Potential Of Mathematical Modeling In Fruit Quality

African Journal of Biotechnology Vol. 9(3), pp. 260-267, 18 January 2010 Available online at http://www.academicjournals.org/AJB ISSN 1684–5315 © 2010 Academic Journals

Review

Potential of mathematical modeling in fruit quality
M. A. Vazquez-Cruz1, I. Torres-Pacheco1, R. Miranda-Lopez2, O. Cornejo-Perez1, A. Roque Osornio-Ríos3, Rene Romero-Troncoso4 and R. G. Guevara-Gonzalez1*Laboratorio de Biosistemas, Division de Estudios de Posgrado, Facultad de Ingeniería, Universidad Autonoma de Queretaro, Cerro de las Campanas s/n, C.P. 76010, Queretaro, Qro, Mexico. 2 Departamento de Ingeniería Bioquímica, Instituto Tecnologico de Celaya, Av. Tecnologico esq. Av. García Cubas s/n, Celaya, Guanajuato, 38000, Mexico. 3 Facultad de Ingeniería, Campus-San Juan del Río Universidad Autonoma deQueretaro/Río Moctezuma 249, Col. San Cayetano, 76807, San Juan del Río, Queretaro, Mexico. 4 Facultad de Ingeniería Mecanica, Electrica y Electronica, Universidad de Guanajuato. Campus Salamanca, Universidad de Guanajuato/Carr. Salamanca-Valle Km. 3.5+1.8, Comunidad de Palo Blanco, 36700, Salamanca, Guanajuato, Mexico.
Accepted 17 December, 2009
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A review of mathematical modeling appliedto fruit quality showed that these models ranged in resolution from simple yield equations to complex representations of processes as respiration, photosynthesis and assimilation of nutrients. The latter models take into account complex genotypeenvironment interactions to estimate their effects on growth and yield. Recently, models are used to estimate seasonal changes in quality traits as fruitsize, dry matter, water content and the concentration of sugars and acids, which are very important for flavor and aroma. These models have demonstrated their ability to generate relationships between physiological variables and quality attributes (allometric relations). This new kind of hybrid models has sufficient complexity to predict quality traits behavior. Key words: Mathematical modeling,fruit quality, respiration, photosynthesis and assimilation of nutrients. INTRODUCTION Fruit quality is a complex issue defined as a sophisticated chain of biological processes (Genard et al., 2007). These processes (transpiration, respiration, photosynthesis) involve exchanges between the fruit and its environment. Quantitative integration of these processes to monitor fruit’s behavior is a taskinvolving physiological modeling. Nowadays, the interest in mathematical modeling about the quality changes during fruit maturation has been increased (Wegehenkel and Mirschel, 2005). It is possible through simulation to evaluate the quality of final products in order to identify critical points during postharvest handling and to adjust or improve the decision making related to harvest dates andproduct commerciallization. Adequate models should be mechanistic enough to give a representative description of physiological processes and explain variations in some quality traits. Recently, models have become more accurate and better able to predict the outcome of complex issues such as genotype-environment interactions. Furthermore, efforts have been made to define fruit quality and integratingit with crop growth models. These models are based on accurate descriptions of early stages of growth, including fresh fruit mass, dry matter content and concentration of sugars. The goodness-of-fit of a proposed model for each crop is evaluated taking into account the criterion of the root mean squared error (RMSE). This is a common parameter used to quantify the mean difference between predictedmodel and experimental data for the case of non-linear models (Quilot et al., 2005; Kobayashi and Us Salam, 2000). The global goodness-of-fit of a model is computed by averaging the relative RMSE (RRMSE) of all experiments (Quilot et al., 2004). Spearman´s rank correlation coefficients could also be calculated. These coefficients compare the ranking of experiments on the basis of observed and...