2.3 Types of Models............................................................................................................... 56
2.3.1 Mechanistic Models.............................................................................................. 57
2.3.2 Phenomenological Models.................................................................................... 58
2.4 Validation.......................................................................................................................... 63
2.4.1 Validation Criteria ................................................................................................ 63
2.4.2 Statistical Tools .................................................................................................... 64
2.5 Applications ...................................................................................................................... 66
2.5.1 Estimating the Biomass of Fish ........................................................................... 66
2.5.2 Fruit Quality Changes .......................................................................................... 67
2.5.3 Modeling of Fruit Quality .................................................................................... 69
2.5.4 Applications of Neural Networks in Agriculture and Biosystems ..................... 71
References.................................................................................................................................. 72
2.1 Introduction
When we meet with the problem of describing the behavior of a real-world
phenomenon or system, there is a need to resort to models. These models allow us to
answer the question about important features and the behavior of the system studied
under different conditions. There are different types of models such as verbal,
mental, physical, and mathematical (Ljung and Gland 1994). In mathematical
modeling, a number of assumptions translate into the language of mathematics. This
has many advantages
1. Mathematics is a very precise language. This helps us to formulate ideas.
2. Mathematics is concise language, with well-defined rules for manipulations.
3. The mathematical results that have been proven over years are available to us.
4. Computers can be used to perform numerical calculations.
There are different mathematical models related to biochemical, physiological,
and physical variables related to biosystems. Biosystems consist in any system of
living creatures, however this term has been widely used for either plant or animal
groups. Systems as constructed wetlands (CWs) have been recognized as effective
means of ‘‘green technology’’ for wastewater treatment because their use of
biological processes (assimilation by the plant tissue and microbial transformations); thus they may be also considered as biosystems (Kumar and Zhao 2011).
Biosystem’s technology uses mathematical models applications in biomass and
productivity forecasting. This can be accomplished by using the instrumentation
systems for measuring variables related to plant production (Espinosa-Calderon
et al. 2011; Gómez et al. 2005; Guzmán-Cruz et al. 2009; Guzmán-Cruz 2010;
Millan-Almaraz et al. 2009).
Mathematical models can be based on several methods and principles such as
steady-state mechanistic, temperature functions, Gaussian integration, stomatal
conductance, nitrogen analysis, dynamic biological systems models, PAR, 3-D
gradients of climatologic parameters, linear regression, nonlinear regression, and
52
M. A. Vázquez-Cruz et al.
2.3.1 Mechanistic Models.............................................................................................. 57
2.3.2 Phenomenological Models.................................................................................... 58
2.4 Validation.......................................................................................................................... 63
2.4.1 Validation Criteria ................................................................................................ 63
2.4.2 Statistical Tools .................................................................................................... 64
2.5 Applications ...................................................................................................................... 66
2.5.1 Estimating the Biomass of Fish ........................................................................... 66
2.5.2 Fruit Quality Changes .......................................................................................... 67
2.5.3 Modeling of Fruit Quality .................................................................................... 69
2.5.4 Applications of Neural Networks in Agriculture and Biosystems ..................... 71
References.................................................................................................................................. 72
2.1 Introduction
When we meet with the problem of describing the behavior of a real-world
phenomenon or system, there is a need to resort to models. These models allow us to
answer the question about important features and the behavior of the system studied
under different conditions. There are different types of models such as verbal,
mental, physical, and mathematical (Ljung and Gland 1994). In mathematical
modeling, a number of assumptions translate into the language of mathematics. This
has many advantages
1. Mathematics is a very precise language. This helps us to formulate ideas.
2. Mathematics is concise language, with well-defined rules for manipulations.
3. The mathematical results that have been proven over years are available to us.
4. Computers can be used to perform numerical calculations.
There are different mathematical models related to biochemical, physiological,
and physical variables related to biosystems. Biosystems consist in any system of
living creatures, however this term has been widely used for either plant or animal
groups. Systems as constructed wetlands (CWs) have been recognized as effective
means of ‘‘green technology’’ for wastewater treatment because their use of
biological processes (assimilation by the plant tissue and microbial transformations); thus they may be also considered as biosystems (Kumar and Zhao 2011).
Biosystem’s technology uses mathematical models applications in biomass and
productivity forecasting. This can be accomplished by using the instrumentation
systems for measuring variables related to plant production (Espinosa-Calderon
et al. 2011; Gómez et al. 2005; Guzmán-Cruz et al. 2009; Guzmán-Cruz 2010;
Millan-Almaraz et al. 2009).
Mathematical models can be based on several methods and principles such as
steady-state mechanistic, temperature functions, Gaussian integration, stomatal
conductance, nitrogen analysis, dynamic biological systems models, PAR, 3-D
gradients of climatologic parameters, linear regression, nonlinear regression, and
52
M. A. Vázquez-Cruz et al.