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Revista mexicana de ciencias agrícolas
versión impresa ISSN 2007-0934
Rev. Mex. Cienc. Agríc vol.13 no.6 Texcoco ago./sep. 2022 Epub 24-Feb-2023
https://doi.org/10.29312/remexca.v13i6.2922
Essays
Mathematical modeling and simulation: a tool for crop protection
1Postgrado en Fitosanidad-Colegio de Postgraduados. Carretera México-Texcoco km 36.5, Montecillo, Texcoco, Estado de México, México. CP. 56264. Tel. 55 59548371. (duranely5@gmail.com; acuaytevaldez@gmail.com).
2Ingeniería en Agronomía-Nova Universitas. Carretera a Puerto Ángel km 34.5, Ocotlán de Morelos, Oaxaca. CP. 71513. Tel. 55 16086172. (acuayte@novauniversitas.edu.mx).
3Instituto Tecnológico Agropecuario de Puebla. Carretera Palomas- Tlapa km 20.5, Tecomatlán, Puebla. CP. 74870. Tel. 595 1085753. (carlos-hdz-3@yahoo.com.mx).
4Posgrado en Ingeniería Agrícola y Uso Integral del Agua-Universidad Autónoma Chapingo-Edificio Efraín Hernández Xolocotzi, PB. Carretera México-Texcoco km 38.5, Chapingo, Estado de México. CP. 56230. Tel. 554 8445105.
The consequences of climate change on crops are a cause for concern, as they cannot adapt quickly to new pathogenic threats. This article reviews the global use of mathematical models in plant health during the 2000-2020 period, through Scopus and Google Scholar. The objective of this study is to show modeling and simulation as an option in crop protection against meteorological risks or variations that occur due to global warming. Mathematical modeling is not an end in itself but a tool that helps in decision making for the sustainable management of crops. The prediction of the risk of occurrence of a pest or disease favors the reduction of the use of pesticides, thus reducing economic losses and damage to the environment. On the other hand, the simulation or numerical solution of mathematical models allows the exploration of hypotheses, it is an invaluable means in the research, since it allows exploring possible future scenarios and finding options of management systems that will be necessary at some point. In Mexico, it is necessary to carry out research for the generation and implementation of mathematical models that allow a lower cost of production and less negative impact on human health and the environment.
Keywords: computation applied to plant health; decision making; disease management
Las consecuencias del cambio climático en los cultivos son motivo de preocupación, ya que éstos no pueden adaptarse rápidamente a las nuevas amenazas patógenas. En este artículo se hace una revisión sobre el uso global de modelos matemáticos en fitosanidad durante el periodo 2000-2020; a través, de Scopus y Google Académico. El objetivo del estudio es presentar la modelación y simulación como una opción en la protección de cultivos ante los riesgos meteorológicos o variaciones que se producen por el calentamiento global. La modelación matemática no es en sí un fin, sino una herramienta que ayuda en la toma de decisiones para el manejo sustentable de los cultivos. La predicción del riesgo de ocurrencia de una plaga o enfermedad favorece la reducción de uso de pesticidas disminuyendo así las pérdidas económicas y el daño al ambiente. Por otra parte, la simulación o solución numérica de los modelos matemáticos, permite la exploración de hipótesis, es un medio invaluable en la investigación, ya que permite explorar posibles escenarios futuros y encontrar opciones de sistemas de manejo que en algún momento serán necesarias. En México es necesario realizar investigaciones para la generación e implementación de modelos matemáticos que permitan un menor costo de producción y menor impacto negativo a la salud humana y al ambiente.
Palabras clave: cómputo aplicado a fitosanidad; manejo de enfermedades; toma de decisiones
The consequences of climate change on crops are a cause for concern, as they cannot adapt quickly to new pathogenic threats (Garrett et al., 2013). To analyze the increase in the intensity and occurrence of pathogens and pests, it is necessary to consider that, historically, climatic variations show fluctuations, mainly in temperature with respect to the annual average (Mora-Aguilera et al., 2014). Actions that connect science with producers regarding the adaptation and control of pests in response to agrometeorological and climatic risks are urgently needed (López, 2014). The modeling of dynamic adaptive systems is a useful tool for the creation of models of simulation of complex systems, which allow the design of scenarios composed of various strategies, and the assessment of their results in the system (Martínez and Vargas, 2016).
Systems simulation is the numerical solution of the dynamic mathematical model of a system. This dynamic model is usually a set of differential equations or equations in differences, which have no exact solution but only numerical. It is necessary to develop dynamic models and simulate to control and optimize a system, as well as increase scientific knowledge (López, 2014) and apply it to pest and disease management based on forecast. For a disease to develop, three aspects known as plant disease triangle are required: a susceptible host plant, a conducive environment and a pathogenic agent. It becomes a pyramid when considering the human factor and its ability to influence some aspects of the plant, of the pathogen and of time (Téliz and Mora, 2007).
Mathematical modeling of systems
During the 60s-70s, the importance of the growing degrees days (GDD) was highlighted to understand the phenology of the plant and its relationship with pests (accumulation of heat units). Due to the abundance of data, analyses were carried out by means of computer systems, the dynamics of growth and production of plants, as well as their pests and the climatological data of the place, were estimated together, thus allowing the development of prediction models for decision-making in the management of cultural practices of the plant or in precise stages of the biology of the pest (Teliz and Mora, 2007).
De Wit and Penning de Vries (1982) proposed the classification of crop growth and development models of the Wageningen modeling school. It is a classification into four production situations: potential growth, water-limited growth, models for nitrogen-limited growth, and nutrient-limited production (Bouman et al., 1996). In the four situations, pests, diseases or weeds can further reduce field production. In practice, real production situations are difficult to assign to any of these four situations, but this practical simplification of schematizing specific situations allows progress, especially at the beginning of a study (De Wit and Penning de Vries, 1982).
The Wageningen group has a long tradition in crop modeling in its agroecological research program, based on the pioneering work of Wit (Van Ittersum et al., 2003). In the 1980s, scientists at Wageningen became involved in the development and application of crop models that could support rational decision-making about pesticide use. These include modeling perennial species in forest systems (Kramer, 1996) and the effects of yield-reducing factors such as weeds (Kropff, 1988), pests (Fransz, 1974), and decision-making support systems for pests and diseases (Rossing, 1993).
Studies such as that of Campbell and Madden (1990) highlighted the importance of predicting the increase of a disease before exceeding the threshold that causes economic losses in the crop. The forecast of the disease in days or weeks before an epidemic occurs allows producers to respond in a timely and efficient manner in the management of crops (Maloy, 1993). In addition, a prediction of low risk of disease occurrence may reduce pesticide use and environmental damage (De Wolf and Isard, 2007). Mathematical models and computational models allow representing the progress of a disease or an epidemic.
The quantitative description of epidemics provides information related to the amount of initial inoculum, environment, plant resistance, prediction system and crop management efficiency (Achicanoy, 2000). Ruiz (2020) classified the models according to their application into: a) teaching; b) research: hypothesis testing, genetic improvement, adaptation to climate change and optimization of inputs; and c) support systems for decision making: pest and disease forecasting, sowing dates, varieties, yield forecasting and irrigation and fertilization management.
There are three types of mathematical models of systems: empirical models, teleonomic models and mechanistic models (Thornley and France, 2007). A mechanistic model is defined by a set or system of nonlinear ordinary equations in differences or differential equations, which describe the behavior of the state variables of the system, those variables that represent the relevant properties or attributes of the system under consideration. Explanatory models are more appropriate for expressing hypotheses mathematically and thus provide a quantitative description and explanation of the most important processes that occur in a biological system. Mechanistic models simulate systems as functions of measured or estimated environmental variables. They are considered more promising to solve the problem, but they are also difficult to develop.
Research in crop protection can be grouped into: a) basic research. It characterizes crop growth and development, biological enemies, factors that determine their adaptation, and predictive models of the behavior of harmful organisms; and b) applied research. Phytosanitary problems are monitored through applications that use simulation models and climate databases. It includes methods and procedures for the assessment of the damage caused by the pest (SIAFEG, 2010).
Researchers in the agricultural area should promote knowledge of systems and control theory (Van Straten, 2012). A system is a simplified representation of a portion of reality. It is a series of selected and chosen elements, with specified limits and predetermined time characteristics (Savary and Willocquet, 2014). There is currently a lot of software available that can help build and run models.
Extensible modeling systems are modeling packages that allow the user to add a specific code if the methods are not sufficient for their purposes (Voinov, 2008). For example, the Stella® program allows focusing only on the components, structure, relationships, and behavior of the system, rather than on the program code itself (ISEE Systems, 2010). Vensim® has the same basic characteristics for modelling as Stella, with the addition of some important functions, such as calibration (automatically adjusts parameters to get the best correspondence between model behavior and data), optimization (the effective algorithm), Kalman filter, Monte Carlo analysis, causal tracing (a tree diagram shows a selected variable and variables that ‘cause’ its change) (Voinov, 2008).
Fortran simulation translator (FST®) is a simulation environment that allows the researcher to develop concepts in terms of mathematical equations. This computer system can be run using subroutines of standard mathematical libraries and developed by the user in the Fortran programming language, so it is a valuable tool, both for research and education (Van Kraalingen et al., 2003). Globally, there are models of growth and yield in climate change scenarios (Noriega-Navarrete et al., 2021). Specific simulation models for a crop; for example, Ceres-wheat in wheat, Corngro in corn, or they can be generic and applied to different species using specific parameters for each crop: Daisy, Epic, Wofost, Cropsyst, and Stics (Steduto, 2006).
There are microclimate models (Pohlheim and Heiβner, 1996; Ruiz, 2009). There is a new family of models called structural-functional models (Boudon, 2012), they use 3D representations of plant architecture to simulate different types of physical, physiological or eco-physiological processes in plants and allow evaluating the effects of these processes on the functioning, development and shape of plants (Rongier et al., 2017) and their interaction with pathogens (Hanan et al., 2002).
The L-systems formalism was introduced by biologist and botanist (Lindenmayer, 1968). In L-systems, the plant is represented by a chain in square brackets, whose elements, called modules, represent the components of plants (metamers, meristems, flowers, etc.). Modules consist of a symbolic name and an optional set of parameters. A set of rules defines how each module transforms over time (Prusinkiewicz, 2021).
Dynamic models
Dynamic models predict how variables of interest change over time. López (2014) describes, according to the theory of dynamical systems, the general procedure of modeling a system (Rabbinge et al., 1989; Van Straten, 2012; López, 2014): 1) definition of a problem and its analysis; 2) development of a conceptual representation of the model through relational or Forrester (1971) diagrams, based on existing knowledge in the literature. This is a qualitative model of the system; 3) the quantitative model can be generated by two options: black box models (BBM) and transparent or mechanistic models (TMM). In BBMs, real experiments are designed and carried out to obtain an empirical model, based on measurements of variables called inputs and outputs of the system.
In the case of TMMs, the set of dynamic equations (differential equations or equations in differences), also called the structure of the model, is postulated (Thornley and France, 2007), based on the conceptual model, the objectives of the model, the theories and data existing in the literature, as well as the existing constraints (data, time, among others).
These techniques are useful for describing all aspects related to agricultural systems, among them the development of pests and diseases; 4) once the nonlinear ordinary differential equations or equations in differences have been generated, they are solved numerically using digital computers through simulation; 5) uncertainty analysis allows quantitatively evaluating the variability in the parameters or input variables of the model, by deducting uncertainty distributions for each variable that the model predicts; 6) a sensitivity analysis of the model is then done to observe how its initial conditions, input variables and parameters affect the behavior of state variables and output variables; 7) through an identifiability analysis, it can be known if the parameter vector of the dynamic model can be determined uniquely from the input variables and output variables.
The methods used in practical identifiability of models are: Monte Carlo simulation, correlation matrix or calculation of the Fisher information matrix and methods based on sensitivity analysis; and 8) parameter estimation or model calibration is performed using existing information in the literature, data from experiments and the results obtained from sensitivity analysis. This is to bring as close as possible the predictions of the state variables and output variables of the model to measurements obtained from the real system.
In both MMs and BBMs, several data sets can be used and a calibrated model can be satisfactorily achieved; 9) the following is the evaluation (validation) stage of the model, this consists of using independent data sets to study the behavior of the model, using the values of its parameters obtained during the calibration phase; and 10) once an evaluated model is obtained, it can be used for some application or carry out another uncertainty analysis. A crucial stage in the development of a model is the verification process, it consists of verifying that the model is ‘as real as life itself’ (Taylor, 2003). The procedure of system modeling is an iterative process that allows returning from one stage to another until the mathematical model is an acceptable representation of the behavior of the real system.
System simulation
Mahalanabis (1982) considers the following stages in systems engineering: modeling, analysis, simulation and design. Simulating is the act of running a mathematical model and obtaining results on the variables of interest (Ruiz, 2020). It is necessary to explore different scenarios through simulation models, to analyze and find crop management options to maintain or increase productivity.
In the simulation of the effect of pests, it should be considered that they can cause great losses, when: the host population is susceptible and genetically uniform, the hosts are grouped or very close together, the pathogen increases rapidly due to its reproductive capacity; the climate and other factors are appropriate for its spreading and development and the period of favorable conditions is optimal to sustain the epidemic (Jarvis, 2000).
Simulation models have become important tools in epidemiology, they allow the exploration of hypotheses, and are an invaluable means of guiding research (APS, 2018). They help solve specific questions (Zadoks and Rabbinge, 1985) and explore the available knowledge of a system. This is due to the link that exists between the levels of integration in biological systems (Rabbinge et al., 1989). Simulation as a scientific approach is unique since it allows the exploration of possible futures. The dependence of agriculture on the climate is of particular importance, due to its high sensitivity to global climate change and climate variability, which makes it essential to understand the interactions between climate change and agricultural production for the stable development of society (Hui et al., 2013).
Simulation can provide a practical and intuitive analysis of plant disease systems and allows exploring the sensitivity of phytopathogenic systems to some of their specified components (Savary and Willocquet, 2014). According to Ruiz (2020), the challenges of crop modeling are: 1) improve the predictive quality of models (fewer models, but better); 2) generate and make accessible meteorological, soil and crop information, necessary to carry out the simulations; 3) develop models for irrigation and fertilization management, considering a public not specialized in modeling; 4) incorporate crop simulation into the study programs of agronomic engineering degrees; and 5) greater collaboration between specialists from different areas for the development, improvement and dissemination of simulation models.
Evaluation (validation) is a demonstration that a model, within a specific application domain, has acceptable predictive precision in that domain (Thornley and France, 2007). Currently with the help of computers, simulations of climate, pest population growth, crop development can be run, generating data for phytopathologists to use in the forecast and management of diseases.
Models applied to plant health
A case of modeling with a phytosanitary approach is that of the apple moth, in which heat units are counted to know the diapause of insects and thus be able to establish optimal moments for efficient control (Jacobo et al., 2005). Other examples of mathematical models for crop protection from pests (Spodoptera frugiperda (Yáñez et al., 2019); Meloidogyne incognita - Trichoderma sp., (Miranda et al., 2016); Lobesia botrana (Dagatti and Becerra, 2015); Liriomiza (Hernández et al., 2009); Aeneolamia postica (García et al., 2006); Spodoptera exigua and Helicoverpha zea (Cabello and Carreño, 2002); H. zea, Helicoverpa armigera and Bemisia tabaci (Gámez et al., 2000) and diseases (Phytophthora ramorum (Magarey, 2007); Phytophthora infestans (Rebellón et al., 2020); Xanthomonas campestris (Rocha, 2020); Cladosporium cladosporioides (Romero et al., 2016); Altenaria tenuissima (Moschini et al., 2014); Gibberella zeae and Magnaporthe grisea (Fernandes et al., 2011); Mycosphaerella fijiensis (Freitez et al., 2009); Phytophthora infestans (Gómez et al., 2002); Botrytis cinerea (Vidal et al., 2001)), as well as ecological niche models that have been used when modeling species distribution (Moniliophthora roreri (Vilchez, 2021); Colletotrichum acutatum (Quishpe, 2020); Xylella fastidiosa (Gutiérrez, 2019); Rhagoletis sp., (Samano, 2019); Phyllophaga ravida (Aragón et al., 2018)), can be found in the literature.
Mexico has a National Laboratory of Modeling and Remote Sensing, which is responsible for offering agricultural producers’ real-time meteorological information to make decisions in their production systems and reduce the risks caused by adverse climatic conditions (INIFAP, 2021). In the country, some studies aimed at the use of modeling in the area of pests and diseases have been carried out (Guzmán et al., 1999; Jacobo et al., 2005; Hernández et al., 2009; Hernández et al., 2013; Duran et al., 2017; Hernández et al., 2020). López et al. (2021; 2022a); López et al. (2022b) generated dynamic models of the development of phytophagous thrips and biological control thrips in avocado, with these, one can simulate the progress of prey populations in their different biological stages and quantify the number of predators that must be introduced for effective biological control.
It is necessary to transfer knowledge through current computational tools and thus support the producers of the different crops in decision-making. Figure 1 shows that the use of simulation models in crops associated with pests and diseases is increasing over time. This is due to the easy access to information, to the use of technology for data analysis and to the rapid processing of the information that relates: elements of the climate, the growth and development of the crop, as well as the behavior of pests and diseases.
The countries that publish the most on modeling applied to plant health are the United States of America, China, England and France. The institutions that have the most publications on this topic are: United States Department of Agriculture, Wageningen University and University of Florida. The scientific journals that publish the most models of pests and diseases are Pest Management Science, Journal of Economic Entomology, Applied and Environmental Microbiology, Environmental Entomology and Ecological Modelling (Scopus, 2022).
Conclusions
The main economic benefit of modeling and simulation of systems is the savings that producers can have by applying only the indispensable number of sprays. Modeling can favor better crop management, less environmental damage, and safe production, which meets the most demanding standards of current and new export markets for some products, such as the European and the Asian where there is a large population and purchasing power.
The type of model will depend on the problem being studied, it can be useful to understand the dynamics of infections or as a forecasting instrument. Therefore, a good understanding of the biological system to be studied and defining data collection in accordance with the objectives of the model is necessary. Systems simulation is a tool that allows the exploration of possible future scenarios and the understanding that some components may have a greater or lesser effect on the plant-pathogen system over time. It can be useful in the analysis of the resistance of the host plant because it allows tracing through time processes that cannot be seen and that can be linked to current advances in molecular improvement.
The temporal-spatial distribution of pests and diseases in agroecosystems can simulate and evaluate scenarios for efficient and sustainable management.
Literatura citada
Achicanoy, L. H. 2000. Descripción cuantitativa de las epidemias de las plantas. Rev. Facultad Nacional Agrícola de Medellín. 1(53): 941-968. [ Links ]
APS. 2018. American Phytopathological Society. Simulation Modeling in Botanical Epidemiology and Crop Loss Analysis. Encontrado. https://www.apsnet.org/edcenter/advanced/topics/BotanicalEpidemiology/Pages/SimulationModels.aspx. [ Links ]
Aragón, G. A.; Guillen, S. D.; Juárez, L. P. y Alía, T. I. 2018. Interacción geográfica del nicho ecológico de Phyllophaga ravida1 y dos cultivos agrícolas en México. Geographic Interaction of the Phyllophaga ravida1 Ecological Niche and Two Crops in Mexico. Southwestern Entomologist. [ Links ]
Boudon, F.; Pradal, C.; Cokelaer, T.; Prusinkisrewicz, P. and Godin, C. 2012. “L-py: an l-system simulation framework for modeling plant development based on a dynamic language,” Frontiers in Plant Science. 3(76). [ Links ]
Bouman, B. A. M.; Van Keulen, H.; Van Laar, H. H. and Rabbinge, R. 1996. The ‘School of de Wit’crop growth simulation models: a pedigree and historical overview. Agricultural Systems. 52(2-3):171-198. [ Links ]
Cabello, T. y Carreño, R. 2002. Modelos logísticos aplicados a la fenología de noctuidos plagas en el sur de España (Lep. Noctuidae). Ministerio de Agricultura, Pesca y Alimentación, Madrid, España. [ Links ]
Campbell, C. L. y Madden, L. V. 1990. Introduction to plant disease epidemiology. Wiley, New York. 532 p. [ Links ]
Dagatti, C. V. y Cristina, B. V. 2015. Ajuste de modelo fenológico para predecir el comportamiento de Lobesia botrana (Lepidoptera: Tortricidae) en un viñedo de Mendoza, Argentina. Revista de la Sociedad Entomológica Argentina. 74(3-4):117-122. [ Links ]
De Wit, C. T. and de Vries, F. P. 1982. L’analyse des systemes de production primaire. In la productivite des paturages Saheliens Pudoc. 918:20-23. [ Links ]
De Wolf, E. D. and Isard, S. A. 2007. Disease cycle approach to plant disease prediction. Annual Review of Phytopathology. 45(9):1-18. [ Links ]
Durán, P. E.; Téliz, O. D.; Pedroza, S. A.; Mora, A. A.; Ávila, Q. G. D. y González, H. H. 2017. Modelo de pronóstico para el control de la antracnosis del aguacate en Michoacán, México. Colegio de Postgraduados. Fitosanidad-Fitopatología. Tesis de Doctorado. 73 p. [ Links ]
Fernandes, J. X. y Pavan, W. X. 2011. Sistemas de predicción para enfermedades em cereales de inverno: fusariosis y brusone. In: Embrapa Trigo-Artigo em anais de congresso (ALICE). In: Pereyra, S.; Ackermann, MD de; Germán, S.; Cabrera, K. (Ed.). Manejo de enfermedades en trigo y cebada : INIA Montevideo. 37-39 pp. [ Links ]
Forrester, J. W. 1971. Principles of systems. Pegasus communications, Inc. Waltham, MA. USA. 392 p. [ Links ]
Fransz, H. G. 1974. The Functional Response to Prey Density in An Acarine System. Simulation Monographs. Pudoc, Wageningen. The Netherlands. 143 p. [ Links ]
Freitez, J. A.; Ablan, M. y Gómez, C. 2009. Propuesta de modelos predictivos del brote de la Sigatoka Negra para las plantaciones de plátano al sur del Lago de Maracaibo, Venezuela. Rev. Científica UDO Agrícola. 9(1):191-198. [ Links ]
García, G. C. G.; López, C. J.; Nava, T. M. E.; Villanueva, J. J. A. y Vera, G. J. 2006. Modelo de predicción de riesgo de daño de la mosca pinta Aeneolamia postica (Walker) Fennah (Hemiptera: Cercopidae). Neotropical Entomology. 35:677-688. [ Links ]
Gámez, M.; Carreño, R.; Ándujar, A. S.; Barranco, P. y Cabello, T. 2000. Modelos matemáticos de depredador-presa en cultivos hortícolas en invernadero en el sudeste de la Península Ibérica. Bol San Veg Plagas. 26:665-672. [ Links ]
Garrett, K. A.; Forbes, G. A.; Gómez, L.; Gonzales, M. A.; Gray, M.; Skelsey, P. y Sparks, A. H. 2013. Cambio climático, enfermedades de las plantas e insectos plaga. In: Jiménez, Z. E. (Coord.). Cambio climático y adaptación en el altiplano boliviano. La Paz (Bolivia). CIDES-UMSA SANREM CRSP Universidad de Missouri Universidad Mayor de San Andres; Fundacion PROINPA; Universidad de la Cordillera; Universidad Nacional Agraria La Molina (UNALM). [ Links ]
Gómez, G.; Suárez, M.; Figueroa, M.; Rivero, T. y Hernández, A. 2002. Pronóstico del tizón tardío (Phytophthora infestans (MONT.) de BARY) de la papa en Cuba. II. evaluación de la efectividad del modelo naumova modificado. Fitosanidad. 6(2):35-39. [ Links ]
Gutiérrez, H. O. y García, L. V. 2019. La dimensión geográfica de las invasiones biológicas en el Antropoceno: el caso de Xylella fastidiosa. [ Links ]
Guzmán, F. A.W.; Alatorre, R. R.; Pérez, D. F. y Nolasco, Q. X. 1999. Grados día de desarrollo de Sphenarium purpurascens (Charpentier)(Orthoptera: Pyrgomorphidae) y su susceptibilidad A Beauviera bassiana (Bals.) Vuill. (Deuteromycotina: Hyphomycetes bajo condiciones de campo. Tesis de maestría. Colegio de Postgraduados, Campus Montecillo, Instituto de Fitosanidad , Especialidad en Entomología y Acarología. [ Links ]
Hanan, J.; Prusinkiewicz, P.; Zalucki, M. and Skirvin, D. 2002. Simulation of insect movement with respect to plant architecture and morphogenesis. Computers and Electronics in Agriculture. 35(2-3):255-269. [ Links ]
Hernández, D. M. G.; Rojas, M. R. I.; Rivera, P. A.; Zavaleta, M. E.; Ochoa, M. D. L. and Carrillo, S. J. A. 2020. Evaluation of Zebra Chip Using Image Analysis. American Journal of Potato Research. 97(6):586-595. [ Links ]
Hernández, R. E.; Vera, G. J.; Ramírez, V. G.; Pérez, E. S.; López, C. J.; Bautista, M. N. y Pinto, V. M. 2009. Pronóstico de la fluctuación poblacional del minador de la hoja de crisantemo Liriomyza huidobrensis Blanchard (Diptera: Agromyzidae), mediante modelos de series de tiempo. Acta Zoológica Mexicana. 25(1):21-32. [ Links ]
Hernández, Z. M. I.; Quijano, C. J. A.; Yáñez, L. R.; Ocampo, V. R.V.; Torres, P. I.; Guevara, G. R.G. and Castro, R. A. E. 2013. Dynamic simulation model of central American locust Schistocerca piceifrons (Orthoptera: Acrididae). Florida Entomologist. 96(4):1274-1283. [ Links ]
Hui, J. L.; Er-da, T.; Wheeler, A.; Challinor, P. and Shuai, J. 2013. climate change modelling and its roles to chinese crops yield. J. Int. Agric. 12(5):892-902. [ Links ]
INIFAP, 2021. http://www.inifap-nortecentro.gob.mx/. http://clima.inifap.gob.mx/lnmysr. [ Links ]
Jarvis, P. J. 2000. Ecological principles and environmental issues. Prentice-Hall, Nueva York, EEUU. [ Links ]
Jacobo, C. J.; Mora, A. G.; Ramírez, L. M.; Vera, G. J.; Pinto, V. X.; López, C. J. y Aceves, N. L. 2005. Caracterización cuantitativa de la diapausa de palomilla de la manzana Cydia pomonella L. en Cuauhtémoc, Chihuahua, México. Agrociencia. 39(2):221-229. [ Links ]
Kramer, K. 1996. Phenology and growth of European trees in relation to climate change. PhD Thesis. Wageningen University, The Netherlands. 210 p. ISBN 905485464/2. [ Links ]
Kropff, M. J. 1988. Modelling the effects of weeds on crop production. Weed Research. 28:465-471. [ Links ]
Lindenmayer, A. 1968. Mathematical models for cellular interactions in development I. Filaments with one-sided inputs. Journal of Theoretical Biology. 18(3):280-299. [ Links ]
López, C. I. L. 2014. Metodología de modelación matemática dinámica de ambientes agrícolas controlados: avances y retos. Universidad Autónoma Chapingo. [ Links ]
López, C. I. L.; Duran, P. E.; Salazar, M. R. y Fitz, R. E. 2022a. Modelo dinámico depredador-presa para Franklinothrips y Scirtothrips en aguacate: simulación y análisis de sensibilidad. In: información, estabilidad y dinámica en los modelos económicos. Asociación Mexicana de Investigación Interdisciplinaria. Pérez, S. F.; Figueroa, H. E.; Salazar, M. R.; Sepúlveda, J. D.; Escamilla, G. P. y Jiménez, G. M. (Comps). ASMIIA AC. Ciudad de México, México. ISBN: 978-607-99921-2-5. 27-42 pp. [ Links ]
López, C. I. L.; Duran, P. E.; Salazar, M. R.; Fitz, R. E. y Sosa, C. J. O. 2021. Dynamic modeling of thrips population in avocado trees. Computación y sistemas. [ Links ]
López, C. I. L.; Duran, P. E.; Fitz, R. E.; Salazar, M. and Rojano, A. A. 2022b. Predator-prey dynamic model for Franklinothrips and Scirtothrips in avocado trees (Persea americana Mill.): simulation and sensitivity analyses. [ Links ]
Magarey, D. R.; Fowler, A. G.; Borchert, M. D.; Sutton, B. T.; Colunga, G. M. and Simpson, A. J. 2007. NAPPFAST: An Internet System for the Weather-Based Mapping of Plant Pathogens. Plant Disease. 91(4):336-345. [ Links ]
Mahalanabis, A. K. 1982. Introductory System Engineering. Wiley, New York. 3-4 pp. [ Links ]
Maloy, O. C. 1993. Plant Disease Control. Wiley, New York. 351-356 pp. [ Links ]
Martínez, A. P. F. y Vargas, H. A. 2016. Modelo dinámico adaptativo para la gestión del agua en el medio urbano. Tecnología y Ciencias del Agua. 7(4):139-154. [ Links ]
Miranda, C. I.; Hernández, O. D.; Hernández, A. Y.; Martínez, C. B. y Rodríguez, H. M. G. 2016. Modelación de la interacción Meloidogyne incognita (Kofoid y White) Chitwood Trichoderma asperellum Samuels, Lieckfeldt & Nirenberg en garbanzo (Cicer arietinum L.). Revista Protección Vegetal. 31(3):194-200. [ Links ]
Mora, A. G.; Acevedo, S. G.; Calderón, E. G.; Flores, S. J.; Domínguez, M. S.; Baker, P. X. y González, G. R. 2014. Consideraciones epidemiológicas del cambio climático en la Fitosanidad de cultivos tropicales. Rev. Mexicana de Fitopatología. 32(2):147-167. [ Links ]
Moschini, R. C.; Bombelli, E. C.; Wright, E. R.; López, M. V.; Perez, C. H. I.; Carmona, J. D. y Rivera, M. C. 2014. Ajuste de modelos logísticos a la tasa de incremento de severidad de manchas foliares ocasionadas por Alternaria tenuissima en arándano= Logistic models adjustment to growth rate of severity of blueberry leaf spot caused by Alternaria tenuissima. Asociación Argentina de Horticultura. [ Links ]
Noriega, N. J. L.; Salazar, M. R. y López, C. I. L. 2021. Revisión: modelos de crecimiento y rendimiento de maíz en escenarios de cambio climático. Rev. Mex. Cienc. Agríc. 12(1):127-140. [ Links ]
Pohlheim, H. and Heißner, A. 1996. Optimal Control of Greenhouse Climate using Genetic Algorithms. in MENDEL’96-2nd International Conference on Genetic Algorithms. Technical University of Brno, Czech Republik. 112-119 pp. [ Links ]
Prusinkiewicz, P. 2021. Algorithmic Botany, Website of the Biological Modeling and Visualization research group in the Department of Computer Science at the University of Calgary. http://algorithmicbotany.org/. [ Links ]
Quishpe, D. N. T. 2020. Modelo de nicho ecológico para predecir la distribución potencial de Antracnosis (Colletotrichum acutatum) en el cultivo de chocho (Lupinus mutabilis Sweet) en Ecuador. (Bachelor’s thesis, Ecuador, Latacunga: Universidad Técnica de Cotopaxi UTC. [ Links ]
Rabbinge, R.; Ward, S. A. and Van Laar, H. H. 1989. Simulation and systems management in crop protection, PUDOC, Wagenigen. 420 p. [ Links ]
Rebellón, J. D. S.; Rodríguez, D. A. L. y Arias, D. G. 2020. Estudio bioinformático del gen CRN8 en Phytophthora infestans causante de la enfermedad tizón tardío en plantas. Microciencia. 9:57-81. [ Links ]
Rocha, C. C. E. y Leal, L. D. D. 2020. Modelo para la detección de la enfermedad Xanthomonas campestris en hojas de judía aplicando algoritmos de optimización genéticos y de gradiente. Universidad Distrital Francisco José de Caldas, Facultad de Ingeniería. Proyecto curricular Ingeniería de Sistemas . Bogota D.C., Colombia [ Links ]
Romero, C. T.; López, P. P. A.; Ramírez, L. M. y Cuervo, P. J. A. 2016. Modelado cinético del micoparasitismo por Trichoderma harzianum contra Cladosporium cladosporioides aislado de frutos de cacao (Theobroma cacao). Chilean Journal of Agricultural & Animal Sciences. 32(1):32-45. [ Links ]
Rongier, G.; Collon, P.; Renard, P. 2017. Stochastic simulation of channelized sedimentary bodies using a constrained L-system. Computers & Geosciences. 105(2017):158-168. ISSN: 0098-3004. [ Links ]
Rossing, W. A. H. 1993. On damage, uncertainty, and risk in supervised control: aphids and brown rust in winter wheat as an example. PhD Thesis, Wageningen University, The Netherlands. 202 p. ISBN 90-5485-137-6. [ Links ]
Ruiz, G. A. 2009. Modelos para simulación y control del clima de un invernadero con ventilación natural. Tesis de Maestría en Ingeniería. Universidad Autónoma Chapingo. Chapingo, México. 126 p. [ Links ]
Ruiz, G. A. 2020. La modelación del crecimiento de cultivos: conceptos, aplicaciones y retos. Serie de Seminarios Virtuales 2020. Colegio Mexicano de Ingenieros en Irrigación (C0MEII). México. 30 p. [ Links ]
Scopus. 2022. http://www.scopus.com. [ Links ]
Samano, A. L. L. 2019. Nicho ecológico potencial de ocho especies de Rhagoletis (díptera, tephritidae) de importancia agrícola para México. Tesis de maestría. Universidad Autónoma Del Estado De Morelos. Facultad De Ciencias Agropecuarias, Morelos, México. [ Links ]
Savary, S. and Willocquet, L. 2014. Simulation Modeling in Botanical Epidemiology and Crop Loss Analysis . Plant Health Instructor. 147 pp. [ Links ]
SIAFEG, 2010. SIAFEG.http://www.siafeg.com/siafeg/siafeg.htm. [ Links ]
Steduto, P. 2006. Biomasa Water-Productivity. Comparing the growth-engines of crop models. 1-16 p. In: WUEMED Training course. “Integrated approaches to improve drought tolerance in crops”. Department of Agroenvironmental Sciences and Technology, University of Bologna. Bologna. [ Links ]
Taylor, N. 2003. Review of the use of models in informing disease control policy development and adjustment. School of Agriculture, Policy and Development. [ Links ]
Téliz, O. D. y Mora, A. A. 2007. El aguacate y su manejo integrado. Mundiprensa. México. 319 p. [ Links ]
Thornley, J. H. M. and France, J. 2007. Mathematical models in agriculture: quantitative methods for the plant, animal, and ecological sciences. CABI. [ Links ]
Van Ittersum, M. K.; Leffelaar, P. A.; Van Keulen, H.; Kropff, M. J.; Bastiaans, L. y Goudriaan, J. 2003. On approaches and applications of the Wageningen crop models. Eur. J. Agron. 18(3-4):201-234. [ Links ]
Van Kraalingen, D. W. G.; Rappoldt, C. y Van Laar, H. H. 2003. The Fortran simulation translator, a simulation language. Eur J Agron. 18(3-4):359-361. [ Links ]
Van Straten, G. X. 2012. Systems dynamics for bioengineers. Lectures Notes. University of Chapingo, Chapingo, México. 146 p. [ Links ]
Vidal, D. C. I. y Ortega, F. S. 2001. Validación de un modelo de predicción de la enfermedad pudrición gris de la vid, causada por el hongo Botrytis cinerea, en un viñedo de la séptima región (Doctoral dissertation, Universidad de Talca. Chile. [ Links ]
Vilchez, P. C. R. 2021. Potenciales efectos del cambio climático sobre la distribución del hongo (Moniliophthora roreri Cif & Par) en el cultivo de cacao (Theobroma cacao) en Ecuador (Bachelor’s thesis, Quevedo: UTEQ). [ Links ]
Voinov, A. 2008. Systems science and modeling for ecological economics. Elsevier. [ Links ]
Yáñez, L. R.; Vázquez, O. A.; Arreguín, C. J. H.; Soria, R. J. y Quijano, C. J. Á. 2019. Sistema de alerta contra el gusano cogollero Spodoptera frugiperda (JE Smith) (Insecta: Lepidoptera: Noctuidae). Rev. Mex. Cienc. Agríc. 10(2):405-416. [ Links ]
Zadoks, J. C. and Rabbinge, R. 1985. Modelling to a purpose. In: Advances in plant pathology, mathematical modelling of crop diseases. CA. Gilligan, (Ed). Academic Press, London. 231-244 pp. [ Links ]
Received: August 01, 2022; Accepted: September 01, 2022