Geoscience Reference
In-Depth Information
weaker fluctuations (Galushin 1974). Nomadic raptors can help to synchro-
nize small mammal populations geographically by moving to areas of high
prey abundance, thereby making predator dispersal an important component
in regional population fluctuations (Norrdahl and Korpimäki 1996).
Many predator-prey models are unstable. Indeed, such instability may be
inherent in many biological predator-prey interactions and only through spa-
tial structure can such species persist. Metapopulation structures may emerge
as a consequence of predator-prey interactions (McCullough 1996).
Models for spatially structured populations are a complex topic that I can-
not address sufficiently here. Suffice it to say that spatial structure can have
profound consequences for predator-prey dynamics. Because of the complex-
ity of spatially structured population models, these are necessarily computer
simulation models. With the development of geographic information systems
(
GIS
) into which one can build models to superimpose on maps, the ability to
develop spatially structured population models is greatly facilitated. Software
is available that permits a direct interface between population models and
GIS
data layers that characterize habitat (Boyce 1996).
MODEL VALIDATION
To validate means to verify or substantiate. In the context of model validation,
Grant (1986) proposed the following four considerations:
•
Does the model address the problem?
Often the problem is not well articu-
lated, meaning that it is the modeler who defines a precise statement of the
problem. The modeler may feel compelled to focus on questions that are
mathematically tractable or that can be reliably addressed given the available
data. The true natural resource problem being confronted by management
may be a difficult one to answer using modeling, yet failure to confront issues
directly has led to a distrust of modelers by managers (Boyce 1992a).
•
Does the model have reasonable structure and behavior?
Dynamics such as
those predicted by the Lotka-Volterra model are simply too weird to be of bio-
logical interest. Often population data may exist for similar species or popula-
tions that can be used for qualitative assessment of whether the dynamics
emerging from a model are reasonable.
•
Sensitivity analysis.
Sensitivity analysis involves evaluating the response of a
selected response variable to change in system parameters. For example, popu-
lation growth rate is often explored as a function of perturbations to vital rates.
