Modeling the dynamics of tritrophic population interactions.

Introduction Increasingly, population modeling and systems analysis are being used to examine the complex issues that are at the heart of CP/IPM (crop production and integrated pest management) and biological control. The design of economically sound and sustainable crop management strategies requires a thorough understanding of the whole production system including arthropod pests, pathogens, and weeds. More than three decades ago, Huffaker and Croft (1976) stressed the need to rely on systems analysis and interdisciplinary collaboration to accomplish this task. Soon the question arose as to how mathematical techniques employed in the analysis of physical systems could be adapted to solve agroecosystem problems that are principally biological in nature and that focus on population management (Gutierrez and Wang, 1977; Getz and Gutierrez, 1982). Simple models of population dynamics often excluded the biological details for mathematical tractability and hence are frequently inadequate instruments for field application. Individual-based models have been used to explore population interactions (e.g. De Angelis and Gross, 1992), but often the rules for the interactions at the individual level are unknown. Simulation approaches stress biological realism and completeness and some show promise for exploring system structure and function, especially physiologically based models (PBM) (Gutierrez and Wang, 1977), sufficient to gain insights into complex quantitative relationships (see Gilbert et al., 1976; Gutierrez and Baumgärtner, 1984a; b; Graf et al., 1990a; Gutierrez, 1996; Di Cola et al., 1998). In this chapter we will consider only physiologically based multitrophic population dynamics models, or models with the potential to be so extended.