Mathematical Modeling to Estimate Photosynthesis: A State of the Art

Abstract

Photosynthesis is a process that indicates the productivity of crops. The estimation of this variable can be achieved through methods based on mathematical models. Mathematical models are usually classified as empirical, mechanistic, and hybrid. To mathematically model photosynthesis, it is essential to know: the input/output variables and their units; the modeling to be used based on its classification (empirical, mechanistic, or hybrid); existing measurement methods and their invasiveness; the validation shapes and the plant species required for experimentation. Until now, a collection of such information in a single reference has not been found in the literature, so the objective of this manuscript is to analyze the most relevant mathematical models for the photosynthesis estimation and discuss their formulation, complexity, validation, number of samples, units of the input/output variables, and invasiveness in the estimation method. According to the state of the art reviewed here, 67% of the photosynthesis measurement models are mechanistic, 13% are empirical and 20% hybrid. These models estimate gross photosynthesis, net photosynthesis, photosynthesis rate, biomass, or carbon assimilation. Therefore, this review provides an update on the state of research and mathematical modeling of photosynthesis.

Integrated Multi-scale Modelling-Simulation (MMS) and Machine Learning (ML) based Design and Development of Novel Systems/technologies

“…To create a model that is "fit for purpose," a wide range of tasks, knowledge, and skills need to be practiced. The steps in mathematical modeling are as follows [6,7]:…”

“…As depicted in Figure 2, mathematical modeling can be divided into three categories: mechanistic-white box, empirical-black box, and hybrid-gray box, and these, in turn, have subcategories [7][8][9][10].…”

An Overview of Different Fruit Crop Models in the last 40 Years to Date with Their Main Uses

“…Different classes are there within the mathematical models of which empirical models and mechanistic models are most important. Both empirical and mechanistic models can be deterministic which includes the use of definite quantitative predictions or stochastic which uses random predictions and have a range of distributions [11]. They can either be continuous or discrete.…”

Fuzzy Mathematical Model of Photosynthesis in Jalapeño Pepper

“…Many of the methods for inferring photosynthesis are invasive; they physically or chemically interfere with the plant, altering its natural process during measurement. Noninvasive methods do not alter the plant's natural processes since there is no contact with the specimen [2].…”

“…An intermediate model is classified as the semi-empirical or semi-mechanistic model between the black box and white box models. These models are also called gray box or hybrid models; they consist of a combination of empirical and mechanistic models [2].…”