Towards Structurally Realistic Models: Pattern-oriented Modelling Volker Grimm, UFZ Umweltforschungszentrum Leipzig-Halle Sektion Ökosystemanalyse

Contents „philosophies“ of modelling The „Medawar“ zone Pattern-oriented Modelling (POM) Examples (short) Benefits of POM Discussion

Literature Grimm (1994) Ecol Model 75/76: 641 Grimm et al. (1996) Sci Total Env 183:151 Grimm (2001) [German] Railsback (2001) Nat Res Model14: 465 Grimm and Berger (2002) (in press) DeAngelis and Mooij (2002) (in press) Railsback and Harvey (2002) Ecology 83:1817 Wiegand et al. (2002) Oikos (in press) Wiegand et al. (2002) Biodiv Conserv (in press) Grimm et al. (in preparation)...

Philosophies of modelling Old distinction: strategic vs. tactical Holling 1966, May 1974 analytical solutionssimulations no detailsmany details understandingtoo complicated theoryno theory goodbad strategic complexity tactical payoff

However: strategic models: Often untestable because of being so abstract „Glasperlenspiele“ in the realm of logical possibilities? Tautologies? Provide little insight in what really is going on in real systems Nowadays: new tools individual-based, grid-based, rule-based models (bottom-up) Chance, to adjust model resolution to the problem/system But how to find the „right“ resolution of a bottom-up model?

The „Medawar“ zone Loehle, C A guide to increased creativity in research - inspiration or perspiration? BioScience, 40:

The „Medawar“ zone complexity payoff It should be possible to find a range of optimal „resolution“ (level of detail, complexity, richness in structure and mechanism), i.e. neither too simple nor too complex, but just „right“. Optimal: theory + testable predictions = insights about the real world. Question: Who tells us how to find the Medawar zone? Answer: Mother nature herself!

Patterns Patterns = everything beyond random variation Patterns indicate underlying (key-)processes and structures, which generate the patterns Patterns contain information about (key-)processes and structures - but in a „coded“ way Modelling means to „decode“ the patterns of a system If we do this right, the model will be in the Medawar zone and will be structurally realistic.

Patterns? Of course, what else? General research program of (natural) sciences: trying to decode patterns. atomic spectraatomic spectra Kepler’s lawsKepler’s laws Iridium layerIridium layer Chargaff’s rulesChargaff’s rules cyclescycles spatial patternsspatial patterns species-area relationshipspecies-area relationship patch dynamicspatch dynamics... (not too many)... (not too many)

Problem: one pattern is not sufficient For example: Cycles Often, it is rather easy to reproduce one single pattern Different mechanisms (models) reproduce the same pattern A single pattern is usually not sufficient to narrow down model structure Hare-lynx cycles: Additional patterns: constant period, but chaotically varying amplitudes Model structure was narrowed down (Blasius et al. 1999; Kendall et al. 1999)

Pattern-oriented modelling 1. Explicit: question or problem to be tackled. Iter. 2.Formulate (verbally, graphically) a model which reflects the current understanding of the system = assemble working hypotheses (data, empirical knowledge, theory). Iter. 3. Identify patterns at different hierarchical levels, e.g. behaviour of individuals or local spatial units, system-level patterns. Don‘t focus exclusively on „strong“ patterns, but think of anything which distinguishes the system. Iter. 4. Provide a model structure (states, variables, space, stochastics, mechanisms, processes, attributes, etc.) which - in principle - allows that the patterns emerge also in the model. Iter. 5. Implement the model (based on 2. and 4.) and try and see if one or more patterns are reproduced. Iter Iter Iter. 6.Try and identify the minimum model which reprodes all the patterns SIMULTANEOUSLY. 7. Try and answer the original question of the model. 8.Search for independent prediction.

Example 1: Beech forest model Objective of the model: Spatio-temporal dynamics of natural beech forests How large must a natural beech forest be to allow for typical structures and dynamics What drives the dynamics? First model (Wissel 1992): Cellular automaton: local cyclic succession plus neighbour interaction via „sunburning“. Model reproduces mosaic pattern of beech forest. Nice demonstration, but nobody was really convinced.

Example 1: Beech forest model New model (Neuert, Grundmann, Wissel, Rademacher, Grimm) BEFORE: Pattern 1: mosaic pattern Neuer 1999, Neuert et al. 2001, Rademacher et al. 2001

Example 1: Beech forest model New model (Neuert, Grundmann, Wissel, Rademacher, Grimm) BEFORE: Pattern 2: local stand development distinguished by typical patterns in vertical structure 1. Growing stage Many young trees, few old ones, trees in all vertical layers 2. Optimal stage („Hallenwald“) Closed canopy, no understory, little mortality, wood biomass maximal (=typical managed forest of about 100 years) 3. Decaying stage Canopy trees die successively (age, storms), canopy gaps, emergence of lower layers

1-8 trees, each 1-8 units large individual-based 1-8 trees, each 1 unit large individual-based % cover m - 20 m - 30 m - 40 m Provide model structure which allows - in principle - the vertical pattern to emerge:

Local processes (within cells; shading and shade tolerance); and: Neighbourhood processes:

Results of BEFORE Cover in layers Stages within cellsStages (moving average)

Richness in model structure and mechanisms

Allowed for independent predictions regarding distribution of „giant“ trees Allowed for independent predictions regarding distribution of „giant“ trees Rademacher et al Allowed to augment the model by modules addressing dead wood (woody debris) Allowed to augment the model by modules addressing dead wood (woody debris) in prep. complexity payoff W ´BEFORE

Example 2: stream trout model In a stream trout model, three different „theories“ on habitat choice were available, one based on a classical model of habitat choice. To filter out the most appropriate theory, the following six behavioural patterns, drawn from the literature, were used: 1. The dominant fish aquires the best feeding site; if removed, the next dominant fish moves up the hierarchy. 2. During flood flows, adult trout move to the stream margins where stream velocities are low. 3. Juvenile trout use higher velocities when competing with larger trout. 4. Juvenile trout use faster and shallower habitats in the presence of predatory fish. 5. Trout use higher velocities on average when temperatures are higher. 6. When general food availability is decreased, trout shift to habitat with higher mortality risks but also higher food intake. Only one of the theories was able to reproduce all six patterns simultaneously. Railsback (2001) Nat Res Model14: 465 Railsback and Harvey (2002) Ecology 83:1817

Structural realism Using multiple patterns for deciding on model structure leads to models, which are „structurally realistic“, i.e. they capture the essenced of the (hierarchical) structure of the system so rich in structure and mechanisms that they allow for independent predictions are easily adjusted to other problems regarding the same system („cranking out papers“) Komplexität payoff

Benefits of POM models Structural realism Applicable to situations beyond the situation which was used for the original parameterisation (in contrast to fitting a model) Easier to understand and communicate because you are dealing with key structures and processes Model structure is less ad hoc, but narrowed down by the patterns Patterns may also be used to indirectly determine parameters (fitting of structurally realistic model to multiple patterns) Wiegand et al a/b

Limitations and pitfalls A model is a model is a model !!! Distrust patterns: human minds are inclined to perceive patterns everywhere Be careful not to hardwire the patterns in the model structure („imposed behaviour“) Railsback 2001 (POM is not restricted to bottom-up models, but also powerful with analytically formulated models)

Summary Pattern-oriented modelling is good for you!