Ecological Modelling 197: 320-330, 2006.
Abstract.
Ecological data frequently containmultiple patterns. A process model of the system producing
the data should be able to recreate those patterns.We describe amethod and associated
software where components of the pattern are used as multiple criteria to assess a model
during its construction. Successive improvements aremade to themodel so that it describes
more components of the pattern effectively.
The software, Pareto Evolve is an evolutionary algorithm. Initially it creates many individual
sets of model parameters, each is used in the model to produce results that are then
compared to patterns in a data set. Different individuals may achieve different components
of the pattern and Pareto Evolve calculates those that are most effective and uses them to
produce new individuals. This is done by changing parameter values of individuals, called
mutation, or exchanging parameter values between individuals, called crossover. This process
is repeated over many generations so that a most effective parameterization evolves.
We illustrate this method with a model for hourly increments of extension of the leading
shoot of a conifer tree. The particular task here is to model water uptake by the plant in
response to water loss due to transpiration, calculate a water deficit between uptake and
loss, and calculate contraction and re-expansion of shoot tissue due to diurnal changes
in tissue water deficit. We choose criteria corresponding to different phases in the diurnal
pattern of expansion and model for up to six consecutive days. A value is set marking the
limit within which the model must achieve the criteria for it to be judged as success.
This value is called a binary discrepancy measure. Pareto Evolve is used to make multiple
searches with successively smaller binary discrepancy measures until all criteria
are no longer achieved. At this point different parameter sets achieve different groups
of criteria and we use these as indicators of how the structure of the model must
be improved to achieve an overall better fit. In our example we find that contraction
is more rapid than re-expansion, which is a hysteresis effect, and that re-expansion
of tissue continues after water deficit within the tissue is estimated to have been
removed.
We discuss how this method can be used in model development and particularly
how multiple criteria assessment can be used in model development.