Models can be classified into different types: conceptual, physical or mathematical (Acock and Acock 1991). Every hypothesis, that is tested, has a conceptual model supporting it. The physical down-scaled representations (physical models) of the system have been used by engineers for a long time. But, they are rarely used to represent biological systems. However, a plant in an experimental plot or container can be considered as a physical model of the crop in the field. When the behavior of a system is described mathematically, through equations, then the representation of the system is a mathematical model. The mathematical model represents quantitatively assumed hypotheses about the real system, allowing one to deduce its consequences. They have gradually become more popular, yet more sophisticated, because advanced level of computing and logical operations has become more accessible with computers.
Mathematical models can be classified into a number of classes, but the two main ones are (i) empirical, sometimes called correlative or statistical models describing relationships among variables without referring to the correlated processes and (ii) mechanistic models, at the level of processes or simulators, which are also called explanatory models, trying to represent cause-effect relationships among the variables. The major objective of mathematical modeling is, evidently, to produce a tool that can be used to test hypotheses, to generate alternative hypotheses, to suggest experiments, to refute them, and furthermore, to predict the behavior of the system in unknown situations. The mathematical models follow exactly the basic rules of the scientific method which are: (i) observation of a system; (ii) formulation of a hypothesis in the attempt of explaining the observations; (iii) prediction of the system behavior through simulation; and (iv) experimentation to test the validity of the hypothesis (validation of the model). But, there is no such thing as a right or wrong model, but models provide variable degrees of suitability for a certain circumstance. There is no universal model that provides a solution to all problems, however, models should continue to be developed and adapted to several particular situations. In the plant growth and development, an empirical model can describe the plant behavior, based on direct observations at the plant level, while a mechanistic model of vegetative growth describes the plant performance based on the knowledge of the processes that are taking place.
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