Chapter 8 Modeling Predator–Prey Dynamics 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 contributions were to the roots | 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 of400 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 contributions were to the roots of rational approaches to conducting science. An advocate of mathematical rationalism Galileo made a case against the Aristotelian 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 building 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 rigorous 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 ponderously enhances our understanding of nature. Like Galileo I insist that the book 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. Predator-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 254 MARK S. BOYCE complex model and distinguishing stochastic variation from deterministic .
