Geoscience Reference
In-Depth Information
a series of precise assumptions you can deduce mathematically what must
ensue, once you know the structure of the system under study. Whether these
predictions apply to the real world is another matter altogether. Mathematical
models have overwhelmed ecology with adverse consequences. The literature
is now filled with unrealistic, repetitive models with simplified assumptions
and no connection to variables field ecologists can measure. You can generate
models more quickly than you can test their assumptions. In an ideal world
there would be rapid and continuous feedback between the modeler and the
empiricist so that assumptions could be tested and modified. This happens too
infrequently in ecology, partly because of the time limitations of most studies.
The great advantage of building a mathematical model is to enunciate clearly
your assumptions. This alone is worth a modeling effort, even if you never
solve the equations.
Recommendation 3: Use a mathematical model of your hypotheses to
articulate your assumptions explicitly.
Many mathematical models, such as the Lotka-Volterra predator-prey equa-
tions, begin with very general, simple assumptions about ecological interac-
tions. Therefore, they are useless for ecologists except as a guide of what not to
do. If we have learned anything from the past 50 years it is that ecological sys-
tems do not operate on general, simple assumptions. But this
simplicity
has
been the great attraction of mathematical models in ecology, along with
gener-
ality
(Levins 1966), and we need to concentrate on
precision
as a key feature of
models that will bridge the gap between models and data. Precise models con-
tain enough biological realism that they make quantitative predictions about
real-world systems (DeAngelis and Gross 1992).
One unappreciated consequence for ecologists who build realistic and pre-
cise models of ecological systems is that numerical models cannot be verified
or validated (Oreskes et al. 1994). A verified model is a true model and we can-
not know the truth of any model in an open system, as Popper (1963) and
many others have pointed out. Validation of a numerical model implies that it
contains no logical or programming errors. But a numerical model may be
valid but not an accurate representation of the real world. If observed data fit
the model, the model may be confirmed, and at best we can obtain corrobora-
tion of our numerical models. If a numerical model fails, we learn more: that
one or more of the assumptions are not correct. Mathematical models are most
useful when they challenge existing ideas rather than confirm them, the exact
opposite of what most ecologists seem to believe. These strictures on numeri-
