Simulation of Phenological Events Through the Distributed Time Delay Model: Case Study for Flower Buds and Fruits in Coffee
Abstract
The distribution time delay model has been used extensively in ecological modeling to simulate population dynamics mainly on insects, but it has been used also to model growth and development processes in plants. This paper presents the mathematical development of this model in a comprehensive and explicit way to enable understanding of details. The model is developed in a spreadsheet easily reproducible in order to enable the reader to implement and analyze the issues that he considers relevant. Finally, an example is developed, in which we model the distribution of development times of coffee flower buds and fruits, obtaining appropriate adjustment of the model to experimental data.
Downloads
References
Carlini L., Severini M. y Dattilo A. 2001. Il modello a ritardi distribuiti per la simulazione dello sviluppo de una popolazione biologica a tem- peratura constante: Caso Della sepcie Arte mia franciscana. Ricerca svolta nell'ambito del progetto finalizzato CLIMAGRI finanziato dal Ministero delle Politiche Agricole e Forestali D. M. 484 e 504/7303/2000 - Pubblicazione n.5, 22p. http://climagri.entecra.it/argomento5.htm. Consulta: abril de 2010.
D’Oultremont T. y Gutierrez. A. P. 2002. A multitrophic model of a rice-fish agroecosystem II. Linking the flooded rice-fishpond systems. Ecological Modelling 155 (2-3): 159-176.
Drinnan, J. E. 2008. The control of floral development in coffee (Coffea arabica L). Tesis de grado Ph. D. School of Biological Sciences. Queensland University. Australia, 157p.
Edwards H. y Penney D. 2008. Differential Equations and Boundary Value Problems. Computing and Modeling. 3th edition. Prentice Hall. New Jersey. 309 p.
Fox J. 2002. Nonlinear regression and nonlinear least squares. Appendix to An R and S-PLUS Companion to Applied Regression 5p. http:// cran.r-project.org/doc/contrib/Fox-Compa- nion/appendix-nonlinear-regression.pdf. Con- sulta: noviembre de 2009.
Gutierrez A. P., Pizzamiglio M., Dos Santos W., Tennyson R. y Villacorta A. 1984. A general distributed delay time varying life table plant population model: Cotton (Gossypium hirsutum L.) growth and development as an example. Ecological Modelling 28: 3-4. 231-249.
Gutierrez A. P. 1996. Applied Population Ecology. John Wiley & Sons. U.S.A.
Gutierrez A., Ponsard S. y Ellis C. K. 2006. Physiologically based demographics of Bt cotton-pest interactions. I. Pink bollworm resistance, refuge and risk. Ecological Modelling 191 (3-4): 346-359.
Gutierrez A. P., D’Oultremont T., Ellis C. K. y Ponti L. 2006. Climatic limits of pink bollworm in Arizona and California: Effects of climate warming. Acta oecologica 30: 353-364.
Gutierrez A. P. y Ponsard S.2006. Physiologically based demographics of Bt cotton-pest interactions. I. Pink bollworm resistance, refuge and risk. Ecological Modelling. 191 (3-4): 346-359.
Gutierrez A. P., Daane K., Ponti L., Walton V. y Ellis C. K. 2008. Prospective evaluation of the biological control of vine mealybug: refuge effects and climate. Journal of Applied Ecology 45: 524-536.
Gutierrez A. P. y Ponti L. 2013. Deconstructing the control of the two spotted alfalfa aphid Therioaphis maculata. Agricultural and forest entomology 15:272-284.
Manetsch T. 1966. Transfer function representation of the aggregate behavior of a class of economic processes. IEEE transactions on Automatic Control 11 (4): 693-69.
Manetsch T. 1976. Time-varying distributed delays and their use in aggregate models of large systems. IEEE transactions on Systems, Man and Cybernetics 6 (8): 547-553.
R Development Core Team. 2013. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing. Vienna, Austria. http://www.R-project.org/
Ramírez J. 2009. Determinación de la relación genética entre características de floración y fructificación con el rendimiento en una población F2 de Coffea arabica L. (Caturra x CCC 1146). Tesis M. Sc,. Facultad de Ciencias Agro- pecuarias. Universidad Nacional de Colombia. Medellín. 75p.
Rochat J y Gutierrez A. P. 2001. Weather-Mediated Regulation of Olive Scale by Two Parasitoids. Journal of Animal Ecology 70 (3): 476-490.
Rodríguez D., Cure J. R., Cotes J. M., Gutierrez P. y Cantor F. 2011. A coffee agroecosystem model I: growth and development of the coffee plant. Ecological Modelling 222: 3626-3639.
Rodríguez D., Cure J. R., Gutierrez A. P., Cotes J. M. y Cantor F. 2012. A coffee agroecosystem model II: Dynamics of coffee berry borer. Eco- logical Modelling 248: 203-214.
Salazar M., Chaves B., Riaño N., Arcila J. y Jaramillo A. 1994. Crecimiento del fruto de café Coffea arabica L. var. Colombia. Revista Cenicafé 45 (2): 41-50.
Vansickle J. 1977. Attrition in Distributed Delay Models. IEEE Transactions on Systems, Man and Cybernetics 7(9): 635-638.
Ziegler C. R., Drummond F. A., Donahue D. W. y Smith S. N. 2000. Agrelation: A Computerized decision-making tool for Colorado potato beetle population management and environmental quality concerns. Technical bulletin # 176. Maine agricultural and forest experiment station. University of Maine. 47 p.