## Eleven Different Model Types Tools

Ecological modeling, as a tool in environmental management, rose in popularity significantly during the 1970s. During this time, the journal Ecological Modelling was launched as a forum for such research. Mainly three model types were applied at that time, namely population dynamic models with or without age structure represented by matrices, biogeochemical or bioenergetic dynamic models based on differential equations, and static models, corresponding to all differential equations, were zero. The latter type was mainly applied to describe an extreme or average situation.

It was, however, acknowledged that other model types to solve more comprehensive modeling problems were urgently needed. The needs can be formulated as questions:

1. Ecosystems are middle number systems, in the sense that the number of components are orders of magnitude smaller than the number of atoms in a system. All the components are different and that is often important for a proper description of the ecosystem reactions to consider the differences in properties among individuals.

2. The species are adaptable and may change their properties to meet the changes in forcing functions. Furthermore, the species may be replaced by other species better fitted to the combinations of forcing

Modeled/measured |
Organization |
Pattern |
Model type |

Number of individuals |
Conservations of genes |
Life cycles |
Biodemographic |

Energy |
Conservations of energy |
Energy flow |
Bioenergetic |

Mass or concentration |
Conservations of mass |
Element flow |
Biogeochemical |

Table 2 Classification by model pairs

Pair 1: Is the model applied for research or management? Research models Management models

Pair 2: Is the model deterministic or stochastic? Deterministic models Stochastic models

Pair 3: Does the model apply matrices or differential equations? Matrix models Compartment models

Pair 4: Are the variables dependent or not on time? Dynamic models Static models

Pair 5: Are the equations linear or nonlinear Linear models Nonlinear models

Pair 6: Is the model based on causality or is no causality included? Causal models Black box models

Pair 7: Are the parameters (the properties of the state variables) dependent on time and/or space or constant? Distributed models Lumped models

Pair 8: Is a reductionistic or holistic model approach applied? Reductionistic models Holistic models

Pair 9: Is the model considering spatial distribution? Spatial models Nonspatial models

Pair 10: Are the equations solved numerically or analytically? Numerical models Analytical models

Pair 11: Are the model results discrete or continuous? Discrete models Continuous models functions. How to account for these changes? Even the networks may be changed if more biological components with very different properties are replaced by other species. How to account for these structural changes?

3. Can we model a system that has only uncertain observations/data?

4. How to account for stochastic forcing functions and processes?

5. How to develop models for a heterogeneous data set, that is, based on observations from many different ecosystems?

6. How to develop models of ecosystems, when our knowledge is mainly based on a theory or rules/properties/ propositions?

7. How to consider toxic substances in the environment? Does development of a toxic substance model require a special model type?

8. How to describe the spatial distribution, which is often crucial for the understanding of ecosystem processes?

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