dt = r*N1*[1 – (N1 + a12*N2)/K1)]  No change: dN1/dt = 0   K1 – N1 – a12*N2 = 0   N1 = K1 – a12*N2  “zero isocline”  separates two regions: N1 increasing/decreasing

K1 K1 α12 K2/α21 N1 N2 K2

Model-Based Systems & Qualitative Reasoning Group of the Technical University of Munich

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Result of Interspecific Competition

 Combination of the diagrams  Depends on relative positions of zero isoclines  Case 1: K1 > K2*a12  K1*a21 > K2  Combine vectors

K1 N1 N2 K1 α12 K2/α21 N1 N2 K2 K1 N1 N2 K1 α12 K2 K2/α21

Model-Based Systems & Qualitative Reasoning Group of the Technical University of Munich

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Result of Interspecific Competition – Other Cases

 K1 < K2*a12  K1*a21 < K2  K1 > K2*a12  K1*a21 < K2  K1 < K2*a12  K1*a21 > K2

K1 N1 N2 K1 α12 K2 K2/α21 K1 N1 N2 K1 α12 K2 K2/α21 K1 N1 N2 K1 α12 K2 K2/α21

Model-Based Systems & Qualitative Reasoning Group of the Technical University of Munich

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Lotka-Volterra: One Species Stronger Interspecific Competitor

 Case 1: K1 > K2*a12  K1*a21 > K2  Intraspecific competition within species 1 more effective than interspecific competition exerted by species 2  Interspecific competition of species 1 on species 2 stronger than intraspecific competition of species 2  Species 2  extinction  Case 2: dual case

K1 N1 N2 K1 α12 K2 K2/α21

Model-Based Systems & Qualitative Reasoning Group of the Technical University of Munich

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Lotka-Volterra: Weak Interspecific Competition

 Case 3: K1 > K2*a12  K1*a21 < K2  Interspecific competition is weaker than intraspecific competition for both species  Coexistence of both species

K1 N1 N2 K1 α12 K2 K2/α21

Model-Based Systems & Qualitative Reasoning Group of the Technical University of Munich

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Lotka-Volterra: Strong Interspecific Competition

 Case 4: K1 < K2*a12  K1*a21 > K2  Interspecific competition is stronger than intraspecific competition for both species  Surviving species depends on initial conditions

K1 N1 N2 K1 α12 K2 K2/α21

Model-Based Systems & Qualitative Reasoning Group of the Technical University of Munich

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Ecological Modeling and Decision Support Systems Prey-Predator Model

Model-Based Systems & Qualitative Reasoning Group of the Technical University of Munich

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Predator-Prey Model – Prey

 Prey, more generally: resource organism (also plants)  Population size: N  Assumed: (exponential) growth without predation  dN/dt = r*N  Rate of predation: proportional to – N – P (population size predator) – a: efficiency of predation   dN/dt = r*N – a*P*N

Model-Based Systems & Qualitative Reasoning Group of the Technical University of Munich

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Predator-Prey-Model – Predator

 Assumed: (exponential) decline without food:  dP/dt = -q·P  Impact of predation proportional to – a*P*N (rate of predation) – f: predation impact on reproduction   dP/dt = f*a*P*N – q*P

Model-Based Systems & Qualitative Reasoning Group of the Technical University of Munich

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Lotka-Volterra Predator-Prey Model

 dN/dt = r*N – a*P*N  dP/dt = f*a*P*N – q*P Isoclines  P = r/a  N = q/(f*a) Time P N P N r a N P P N

q f*a

Model-Based Systems & Qualitative Reasoning Group of the Technical University of Munich

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Ecological Modeling and Decision Support Systems Numerical Modeling – Examples and Limitations

Model-Based Systems & Qualitative Reasoning Group of the Technical University of Munich

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System Dynamics Modeling

 Simulistics: http://www.simulistics.com/overview.htm

Model-Based Systems & Qualitative Reasoning Group of the Technical University of Munich

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Exercise: Construct a Model of Vulture Population

Adult vultures in year t, Nt Survival Maturation and survival Adult vultures in year t-1, Nt-1 Vulture births in year t-5 Baseline survival, S Probability of carcasses with diclofenac, C Effect of diclofenac Rate at which carcasses are eaten, F

Model-Based Systems & Qualitative Reasoning Group of the Technical University of Munich

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The Lomba Reservoir (Porto Alegre)

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Algal Bloom

Model-Based Systems & Qualitative Reasoning Group of the Technical University of Munich

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Algal Bloom

Model-Based Systems & Qualitative Reasoning Group of the Technical University of Munich

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A Numerical Model of Algal Bloom

P d P e H I I I I P d P e H I I I I

T s s T s s

=    + > =    

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1 1 24 1

20 20 20 20 max, ( ) max, ( )

(ln( ) ), ,

a a

e e fall s falls

 P: production rate  Pmax,20: maximal production rate at 20º C  d: length of the day  Is: intensity of light at saturation of growth  I0: intensity of light at surface  a: temperature coefficient  ε: light reduction coefficient  H: depth

Model-Based Systems & Qualitative Reasoning Group of the Technical University of Munich

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Model Re-Use and Adapation - Requirements

P d P e H I I I I P d P e H I I I I

T s s T s s

=    + > =    

• 24

1 1 24 1

20 20 20 20 max, ( ) max, ( )

(ln( ) ), ,

a a

e e fall s falls

 Can (part of) the model be reused/adapted/complemented?  Decomposition into elementary fragments  Conceptual model  Preconditions/modeling assumptions  Turbidity? Suspended Solids? Distribution?  Wind, waves  Nutrients  Limits Light - duration Light - intensity Temperature Depth

Model-Based Systems & Qualitative Reasoning Group of the Technical University of Munich

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Ecological Modeling - Requirements

P d P e H I I I I P d P e H I I I I

T s s T s s

=    + > =    

• 24

1 1 24 1

20 20 20 20 max, ( ) max, ( )

(ln( ) ), ,

a a

e e fall s falls

 Support for establishing the model   requires a conceptual model  Numerical model: only an approximation  Qualitative knowledge and information   qualitative model  Re-usability of the model   compositional model   model libraries

Model-Based Systems & Qualitative Reasoning Group of the Technical University of Munich

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Summary

 “Classical” numerical models  Utility  and limitations 1 The topic 2 Decision support systems 3 Modeling 3.2 Numerical models