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cal models apply more to complex models (e.g., population viability models)
than to simple models (e.g., age-based demographic models).
Numerical models in which we have reasonable confidence can be used in
ecology for sensitivity analysis, a very important activity. We can explore
“what-if ” scenarios rapidly and the only dangers are believing the results of
such simulations when the model is not yet confirmed and extrapolating
beyond the bounds of the model (Walters 1993).
Hypotheses and Paradigms
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Hypotheses are specified within a paradigm and the significance of the hy-
pothesis is set by the paradigm. A paradigm is a world view, a broad approach
to problems addressed in a field of science (Kuhn 1970; McIntosh 1992). The
Darwinian paradigm is the best example in biology. Most ecologists do not
realize the paradigms in which they operate, and there is no list of the com-
peting paradigms of ecology. The density-dependent paradigm is one example
in population ecology, and the equilibrium paradigm is an example from com-
munity ecology. Paradigms define problems that are thought to be fundamen-
tal to an area of science. Problems that loom large in one paradigm are dis-
missed as unimportant in an opposing paradigm, as you can attest if you read
the controversies over Darwinian evolution and creationism.
Paradigms cannot be tested and they cannot be said to be true or false.
They are judged more by their utility: Do they help us to understand our
observations and solve our puzzles? Do they suggest connections between the-
ories and experiments yet to be done? Hypotheses are nested within a para-
digm and supporters of different paradigms often talk past each other because
they use words and concepts differently and recognize different problems as
significant.
The density-dependent paradigm is one that I have argued has long out-
lived its utility and needs replacing (Krebs 1995). The alternative view is that
a few bandages will make it work well again (Sinclair and Pech 1996). My chal-
lenge for any ecological paradigm is this: Name the practical ecological prob-
lems that this paradigm has helped to solve and those it has made worse. In its
preoccupation with numbers, the density-dependent paradigm neglects the
quality of individuals and environmental changes, which makes the equilib-
rium orientation of this approach highly suspect.
Consider a simple example of a recommendation one would make from
the density-dependent paradigm to a conservation biologist studying an en-
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