Online Resource 4: Data and analyses of list of state variables of selected AEMs.
The last step we take in our search for model diversity is the comparison of state variables for 23 different models that were selected based on information availability. A following step would be to compare the models by their mathematical formulations, but this will be beyond the scope of our comparison.
Method
Lists of state variables were collected for 24 different AEMs. Similarly to biodiversity research, each model is treated as study site and scored for the presence of different state variables as if they were species. The resulting binary table is analysed for model similarity by using Sørensen index (Sørensen 1948):
Here M and N are two different models. The result is a similarity matrix with Sørensen indices varying between 0 (no overlap between the models) and 1 (models are complete identical). Two types of analyses have been performed on the similarity matrix: first a clustering analysis by creating an hierarchical clustering tree (dendrogram) based on the unweighted average (Sokal 1958) and secondly the mean similarity of each model was tested (one-sample Monte-Carlo permutation test; 999 permutations) against the distribution of a null model (999 permutations) where variables were shuffled between models while keeping row and column totals constant. By doing so we were able to correct for model complexity as more complex models will, by default, have a higher chance to show overlap in state variables. To illustrate, two models having both a hundred state variables will have more variables in common by pure chance than two models that have only 2 state variables. By testing the actual similarity of each model against a null model we tested the hypothesis that the model is not more or less similar than would be expected based on the total number of state variables of that model and (dis)similarity with other models is in fact caused by the specific state variables of the given model.
Results
We found almost 550 unique state variables, divided over the water column compartment (63%), sediment compartment (27%) and marsh compartment (10%) (See online supplementary material). The number of state variables in each model varies from a few to more than hundred, but seems to level off around the 120 state variables (Figure 4 main text, grey bars at the right). It should be noted that in some (especially the larger) models not all state variables are always included simultaneously in each model application, but rather subsets of variables are being used. The Sørensen index matrix in Figure 4 of the main text shows that models with a few parameters (e.g. Charisma or Vollenweider) have no or minor overlap with other models, likely since they have a specific modelling domain. It seems that overlap increases with model complexity, with the maximum overlap (Qs=0.7) between the two complex models CE-QUAL-W2 and Delft3D-WAQ. Despite the high overlap for some models, the average similarity between models is lower than there is dissimilarity; more than 80% of the values for Sørensen index are below 0.25. Based on Sørensen similarity index, three groups of models can be distinguished: general models with a relative high overlap, intermediate models with an intermediate level of overlap and specialized models with low overlap. Generally the number of state variables is increasing from specialized models to general models (Figure C1, dendrogram). The Atlantis model has an exceptional high number of state variables with respect to other models that are grouped in the ‘intermediate models’. Apparently, Atlantis has such a low similarity index (denoted with a red arrow in Figure 4) that classification in the intermediate model group is best in terms of overlap. Atlantis application we included is reef focussed, containing specific reef species (Weijerman et al. in review). Some models are more similar to other models than would be expected based on their number of state variables. This holds for CCHE, MyLake Delft3D-WAQ and CE-Qual-W2. These models are simulating general groups rather than having a confined specialism and clustered within the group ‘intermediate models’ in case of low number of state variables and in the group ‘general models’ in case of high number of state variables.
Fig C1 Dendrogram of the Sørensen similarity index together with the amount of state variables of each model. Model numbers refer to 1. Charisma 2. Vollenweider 3. PCLake (Subm. macrophytes) 4. SALMO 5. PROTECH 6. Mike ECO Lab Eutrophication Model 1 7. Pamolare II 8. Eemod_dnsmod (N-cycle) 9. NEMURO.FISH 10. Piscator 11. RIVE(rStrahler) 12. CCHE-models 13. INCA-suite 14. BROM 15. Papyrus Simulator 16. PCDitch 17. MyLake 18. ERSEM 19. EMS 20. PCLake 21. CAEDYM 22. Atlantis 23. Delft3D-WAQ 24. CE-QUAL-W2 .
References
Sokal, RR 1958. A statistical method for evaluating systematic relationships. Univ Kans Sci Bull 38:1409-1438.
Sørensen, T 1948. A method of establishing groups of equal amplitude in plant sociology based on similarity of species and its application to analyses of the vegetation on Danish commons. Biol Skrif 5:1-34.
Weijerman, M, Fulton, EA, Kaplan, IC, Gorton, R, Leemans, R, Mooij, WM and Brainard, RE in review. An integrated coral reef ecosystem model to support adaptive management under a changing climate. PlosOne.
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