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

Outline 1 The topic 2 Decision support systems 3 Modeling 3.2 Numerical models  “Classical” numerical models  Utility  and limitations Model-Based Systems & Qualitative Reasoning WS 14/15 EMDS 3 - 34 Group of the Technical University of Munich

Ecological Modeling and Decision Support Systems Populations and Impact on Populations Model-Based Systems & Qualitative Reasoning WS 14/15 EMDS 3 - 35 - 35 Group of the Technical University of Munich

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 WS 14/15 EMDS 3 - 36 Group of the Technical University of Munich

Influences on Population Size  Birth  Death  Movement – Emigration – Immigration Model-Based Systems & Qualitative Reasoning WS 14/15 EMDS 3 - 37 Group of the Technical University of Munich

Life History (of Unitary Organisms) The basic pattern: sequence  Juvenile phase (growth of individual organism)  Reproductive phase  Post-reproductive phase Reproductive output Reproductive phase Post- reproductive Juvenile phase phase birth death Model-Based Systems & Qualitative Reasoning WS 14/15 EMDS 3 - 38 Group of the Technical University of Munich

Qualitative Types of Life Histories  Iteroparous species: repeated breeding – seasonal – continuous  Semelparous species: breeding only once Reproductive phase Juvenile phase Year 1 Year 2 Year 3 Year 4 Year 5 Year 1 Year 2 Year 3 Death Juvenile phase Year 1 Year 2 Year 3 Year n Death Model-Based Systems & Qualitative Reasoning WS 14/15 EMDS 3 - 39 Group of the Technical University of Munich

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 WS 14/15 EMDS 3 - 40 Group of the Technical University of Munich

Population Growth  N: number of individuals in population N  N(t) = ?  dN/dt = ?  New individuals not by transformation of ? material  Reproduction of existing individuals t  r: intrisic rate of natural increase,  i.e. reproduction rate per individual ObservedPopulation trout • dN/dt = r*N X X  N(t) = e r*t X X X X X X X  Realistic? X t Model-Based Systems & Qualitative Reasoning WS 14/15 EMDS 3 - 41 Group of the Technical University of Munich

Ecological Modeling and Decision Support Systems Population Growth and Intraspecific Competition Model-Based Systems & Qualitative Reasoning WS 14/15 EMDS 3 - 42 - 42 Group of the Technical University of Munich

Population Growth with Intraspecific Competition  Individual organisms compete for resources 1/N* dN/dt  Net rate equals r only for small population r  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)] N K  “logistic equation” N K  Realistic?  Why linear decrease?  What influences the function? t Model-Based Systems & Qualitative Reasoning WS 14/15 EMDS 3 - 43 Group of the Technical University of Munich

Intraspecific Competition  Indirectly, via resource depletion: exploitation  Directly, actively, by fighting: interference competition  Effects can be density-dependent Model-Based Systems & Qualitative Reasoning WS 14/15 EMDS 3 - 44 Group of the Technical University of Munich

“Capturing the Essence of Ecological Processes”? “ … a pattern generated by such a model … is 1/N* dN/dt not of interest, or important, because it is generated by the model. … Rather, the r 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 K N  dN/dt = rN*[1 – (N/K)] ??? K  Yes, it may reflect the processes  But leaves them implicit!  Where is “birth”, “competition”, “death”, … ? t Model-Based Systems & Qualitative Reasoning WS 14/15 EMDS 3 - 45 Group of the Technical University of Munich

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 ObservedPopulation trout ObservedPopulation trout X X X X X X X X X X ObservedPopulation trout X X X X X X X X X X t X X X X t X X X X X X t Model-Based Systems & Qualitative Reasoning WS 14/15 EMDS 3 - 46 Group of the Technical University of Munich

Ecological Modeling and Decision Support Systems Population Growth and Interspecific Competition Model-Based Systems & Qualitative Reasoning WS 14/15 EMDS 3 - 47 - 47 Group of the Technical University of Munich

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 WS 14/15 EMDS 3 - 48 Group of the Technical University of Munich

Lotka-Volterra Model of Interspecific Competition  Two species with size N 1 , N 2  In dN/dt = rN*[1 – (N/K)]:  N  N 1 + N 2 ?  Competitive effect can be different!  E.g. hyena vs. vulture vs. jackal  a 12 = 1/ n 2 : competition coefficient  n 2 individuals of species 2 have same competitive effect on species 1 as one individual of species 1  N  N 1 + a 12 *N 2  dN 1 /dt = r*N 1 *[1 – (N 1 + a 12 *N 2 )/K 1 )]  dN 2 /dt = r*N 2 *[1 – (N 2 + a 21 *N 1 )/K 2 )]  Lotka-Volterra model Model-Based Systems & Qualitative Reasoning WS 14/15 EMDS 3 - 49 Group of the Technical University of Munich

Population Change from Lotka-Volterra  dN 1 /dt = r*N 1 *[1 – (N 1 + a 12 *N 2 )/K 1 )]  No change: dN 1 /dt = 0   K 1 – N 1 – a 12 *N 2 = 0   N 1 = K 1 – a 12 *N 2  “zero isocline ”  separates two regions: N 1 increasing/decreasing K 1 K 2 α 12 N 2 N 2 K 2 / α 21 K 1 N 1 N 1 Model-Based Systems & Qualitative Reasoning WS 14/15 EMDS 3 - 50 Group of the Technical University of Munich

Result of Interspecific Competition  Combination of the diagrams  Depends on relative positions of zero isoclines  Case 1: K 1 > K 2 * a 12  K 1 * a 21 > K 2  Combine vectors N 2 K 1 α 12 K 1 K 2 α 12 K 2 N 2 N 2 N 1 K 2 / α 21 K 2 / α 21 K 1 K 1 N 1 N 1 Model-Based Systems & Qualitative Reasoning WS 14/15 EMDS 3 - 51 Group of the Technical University of Munich

Result of Interspecific Competition – Other Cases  K 1 < K 2 * a 12  K 1 * a 21 < K 2  K 1 > K 2 * a 12  K 1 * a 21 < K 2  K 1 < K 2 * a 12  K 1 * a 21 > K 2 K 2 K 1 K 2 α 12 K 1 α 12 K 2 K 1 α 12 N 2 N 2 N 2 K 2 / α 21 K 2 / α 21 K 2 / α 21 K 1 K 1 K 1 N 1 N 1 N 1 Model-Based Systems & Qualitative Reasoning WS 14/15 EMDS 3 - 52 Group of the Technical University of Munich

Lotka-Volterra: One Species Stronger Interspecific Competitor  Case 1: K 1 > K 2 * a 12  K 1 * a 21 > K 2  Intraspecific competition within species 1 more effective than interspecific competition exerted by species 2  Interspecific competition of species 1 on N 2 species 2 stronger than intraspecific K 1 competition of species 2 α 12  Species 2  extinction K 2  Case 2: dual case N 1 K 2 / α 21 K 1 Model-Based Systems & Qualitative Reasoning WS 14/15 EMDS 3 - 53 Group of the Technical University of Munich

Lotka-Volterra: Weak Interspecific Competition  Case 3: K 1 > K 2 * a 12  K 1 * a 21 < K 2  Interspecific competition is weaker than intraspecific competition for both species  Coexistence of both species K 1 α 12 K 2 N 2 K 2 / α 21 K 1 N 1 Model-Based Systems & Qualitative Reasoning WS 14/15 EMDS 3 - 54 Group of the Technical University of Munich

Lotka-Volterra: Strong Interspecific Competition  Case 4: K 1 < K 2 * a 12  K 1 * a 21 > K 2  Interspecific competition is stronger than intraspecific competition for both species  Surviving species depends on initial conditions K 2 K 1 α 12 N 2 K 2 / α 21 K 1 N 1 Model-Based Systems & Qualitative Reasoning WS 14/15 EMDS 3 - 55 Group of the Technical University of Munich

Ecological Modeling and Decision Support Systems Prey-Predator Model Model-Based Systems & Qualitative Reasoning WS 14/15 EMDS 3 - 56 - 56 Group of the Technical University of Munich