Geoscience Reference
In-Depth Information
Chapter 8
Modeling Predator-Prey Dynamics
MARK S. BOYCE
Our gathering in Sicily from which contributions to this volume developed
coincided with the continuing celebration of 400 years of modern science since
Galileo Galilei (1564-1642). Although Galileo is most often remembered for
his work in astronomy and physics, I suggest that his most fundamental con-
tributions were to the roots of rational approaches to conducting science. An
advocate of mathematical rationalism, Galileo made a case against the Aris-
totelian logicoverbal approach to science (Galilei 1638) and in 1623 insisted
that the “Book of Nature is written in the language of mathematics” (McMullin
1988). Backed by a rigorous mathematical basis for logic and hypothesis build-
ing, Galileo founded the modern experimental method. The method of Galileo
was the combination of calculation with experiment, transforming the concrete
into the abstract and assiduously comparing results (Settle 1988).
Studies of predator-prey dynamics will benefit if we follow Galileo's rigor-
ous approach. We start with logical mathematical models for predator-prey
interactions. This logical framework then should provide the stimulus by
which we design experiments and collect field data. Science is the iteration
between observation and theory development that gradually, even ponder-
ously, enhances our understanding of nature. Like Galileo, I insist that the
topic of predator-prey dynamics is written in mathematical form.
In wildlife ecology, the interface between theory and empiricism is poorly
developed. For predator-prey systems, choosing appropriate model structure
is key to anticipating dynamics and system responses to management. Preda-
tor-prey interactions can possess remarkably complex dynamics, including
various routes to chaos (Schaffer 1988). This presents several problems for the
empiricist, including the difficulty of estimating all of the parameters in a
