diffusion-reaction (Bernacchi et al. 2009; Boonen et al. 2002; Farquhar et al. 2001;
Gómez et al. 2005; Hoffman et al. 2004; Lombardozzi and Sparks 2012; Müller
et al. 2009; Murray 2002).
2.2 Building a Mathematical Model
Essential for building a model is determining its scope. The process by which a
mathematical model can be use to solve real world situations is usually called the
mathematical modeling process (Miwa 1986a). Typically the process consists of the
following four steps: (1) mathematical formulation, (2) programming, (3) parameter
estimation, and (4) model evaluation (Soltani and Sinclair 2012). Sometimes, the
developers of crop models do not always explicitly proceed through each step; it is
valuable to be clear about these steps. If each step is not fully developed, the resultant
model may be seriously compromised if its use is attempted outside the context in
which the developer visualized it. It is likely a more robust model will result from the
modeling process that recognizes each of these stages (Haefner 2005; Sinclair and
Seligman 2000). The most important stage in this process is the formulation stage,
assumptions based on deliberate suppression or neglect of irrelevant details are set
up. If these assumptions are not appropriately setup, the nature of the situation is
distorted, and the problem cannot be solved correctly. The setting up of adequate
assumptions can be considered as the most important decision in performing
mathematical modeling. Therefore, it is necessary to consider the role of assumptions in mathematical modeling process (Miwa 1986b).
2.2.1 Definition of Objectives
Before starting a modeling project, it is important to be clear about the model
objectives. This step determines the future direction of the project in two ways. At
the beginning of the modeling process, the objectives of the modeling effort should
be explicitly and fully defined. A clear statement of specific objectives is essential
to define needs and nature of a crop model (Sinclair and Seligman 1996).
It is more likely that success will be achieved when the objectives are clear,
modest, and tractable (Sinclair and Seligman 1996). Criteria for judging the
acceptability of a model should be defined in relation to the model’s objectives. It
is possible to quantitatively define stopping rules, in terms of statistical criteria
concerning model predictions relative to a sample of observations.
Based on the objective, a list of specific hypotheses to be included in the model
is prepared. Initially, it may be useful to list the hypotheses in the form of words
and sentences. Some of the following points need to be considered in identifying
hypotheses to be used to construct the model: (1) Models need to have generality,
(2) Hypotheses will require input data either as parameters or driving variables,
2 Mathematical Modeling of Biosystems
53
Gómez et al. 2005; Hoffman et al. 2004; Lombardozzi and Sparks 2012; Müller
et al. 2009; Murray 2002).
2.2 Building a Mathematical Model
Essential for building a model is determining its scope. The process by which a
mathematical model can be use to solve real world situations is usually called the
mathematical modeling process (Miwa 1986a). Typically the process consists of the
following four steps: (1) mathematical formulation, (2) programming, (3) parameter
estimation, and (4) model evaluation (Soltani and Sinclair 2012). Sometimes, the
developers of crop models do not always explicitly proceed through each step; it is
valuable to be clear about these steps. If each step is not fully developed, the resultant
model may be seriously compromised if its use is attempted outside the context in
which the developer visualized it. It is likely a more robust model will result from the
modeling process that recognizes each of these stages (Haefner 2005; Sinclair and
Seligman 2000). The most important stage in this process is the formulation stage,
assumptions based on deliberate suppression or neglect of irrelevant details are set
up. If these assumptions are not appropriately setup, the nature of the situation is
distorted, and the problem cannot be solved correctly. The setting up of adequate
assumptions can be considered as the most important decision in performing
mathematical modeling. Therefore, it is necessary to consider the role of assumptions in mathematical modeling process (Miwa 1986b).
2.2.1 Definition of Objectives
Before starting a modeling project, it is important to be clear about the model
objectives. This step determines the future direction of the project in two ways. At
the beginning of the modeling process, the objectives of the modeling effort should
be explicitly and fully defined. A clear statement of specific objectives is essential
to define needs and nature of a crop model (Sinclair and Seligman 1996).
It is more likely that success will be achieved when the objectives are clear,
modest, and tractable (Sinclair and Seligman 1996). Criteria for judging the
acceptability of a model should be defined in relation to the model’s objectives. It
is possible to quantitatively define stopping rules, in terms of statistical criteria
concerning model predictions relative to a sample of observations.
Based on the objective, a list of specific hypotheses to be included in the model
is prepared. Initially, it may be useful to list the hypotheses in the form of words
and sentences. Some of the following points need to be considered in identifying
hypotheses to be used to construct the model: (1) Models need to have generality,
(2) Hypotheses will require input data either as parameters or driving variables,
2 Mathematical Modeling of Biosystems
53