Optimizing Model Complexity and Dealing with Uncertainty

IBMs are more complex than most mathematical population models, because they consider local interactions of individuals that are different and autonomous. This fact has led to the stereotype that IBMs are so complex that they are as hard to understand as nature itself, but this certainly is not true because even the most complex IBMs still are simplified representations of reality. Nevertheless, complexity is a challenge. Many IBMs seem to be more complex than really needed; specific techniques to test and analyze complex IBMs are not routinely used, which severely limits the potential for general insights. Recently, however, the general strategy of pattern-oriented modeling (POM) has been formulated which allows to optimize model complexity. POM is also useful for dealing with another important challenge of individual-based modeling: uncertainty of model structure and parameters. How can we know which process to include in a model and how to represent this process, for example dispersal? And how can we determine uncertain parameters?

POM is based on the notion that patterns observed in real systems are indicators of the system's internal organization. If we are able to understand how these patterns emerge then we can learn about the key processes that determine the systems structure and drive its dynamics. A pattern is defined as anything beyond random variation, or any signal beyond noise. Some patterns are striking, like cycles in the abundance ofsmall mammals, outbreaks of forest insects, or patchy and wave-like spatial patterns. Other patterns are less obvious but nevertheless contain information about the system's key processes: patterns in age and size structure, typical recovery dynamics after disturbance events, the fact that certain system-level state variables like biomass or number ofspecies remain within certain limits, etc.

Patterns are the key to decode the internal organization of any system: atomic spectra helped decode the structure of atoms, the redshift in the light of galaxies helped formulate the big bang theory, etc. With complex systems, however, that consist of many interacting building blocks, single patterns are not sufficient to narrow down our theories about the system to one single model.

For example, there are at least eight models that explain the cycles of small mammals in the boreal zone, and more than 20 theories that explain why ecosystems near the equator have much more species than in other zones.

Thus, for complex systems, we need multiple patterns observed at different scales and hierarchical levels. For example, Chargaffs rule of DNA base pairing was not sufficient to decode the structure of DNA. Two additional patterns helped to narrow down the model of the structure to the double helix: patterns from X-ray diffraction of DNA and tautomeric properties of the purine and pyrimidine bases.

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