The Application of Ecological and Environmental Models in Management and Research

1. The Application of Ecological and Environmental Models in Management and Research Sven Erik Jørgensen, DFU, Environmental Chemistry, University Park 2, Copenhagen Ø, 2100,Denmark sej@dfuni.dk

6. Advantages of Modelling: • Models are synthesis of all what we know- observations, theoretical knowledge, knowledge about rates and sizes, knowledge about food items etc. • Models are tools to overview complex systems • Models make it possible to quantify by the use of mathematical formulations and computers

10. Progress 72-88 • A fixed procedure • Different models for different systems and problems - generality only to a certain extent • Balanced complexity observations / system / problems, • Better descriptions of processes and better parameter values • Acceptable validation results, even of prognoses • Ecosystem properties should be included in the model, but how? Flexibility, adaptability, and individuality.

11. Bio-geo-chemical models5: >100 models, 4: 25-99 models, 3: 10-25 models,2: 4-9 models, 1: 1-2 models, 0: No models • Ecosystem # of models • Rivers, lakes, lagoons, estuaries 5 • Wetlands, agricultural land 5 • Forests, fjords, bays 5 • Open sea, national parks, grassland 4 • Savanna, mountain land 2 • Desert, artic/anartic system 1 • Mountain land above timberline 0

12. Bio-geo-chemical models5: >100 models, 4: 25-99 models, 3: 10-25 models,2: 4-9 models, 1: 1-2 models, 0: No models Problems # of models Oxygen depletion, eutrophication 5 Pesticides, acid rain, groundwater pollution 5 Global warming, ERA (toxic substances) 5 Heavy metals, ozone layer, endangered sp. 4 Health / pollution 3 Endocrine disruptors, microclimate 2

16. Adjencency Matrix • From/to 1 2 3 4 5 6 7 • 1 1 0 0 0 0 0 • 2 0 1 0 1 1 0 • 3 0 0 1 1 0 1 • 4 0 0 0 1 0 0 • 5 0 0 0 0 0 1 • 6 0 0 0 0 0 1 • 7 1 1 0 0 0 0

17. A Model consists of the following elements: • State variables describing the state of the system (internal variables) • Forcing functions describing the external impact on the system (external variables) • Equations describing the processes • Parameters (coefficients in the equations) • Constants (physical and chemical)

23. The idea behind the use of differential equations

24. Table Process rate equations Expression Mathematical formulation Application of the process rate expression ________________________________________________________ Zero order rate = k = constant supply is constant f. inst. film kinetics First order rate = k * variable Decomposition of organic matter, decay of radioactive components, exponential population growth Second order rate = k*conc1*conc2 Chemical and biochemical reactions, where the process is based on a reaction of two different components. Monod kinetics rate = k* st.var./ (st.var. + km) Plant growth by limiting nutrient (Liebig’s law) and growth of organisms or populations limited by the food source, f. inst. grazing. Logistic growth rate = k*st.var.* (1 – st.var. / carrying capacity) Growth, where the rate at high values of the st. var. is regulated by another regulation factor Conc. Gradients rate = k * dC /dx Diffusion processes _________________________________________________________

25. Michelis-Menten’s equation

26. 1.Is the model stable in the long term? The model is run for a long period with the same annual variations in the forcing functions to observe whether the values of the state variables are maintained at approximately the same levels. This question presumes that real ecosystems are long term stable, which is not necessarily the case. 2.Does the model react as expected? If the input of for instance toxic substances is increased, we should expect a higher concentration of the toxic substance in the top-carnivore. . This question assumes that we actually know at least some reactions of ecosystems, which is not always the case. In general, playing with the model is recommended at this phase. Through such exercises the modeller gets acquainted with the model and its reactions to perturbations. Models are an experimental tool. The experiments are carried out to compare model results with observations and changes of the model are made according to the modeller's intuition and knowledge of the reactions of the models. 3. It is strongly recommendable to check all the applied units at this phase of model development. Check all equations for consistency of units. Are the unit the same on both sides of the equation sign?

27. Sensitivity • It is possible to examine the sensitivity of parameters, forcing functions or exchange of one equation with another one. • Definition: Sensitivity = Relative change in state variable divided with the corresponding relative change in parameter, for instance: • (D st. var. / st. var )/ (D parameter/ parameter)

28. Example of sensitivity analysis: a eutrophication model with 19 state variables: Parameter (D=10%) State variable Value Growth rate phytoplankton Phytoplankton 0.488 Growth rate phytoplankton Zooplankton 0.620 Growth rate phytoplankton Nitrate-N 0.356 Growth rate zooplankton Zooplankton 2.08 Growth rate zooplankton Phytplankton 4.02 Denitrification rate Phytoplankton 0.190 Denitrification rate Zooplankton 0.110 Denitrification rate Nitrate-N 0.579

43. The spline equation found by very frequent measurements can be applied to find parameters>: • Phyt = a +b time +c time^2 + d time^3 • +e time^4 ….., it means that • dPhyt / dt 0 b + 2c time + 3d time^2 + 4e time^3………In the differential equation • dPhyt / dt = maxgr*Phyt*min (PS / (PS + kp), NS / ( NS + kn)) – sed*Phyt …. • Phyt, PS, NS and even dPhyt / dt are known • As unknown we can use maxgr, kp, kn, sed

45. Classification of Model / model pairs • 1) Management / Research models • 2) Steady state / dynamic models • 3) Deterministic / Stochastic models • 4) Linear / non-linear models • 5) Lumped models / Distributed models (in time and space) • 6) Reductionistic / holistic models

47. CLASSIFICATION OF MODELS Type Organization Pattern Measurements __________________________________________________ Population Conservation Life cycles # individuals Dynamics of genes __________________________________________________ Bioenergetic Energy conserv. Energy flow Energy __________________________________________________ Biogeoche- Mass conserv. Mass flow Mass or mical concentr. __________________________________________________

48. Institutionalized or mediated modelling (IMM) • The conceptual model is built by a team consisting of all interested parties (environmental managers, scientists, NGO’s, organizations etc.). The scope of the model is discussed and the team agrees on the scope and how the system is working, the important processes, the important components and the conceptual diagram

49. Advantages of IMM • 1) the level of shared understanding increases • 2) a consensus is built about the structure of a complex problem for a complex system, because all interests are represented in the stepwise model development • 3) the result of the modelling process, the model, serves as a tool to disseminate the insights gained by the modelling procedure. • 4) the effectiveness of the decision making is increased • 5) team building is facilitated • 6) the process is emphasized over the product • 7) the knowledge state-of-the-art is captured and organized.

50. Thank you for your attention