Geoscience Reference
In-Depth Information
Fitting the Model to Data
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“Data analysis through model building and selection should begin with an
array of models that seem biologically reasonable.”
Burnham and Anderson (1992)
Seldom do we have sufficient data to do justice to estimating all of the param-
eters necessary to reconstruct the interesting dynamics of predator-prey
interactions. One approach that has met with limited success is to build
predator-prey models piecewise. For example, the predator-prey model in
equations 8.13 and 8.14 contains a density-dependent portion for the prey in
the absence of predators, a functional response, a numerical response, and a rate
of decline in the absence of prey. For some populations each of these pieces
could be constructed independently with field data and then combined to study
the model dynamics.
The traditional approach to model building has been to use goodness-of-
fit tests or between-model tests. As an alternative, Burnham and Anderson
(1992) advocate the use of AIC for models that can be posed in a maximum
likelihood framework or Mallow's C p for regression models. For building
the model piecewise, I believe that information criteria procedures could prove
useful.
BAYESIAN STATISTICS
Bayesian statistics holds promise for accommodating complex models and
uncertainty about model parameters. Recent contributions in the application
of Bayesian techniques appear to have few reservations about tackling prob-
lems at the level of complexity outlined among the models described earlier in
this chapter (McAllister et al. 1994). A recent issue of Ecological Applications
featured a series of papers on Bayesian statistics (Ellison 1996). Given the cur-
rent excitement over these techniques, I am confident that useful applications
to predator-prey modeling will be developed in the near future.
BEST GUESS FOLLOWED BY ADAPTIVE MANAGEMENT
Most detailed predator-prey models are too complex for the available data.
Modeling by the principle of parsimony fails because any principled ecologist
is unwilling to give up the structural details of the model that give it the
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