Modelling approaches for addressing complexity in plant health management

Harmful organisms affect the quality and quantity of food production. In a world of increasing changes in climatic, economic and social conditions, the design of effective measures against these organisms requires more accurate information. Mathematical models provide a scientific and quantitative language to describe the complex relationships that causes pest outbreaks. With the goal of analysing options to deal with this complexity, we discuss different mathematical approaches to modelling. The best model to support plant protection decisions will vary with each situation. Mathematical models range from very simple correlations between events to complex comprehensive systems of differential equations used to represent the dynamics of processes. Large-scale scenarios at the national or continental level can be supported adequately with simple, static and general models. Analytical or descriptive dynamic models are the best options to support pest management in well-defined regions or locations with little variation in external factors. Explanatory dynamic models are needed when great variations in pest behaviour are expected as a result of higher-order interactions with the host and the environment. If necessary, a quantitative analysis can be performed using mathematical modelling. In practice, the feasibility of such a quantitative analysis will depend on the time available for decision-making and data collection concerning the problem.   Key words:  Mathematical models, plant health, predictive models.