Patterns for Reducing Parameter Uncertainty

With IBMs, easily too many parameters are too uncertain, or even completely unknown, to use the model for any practical purpose. It has also been argued that the complexity of IBMs leads to error propagation: even moderate uncertainties of individual parameters would multiply to such a large uncertainty at the system level that the model becomes useless. If, however, the IBM was designed according to POM, it should be structurally realistic, that is, reflect the key structures of the real systems and allow for independent predictions for model validation. This structural realism makes it possible to determine entire sets of unknown parameters by inverse modeling: the model is fitted to the entire set of observed patterns. Technically, this is straightforward: for each unknown parameter, a range and a number of values within this range is specified. Then the set of all possible parameter combinations is constructed, which can be very large. Specific techniques, such as Latin hypercube sampling, exist for reducing the number of parameter sets, but typically thousands of parameter sets need to be analyzed. The model is run for each parameter set and checked if it is able to reproduce a certain pattern, otherwise the parameter set is discarded. This is repeated for two or more patterns. Eventually, typically less then 50 parameter sets remain that are able to reproduce all patterns simultaneously (Table 2). It has been shown in several

Table 2 Pattern-oriented parametrization of an IBM describing brown bears spreading from Slovenia into the Alps. Five different observed patterns are used as filters to reduce the number of possible parameter sets. Note that pattern 5 is as good a filter as patterns 2-4 in combination

Number of model

parametrizations in

Pattern

agreement with

description

Patterns

observed pattern

Filter no.

0

557

Density of females

1

506

in transition area

Bear observation

2

138

in central Austria

Bear observation

3

154

intheCarnicAlps

Bear observation

4

180

in the

Karawanken

Census time series

5

12

of females with

cubs

2 + 3 + 4

13

5 +1

10

2 + 3 + 4 +1

11

Modified from Wiegand T, Revilla E, and Knauer F (2004) Dealing with uncertainty in spatially explicit population models. Biodiversity and Conservation 13: 53-78.

Modified from Wiegand T, Revilla E, and Knauer F (2004) Dealing with uncertainty in spatially explicit population models. Biodiversity and Conservation 13: 53-78.

examples that uncertainty in model output of this remaining parameter set is largely reduced, so that the model can even be used to support management decisions.

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