Several approaches are available for modeling dynamic agroecosystems. They vary from those using process-based or mechanistic-type models to those using statistically based or regression-type models. Mechanistic models may be defined by differential equations (ordinary or partial) or by a combination of differential equations and algebraic equations describing process interactions between the components and states of an agroecosystem (based on underpinning physical, chemical, and/or biological relationships). Regression models on the other hand are based on statistical analysis, that is, identifying a regression-type relationship correlating the inputs (i.e., soil, crop, management, environmental) to the outputs (quantifiable states of the system). Both statistical and mechanistic models use linear and nonlinear mathematical equations to describe the quantitative responses of various processes, and both types of models have advantages and disadvantages. The main advantage of the mechanistic-type models is that they relate to the description (physical, chemical, and/or biological) of the agricultural system, typically have wider generality of application, and can provide more insight into the response of different underlying processes to system management. Disadvantages of the mechanistic-type models are that they are often more complex than their counterpart empirical ones, and are more difficult to parametrize and evaluate. Empirical models provide a concise description about the observations on which they are based and do not need to rely on lower-level system attributes; however, they do not imply causality or even knowledge about underlying processes (although they may provide some insight into these). In addition, extrapolation beyond the data range from which the empirical model was derived involves caution. In this article, we focus on the larger and more complex mechanistic models that typically can simulate a wide range of soil-plant-atmosphere processes and thus have applicability to a diverse range of agroecosystems.
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