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An introduction to some individual-based methods and to the exercises

An introduction to some individual-based methods and to the exercises. Wolf M. Mooij Netherlands Institute of Ecology. The logistic difference equation. N t+1 = r N t (1 - N t ).

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An introduction to some individual-based methods and to the exercises

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  1. An introduction to some individual-based methods and to the exercises Wolf M. Mooij Netherlands Institute of Ecology

  2. The logistic difference equation Nt+1 = r Nt (1 - Nt) Example of a deterministic, non-spatially explicit, unstructured, single species, population dynamical model based on difference equations

  3. Problem: Given the research question, how to find the right model from the many models currently around in ecology Need for a classification of models Disclaimer: the one presented here is just one of many possible classifications

  4. How many species do we want to take into account? • Single species • Prey predator • Tritrophic • Multispecies • Foodweb

  5. Which part of the life-cycle do we want to take into account? • Cohort-dynamics (only mortality) • Population-dynamics (incl. reproduction)

  6. Do we explicitly want to take space into account? • Spatially implicit • Spatially explicit -> at what scale?

  7. How do we want to deal with variation between individuals? • Unstructured model • Individual-based distribution model (matrix model, physiologically structured model) • Individual-based configuration model (individual-by-individual model)

  8. Do we want to take stochastic processes into account? • Deterministic model • Stochastic model

  9. Which mathematical format are we going to use? • Difference equations (including matrices) -> at what time scale • Differential equations (ordinary and partial) • Logical if-then rules

  10. The logistic model implemented as difference equation Nt+1 = r Nt (1 - Nt) • single species • population dynamical • spatially implicit • unstructured • deterministic • based on difference equations

  11. The logistic model implemented as differential equation dN/dt = r N (1 – N/K) • single species • population dynamical • spatially implicit • unstructured • deterministic • based on differential equations

  12. The big confusion between differential and difference equations: Euler integration Differential equation: dN/dt = r Nt (1 – Nt/K) Euler approximation: Nt+t = Nt + r Nt (1 – Nt/K) t Difference equation: Nt+1 = Nt + r Nt (1 – Nt/K) The latter two equations represent different models, especially when rates (r) are high!

  13. The Rosenzweig-MacArthur prey-predator model dV/dt = r V(1 – N/K) – a V P/ (H + V) dP/dt = a c V P/ (H + V) – m P • prey-predator • population dynamical • spatially implicit • unstructured • deterministic • based on differential equations

  14. Tritrophic, multispecies, and foodweb extensions of these lotka-volterra type of models • tritrophic, multispecies, foodweb • population dynamical • spatially implicit • unstructured • deterministic • based on differential equations

  15. The Scheffer et al. cohort-dynamics prey-predator model dF/dt = gmax F (1 – F/K) - N cref W2/3 F2/(F2 + H2) dN/dt = - m N (1–W/Wmax)p/((1–W/Wmax)p + Lcritp) dW/dt = e cref W2/3 F2 / (F2 + H2) – rref W2/3 • prey-predator • cohort-dynamics • spatially implicit • unstructured!!! • deterministic • based on differential equations

  16. The Scheffer et al. cohort-dynamics prey-predator model (version 1.00) dF/dt = gmax F (1 – F/K) – N C dN/dt = - m N Lp/(Lp + Lcritp) dW/dt = e C - R • prey-predator • cohort-dynamics • spatially implicit • unstructured • deterministic • based on differential equations

  17. The Scheffer et al. cohort-dynamics prey-predator model (version 1.01) dF/dt = gmax F (1 – F/K) – N C Pmort(Ni) = - m Lp/(Lp + Lcritp) dW/dt = e C - R • prey-predator • cohort-dynamics • spatially implicit • unstructured • stochastic • based on differential equations

  18. The Scheffer et al. cohort-dynamics prey-predator model (version 1.02) N dF/dt = gmax F (1 – F/K) –  Ci Pmort(Ni) = - m Lip/(Lip + Lcritp) dWi/dt = e Ci - Ri • prey-predator • cohort-dynamics • spatially implicit • individual-based (configuration with i individuals) • stochastic • based on differential equations

  19. The Scheffer et al. cohort-dynamics prey-predator model (version 1.03) N dF/dt = gmax F (1 – F/K) –  Ci Ni dNi/dt = - m Ni Lip/(Lip + Lcritp) dWi/dt = e Ci - Ri • prey-predator • cohort-dynamics • spatially implicit • individual-based (distribution with i classes) • deterministic • based on differential equations

  20. The Scheffer et al. cohort-dynamics prey-predator model deterministic stochastic unstructured v1.00 v1.01 structured v1.03 v1.02 Advantages and disadvantages of each approach will be discussed during the exercises

  21. Potential of each version • v1.00 (unstr, determ): Periodic die offs • v1.01 (unstr, stoch): Extinction probability • v1.03 (dist, determ): Fitness of strains • v1.02 (conf, stoch): Rate of strain replacement • Which model is best?

  22. Esa Ranta’s Large-scale synchronization model No ind. variation Ind. variation No Moran effect Synchronized Not synchronized Moran effect Synchronized Synchronized

  23. Nine layers in model construction and analysis • Language: C++, Visual-Basic • Libraries: Runga-Kutta integration, etc. • Frameworks: OSIRIS, EXCEL • Type: Prey-predator cohort model • Model: Scheffer et al. model • Version: Unstr./config./distr., determ./stoch. • Sensitivity: Parameter H • Scenario: Brown trout • Repetition: Demographic stochasticity

  24. OSIRIS: Object-oriented Simulation Framework for Individual-based Simulations “A personal solution to a shared problem” Developed and used as a personal research tool, now also used in cooperation with others Written in C++ (ca. 10000 lines) Main aspects: predefined simulation objects, event queue, standardized input and output Interface via EXCEL (through ASCII files)

  25. Five predefined simulation objects • Analyser (as many as there are analysis) • System (one only) • Habitat (as many as there are spatial units) • Population (as many as there are species) • Individual (as many as there are individuals)

  26. datatasks Analyser System Habitat Population Individual datatasks datatasks datatasks datatasks

  27. Simulating dynamics with an event queue state at time t dynamicsstate at time t+t task id 1 perform task 1 task id 3 task id 2 task id 2 task id 3 task id 1 task id 4 task id 4 task id 5 task id 5

  28. Excel Notepad Borland C++ E x e c u t a b l e Input workbook PCLake code Input files Log workbook Interface code Output workbook OSIRIS library Output files Tools library Report workbook

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