# Mathematical Modeling to Estimate Photosynthesis: A State of the Art
## 3 Discussion
However, it is notoriously sensitive to small dynamic changes in environmental conditions; this means that quantifying nature on different time scales is not easy. For this reason, most of the mathematical models reviewed in this article measure variables in steady state, that is, in controlled environments. It is important and convenient to measure the properties of a plant under steady-state conditions, but this does not always allow accurately prediction of how the plant will respond in a complex field environment [125; 126; 127; 128; 129; 130]. For the analysis of physiological processes, it is important to take into account that plants are living beings, so each plant has a different photosynthetic response [11; 131]. This is due to factors such as the age of the plant, its nutrition, the type of plant, its habitat, whether it is aquatic or terrestrial [132; 133], and the climate in which it is found, as well as the type of species [134; 135; 136; 137]. In the revised models, plants of different species were used to carry out the photosynthesis estimation validations, classified for both aqueous and terrestrial environments (Figure 6). As mentioned by [PERSON] [138], most of the studies on photosynthetic activity in different species have been carried out on individual leaves, without considering that due to various factors, what happens in one leaf may not be what is happening in the other leaves of the same plant and the crop in general [139; 140; 141]. For this reason, another important aspect to consider in the analysis and validation of a mathematical model for estimating photosynthesis is the number of plants required for the experimental part of the model, since it is more significant to experiment with a complete crop than to do so with just one plant per species [11]. In this review, the number of plants used in each article was sought; however, not all the articles specified this information, leaving in doubt whether it is a significant piece of data to evaluate the reliability of the model. Various principles and methods have been proposed to select the best model for a system among the various existing models [142; 143; 144; 88]. These quality criteria, which can be used separately or in some combination, are as follows:  
1. To have the minimum number of model parameters with a reasonable error. 2. To have the simplest form with minimal error. 3. To be based on physical, chemical, and biological laws as much as possible. 4. To have the minimum deviation between the predicted and empirical values. 5. To have the minimum output variance. Figure 6: Plant species used in the mathematical models classified by aqueous and terrestrial environments. Refs. [79; 80; 77; 78; 74; 76; 79; 81; 82; 83; 84; 85; 86; 87; 88; 89; 90; 91; 92; 93; 94; 95; 96; 97; 98; 99; 100; 101; 102; 103; 104; 105; 106; 107; 108; 109; 110; 111]. According to [PERSON] [146], another useful statistic to measure the global quality of a model is the coefficient of determination (R\({}^{2}\)) since it measures the proportion or percentage of variability in the experimental data. To interpret these coefficients, it is true that \(0\leq\) R\({}^{2}\leq 1\), values close to 1 are desirable. In general, for prediction purposes, an adjusted coefficient of determination of at least 70% is recommended. Although the coefficient of determination is an important factor to consider for the validation of the models, only some authors showed this evidence in the literature review. As we have seen so far, the estimation of photosynthesis is not an easy process to measure, as many factors can modify the final results, in other words, it is not possible to use the same model for all types of plants. Years after the publication of [PERSON], [PERSON] and [PERSON]'s landmark C3 photosynthesis model, photosynthesis modeling remains an active field of research. These models have allowed the formulation and testing of new hypotheses, which has led to their refinement [147].