# Mathematical Modeling to Estimate Photosynthesis: A State of the Art
### Mathematical Modeling
At the black box, at the beginning of the spectrum, models can perform reliable predictions based on data. At the white box end of the spectrum, mathematical models can be applied to the design, testing, and optimization of computer processes before they are physically carried out. On each of the S, Q, and M axes in Figure 2b, the mathematical models are classified based on a series of criteria compiled from various classification attempts in the literature [36]. There are different mathematical models related to biochemical, physical, and agroecological variables that estimate photosynthesis at the leaf, plant, or group of plant levels. Figure 2: The three dimensions of an SQM mathematical model, where the (S) systems are ranked at the top of the bar; immediately below the bar, there is a list of objectives that the mathematical models in each of the segments can have (which is Q); at the lower end are the corresponding mathematical structures (M) ranging from algebraic equations (Aes) to differential equations (Des). (a) Classification of mathematical models between black and white box models. (b) Classification of mathematical models in the SQM space. Modified from [36]. Therefore, the study of mathematical modeling focused on the photosynthetic process becomes important in the agricultural sector. Since it is a direct indicator of a plant's health. It also makes it possible to assess the consequences of global climate change on crop growth, since the high concentration of CO2, the increase in temperature and altered rainfall patterns can have serious effects on crop production in the near future [44]. However, to the best of the authors' knowledge, a study on the diversity of mathematical modeling in the field of scientific research has not been approached nor focused on: the mathematical formulation, the complexity of the model, the validation, the type of crop (at the leaf, plant or canopy level), the analysis of the diversity of variables used with their respective units, as well as the invasiveness in their measurements. Hence, this manuscript presents a selective review of mathematical modeling to estimate photosynthesis. In the literature, there is a review of the mathematical modeling of photosynthesis developed by [PERSON]. However, here only several models derived from the C3 model by [PERSON], [PERSON], and [PERSON] are discussed and compared. The models described and reviewed here describe the assimilation rates of CO2 in a steady state and provide a set of hypotheses collected in a quantitative way that can be used as research tools to interpret experiments both in the field and in the laboratory. Additionally, it also provides tools for reflective experiments [49]. Conversely, the present paper provides a new vision of the state of the art in mathematical models with certain specifications. This information can be used to develop new mathematical models to estimate photosynthesis with new variables related to the plant's habitat and with greater relevance to be implemented in electronic systems during the development of photosynthesis estimation equipment. The objective of this manuscript is to present mathematical models with different characteristics to estimate photosynthesis; discuss its formulation, complexity, validation, applications, and invasiveness in the estimation method; show that the units corresponding to photosynthesis depend on the measurable biochemical, physical, and agroecological variables used for the estimation; analyze the relevance of the behavior trend in the photosynthetic process and prioritize over the specific magnitude itself. Therefore, in the authors' opinion, this study provides a great opportunity to contribute to the mathematical-modeling knowledge to estimate photosynthesis. The content of this work is organized in the following sections. Section 2 describes the criteria for the selection of mathematical models according to their classification and characteristics. In Section 3, a critical review of the white box, black box, and gray box models is given.