Modelos matemáticos para la predicción de los rendimientos y calidad de la madera aserradaMathematical models for the prediction of the yields and quality of sawn woodDailyn Estremera-Rivas; Yuris Rodríguez-MatosEmpresa Agroforestal Sierra Cristal. Guantánamo, CubaUniversidad de Guantánamo, CubaCorreo(s) electrónico(s) dailyn.estremera@nauta.cuyurisrm@cug.co.cu, yurisrodriguezm@gmail.comORCID: http://orcid.org/0000-0001-9202-6280 http://orcid.org/0000-0002-5032-6362 Recibido: 20 de octubre de 2020 Aceptado: 26 de noviembre de 2020ResumenLa investigación se realizó en rodales de Pinus cubensis Griseb y aserradero en la Empresa Agroforestal Sierra Cristal, desde enero de 2019 a diciembre 2020, con el objetivo de estimar modelos matemáticos que posibiliten predecir el rendimiento y calidad de la madera aserrada. Se evaluó la influencia de los parámetros dendrométricos y presencia de nudos, a partir de la magnitud del diámetro, altura hasta la primera rama, altura de copa, altura total, área basal, conicidad y la calidad de la madera en pie. El modelo de mejor resultados fue el 3: rendimiento = 33,39 + 0,69 d1, 30 -3,13X1 -7,45X2.Palabras clave: Aserradero, Modelos matemáticos, Rendimiento, Dendrométricos. AbstractThe investigation was carried out in rodales of Pinus cubensis Griseb and sawmill in the Company Agroforestal Sierra Cristal, of January 2019 to December 2020, with the objective of estimating mathematical models that facilitate to predict the yield and quality of sawed wood. It was evaluated the influence of the parameters dendrométricos and presence of knots, starting from the magnitude of the diameter, height until the first branch, glass height, total height, basal area, conicidad and in the quality of the Wood in foot. The pattern 3 on yield = 33, 39 + 0, 69 d1,30 -3,13X1 -7,45X2 were that of better results. Key words: Sawmill models, yield, quality, parameters and dendrométricos.IntroducciónÁlvarez, et al. (2010) plantean que en la nueva era de la globalización, la sostenibilidad de los procesos de producción en todo su contexto y las exigencias de los tratados y convenios internacionales, impone nuevos retos a las empresas e instituciones que requieren perfeccionar sus métodos de producción y poder ofertar al mercado un producto que satisfaga los intereses y demandas de la sociedad y principalmente que permita asegurar tanto a las generaciones presentes como futuras los bienes y servicios que proporcionan los bosques.Explican además, que la indústria de la elaboración primaria de la madera a escala mundial se encuentra frente al reto de mejorar los niveles y calidad de los productos y procesos, ya que la madera continúa siendo un producto muy apreciado, no solo por sus características que la hacen insustituible para algunos usos, sino también por su carácter multipropósito y que se obtiene de fuentes de materia prima renovable. La industria del aserrado en Cuba está muy alejada de los resultados de productividad medios anuales de una determinada cantidad de países, expresando que son muchas las causas que provocan esto, pero sin dudas la inadecuada infraestructura desempeña un papel predominante; lo cual ha sido expuesto por Levsque (2009). En Cuba, las plantaciones de Pinus han ido incrementándose considerablemente, atendiendo a que por su versatilidad desempeñan un rol protagónico en los planes de reforestación del país, de acuerdo a la explicación de Linares, et al. (2009). Los cambios experimentados en la tecnología, y la tendencia de tratar de satisfacer las demandas de una población creciente, implican una mayor exactitud en la determinación de los volúmenes de madera así como en el rendimiento y calidad en los aserraderos según lo expuesto por Álvarez, et al. (2003).No obstante, Álvarez, et al. (2010), expresan que en los últimos años se han puesto en marcha aserríos más modernos, con una tecnología más avanzada que favorece la calidad de la madera obtenida, y permite elevar la productividad industrial y la eficiencia técnica y económica.La predicción mediante modelos matemáticos son herramientas muy valiosas que todas las empresas forestales deberían implementar, para optimizar el rendimiento de madera aserrada. Estos modelos constituyen una necesidad para las empresas mejorar sus ingresos y tal vez lo más importante, disminuir la perdida de madera, de acuerdo al planteamiento de Leckoundzou (2011). En los aserraderos de la provincia Santiago de Cuba, existen bajos niveles de productividad y calidad en la madera aserrada, lo que implica la necesidad de una planificación por exceso de las necesidades reales de madera en bolo en los aserraderos y en la implementación de tecnología viable se debe disminuir la extracción de madera de los bosques, ya que se trabajaría de forma integral desde el bosque hasta la industria, prediciendo los volúmenes y grosores de los arboles a talar para alcanzar los rendimientos deseados. De acuerdo a lo que se plantea anteriormente el trabajo tiene como objetivo general: estimar modelos matemáticos que posibilitan la predicción en el rendimiento y calidad de la madera aserrada, a partir de parámetros dendrométricos de los árboles en pie de Pinus cubensis Griseb.DesarrolloLa Empresa Agroforestal Sierra Cristal se encuentra situada en la porción noroeste del municipio Segundo Frente, con una extensión territorial de 19 795, 94 ha. Los datos fueron tomados del lote 2, rodales 9 y 11 de la Unidad Silvícola Corea, mediante un muestreo aleatorio, donde se utilizó como variable de interés el volumen (V.ha-1). Para calcular el tamaño de la muestra, primero fue necesario determinar la intensidad de muestreo (f):f = intensidad de muestreo. QUOTE QUOTE Donde:f= fracción o intensidad de muestreon= cantidad de unidades o superficie muestreadaN = número de unidades de la población o superficie totalComo (1-f) > 0,98; la población es infinita y se utiliza la fórmula siguiente: En función de la varianza: En función del coeficiente de variación:Donde:t= distribución de t de Student para un nivel de significación 0,05, s2= varianza E= error, cv= coeficiente de variación y LE= límite de error.Para determinar los errores de muestreo se emplearon las fórmulas siguientes:Error absoluto: Error relativo: Se empleó un muestreo aleatorio simple, donde el proceso fundamental de selección a partir del cual se derivaron todos los demás procedimientos, fue para aumentar la precisión de las estimaciones y reducir los costos del levantamiento de acuerdo con la metodología de Aldana, et al. (2010).Se levantaron 10 parcelas de 20 x 25 m (500 m2), donde se tomaron 10 árboles en cada una de ellas, los mismos fueron talados, medidos los parámetros dendrométricos y se determinó la calidad de los árboles, luego se trocearon y marcaron para su identificación y traslado al aserrío para ser procesados y obtener información sobre el volumen, rendimiento y calidad.Para determinar la conicidad de las trozas se aplicó la fórmula utilizada por Henry, et al. (2010) y Álvarez et al. (2010a):Para obtener el rendimiento en porcentaje se empleó la relación utilizada por Álvarez, et al. (2010):Metodología para la determinación de la calidad de los árboles en piePara la determinación de la calidad de los árboles en pie se tomó como referencia los trabajos realizados por Murillo y Camacho (1997) y Murillo (2001), los cuales determinaron la calidad del árbol completo o de sus primeras dos trozas (>2,5 m de largo) dividiéndolos en cuatro categorías de calidad como se muestra en la Figura 1.Figura 1. Representación gráfica de la conicidad de las trozas.Fuente Murillo (2001).La asignación de la calidad de la madera se basa en diferentes variables cuantitativas y cualitativas, que se examinan en cada individuo. Las variables que se consideraron son las siguientes: diámetro, conicidad, curvatura, daño mecánico y longitud.Modelación matemática de la influencia de los parámetros dentro métricos de los árboles en pie sobre los rendimientos de madera aserradaPara la estimación de los modelos, se realizaron análisis de correlación y regresión lineal simple. Como variables independientes o predictoras se utilizaron diámetros a la altura de 1.30 m (d1.30), altura comercial, conicidad y calidad de los arboles en pie, se utilizó como variable de respuesta o dependiente el rendimiento de la madera aserrada en correspondencia con los trabajos realizados por Egas, et al. (2001), Aranzeta, et al. (2004) y Ayessa (2011).En la tabla 1 se observa el cálculo del tamaño de la muestra que se realizó para un error de ±10% y una probabilidad del 95%. La variable de interés fue el volumen por hectárea (V.ha-1) y al procesarse estadísticamente, las 10 parcelas de 100 m2 levantadas en el muestreo piloto, se determinó que las mismas eran suficientes, lo que infiere que el muestreo realizado es representativo.Se puede exponer que al determinar el error relativo, indica que existe confiabilidad del tamaño de la muestra, con un error relativo de 7,14% por debajo del propuesto, lo que indica que la muestra realizada es representativo para el volumen por hectárea en el área de investigación.Tabla 1. Tamaño de la muestra en el ecosistema de la especie de mangle. Fuente: Elaboración propiaVariableValorU/MNúmero de muestra10-Media 20,314m3/haVarianza QUOTE 0,004(m3/0,01 ha)2Desviación estándar ( QUOTE )0,066(m3/0,01 ha)2Error relativo (Er)7,14%En la tabla 2 se observa la matriz de correlación de variables para el fuste con el volumen de madera en bolo (Vmb), como variable dependiente respecto a las variables independientes. Diámetro a 1.30 en la parte más fina, diámetro en la mitad, altura del fuste y altura comercial, donde se observa que las variables que más fuerte correlacionan son los tres diámetros, siendo más fuerte con el diámetro a un medio, ya que durante el procesamiento de los datos en la matriz de correlación, se observó, que todas las variables cuantitativas tienen coeficientes altamente significativos, con la variable dependiente rendimiento, (p ≤ 0,001), además el diámetro presenta una mayor fortaleza en su relación lineal. Al coincidir con este resultado lo expuesto por Ayessa (2011).Diámetro 1.30 Altura comercial Altura total Conicidad Índice de sitio Rendimiento Diámetro 1.30 Correlación de Pearson 1,649**,663**-,562**,642**,911**Sig. (bilateral) ,000,000,000,000,000N 100100100100100100Altura comercial Correlación de Pearson ,649**1,763**-,522**,599**,601**Sig. (bilateral) ,000,000,000,000,000N 100100100100100100Altura total Correlación de Pearson ,663**,763**1-,459**,710**,645**Sig. (bilateral) ,000,000,000,000,000N 100100100100100100Conicidad Correlación de Pearson -,562**-,522**-,459**1-,438**-,584**Sig. (bilateral) ,000,000,000,000,000N 100100100100100100Índice de sitio Correlación de Pearson ,642**,599**,710**-,438**1,619**Sig. (bilateral) ,000,000,000,000,000N 100100100100100100Rendimiento Correlación de Pearson ,911**,601**,645**-,584**,619**1Sig. (bilateral) ,000,000,000,000,000N 100100100100100100**. La correlación es significativa al nivel 0,01 (bilateral).Tabla 2. Correlaciones Fuente: Elaboración propiaEl éxito de cualquier técnica multivariante, incluyendo las regresiones múltiples, comienza con la selección de las variables que se van a utilizar en el análisis. Dado que la regresión múltiple muestra una relación de dependencia, se debe especificar qué variable se usa como criterio y qué variables se usan como predictoras. La selección de ambos tipos de variables deberá basarse principalmente en fundamentos conceptuales o teóricos de acuerdo a la explicación de Hair, et al. (1999). Las transformaciones de los datos proporcionan un medio de modificar las variables con la finalidad de mejorar la correlación entre las variables en correspondencia con Hair, et al. (1999).En la tabla 3 se observa en resumen de los modelos, donde el que tuvo mejor comportamiento fue el 3, que incluye el diámetro a 1,30 y la calidad, porque a pesar de que la conicidad resulta significativa la contribución a la disminución de R2 y al error típico no es tan relevante con la complejidad que desde el punto de vista práctico constituye incorporar esta variable al modelo.Ecuación de regresión estimada: Rendimiento= 33,39 + 0,69 d1,-3,13X1 -7,45X2 modelo de mejor comportamiento del ajuste y predicción se corresponde con lo reportado por Barrio et al. (2004) en modelos de rendimiento de los árboles en diversas especies forestales. ModeloRR cuadradoR cuadrado corregidaError típ. de la estimación1,911a,831,8293,0245672,927b,860,8572,7676203,934c,872,8682,6512634,938d,880,8752,579653Tabla 3. Resumen del modelo. Fuente: Elaboración propiaA partir de este modelo permite predecir los rendimientos y calidad de la madera aserrada de la especie de Pinus cubensis y es de importancia para garantizar desde un punto de vista económico una mejor comercialización del producto, además desde el indicador ambiental permite un mejor trabajo en el ecosistema en función de garantizar un ecosistema viable, con un adecuado manejo desde la silvicultura y el aprovechamiento.Conclusiones Existe relación entre el rendimiento de la madera aserrada de Pinus cubensis Griseb, el diámetro a 1.30 y la calidad de los arboles en pie, para estimar los volúmenes de madera a talar según la necesidad de los aserraderos para el cumplimiento de sus planes de producción. El modelo matemático que mejor se comportó fue el 3: rendimiento = 33,39 + 0,69 d1,30 -3,13X1 -7,45X2 , en función de garantizar la predicción de los rendimientos y calidad de la madera aserrada.Referencias bibliográficasAldana, E. (2010). Ordenación de montes. La Habana: Félix Varela. Álvarez, D., Betancourt, Y., Rodríguez, J.F., Pastor, J.F., Villalba, M.J., Alaejos, J., Prades, C., Álvarez, E. y Candano, F. (2010). Aprovechamiento Forestal. Universidad de Pinar del Río. Félix Varela.Alvarez, D. Dorado, M., Fernández, H. (2010). Tecnología de la madera. Universidad de Córdoba. Argentina: Editorial UniversitariaAlvarez, D. Egas, F. A., Esteves, I. Chávez, P., Garcia, J. M. (2003). Análisis matemático para elevar la eficiencia en los aserraderos. Revista Chapingo. Serie Ciencias Forestales y del Ambiente. No. IX, pp. 79-99.Aranzeta. Z, M., Casado Sanz, T V., Pando, F. (2004). Modelo de estimación de volumen de madera aserrada que emplea variables de árboles en pie para Pinus radiata, p. 78.Barrio, M., Álvarez, J. G., Díaz-Maroto, H. (2004). Elaboración de una tarifa con clasificación de productos para Quercus robur L. en Galicia basada en un modelo de cálculo porcentual. Invest. Agrar: Sist. Y Recur. For. 13 (3), 506- 517. Egas, F. A., Álvarez, D., Estévez, I., García, J. M. (2001). Factores fundamentales para aumentar el rendimiento volumétrico en los aserraderos de Cuba. Revista Chapingo. Serie Ciencias Forestales y del Ambiente. Vol. VII (2) 163-168. México. 2001.Hair, J. F., Anderson, R. E., Tatham, R. L., Blanck, W. C. 1999. Análisis multivariante, Quinta edición. Madrid: Prentice Hall Iberia. Henry, P. P., García, J. M., González, A., López, R., García, M. V. y Moreno, I. (2010). Estudio de algunas características morfológicas del fuste de Cedrela odorata L. en plantaciones intensivas. Revista Forestal Baracoa, Vol. 29 (2), pp. 57-65.Leckoundzou. A. (2011). Influencia de diferentes variables dendrométricos y calidad de árboles en pie sobre los rendimientos de madera aserrada de Pinus caribaea Morelet var. Caribaea Barret y Golfari. (Tesis de Doctorado). Pinar del Rio. Cuba.Levsque, M. (2009). Industria forestal primaria. Diagnóstico de la industria forestal en Cuba. Proyecto para el desarrollo del sector forestal. Ministerio de la Agricultura. La Habana. Macdonald, W. (1972). Estudio de la situación de los aserraderos en Cuba. La Habana: INDAF.Murillo, O. (2001). Estado del desarrollo de la evaluación y control de calidad de plantaciones forestales en Costa Rica. En: V Congreso Mexicano de Recursos. Mexicanos. 7-9 noviembre. Guadalajara, Jalisco, México.Murillo, O. y Camacho, P. (1997). Metodología para la evaluación de la calidad de plantaciones recién establecidas. Agronomía Costarricense 21 (2): 189-206.Vol. 6, No.13, octubre- diciembre, año 2021 PAGE \* MERGEFORMAT14Vol. 6, No.13, octubre- diciembre, año 2021Ciencia y Progreso Publicada en línea: julio, 2021, RNPS: 2477, ISSN: 2707-7098 http://cienciayprogreso.cug.co.cuDailyn Estremera, Yuris Rodríguez: Modelos matemáticos para la predicción de los rendimientos y 183GmgAAAAAAAKAY4AMACQAAAABRRQEACQAAAzQBAAADABwAAAAAAAUAAAAJAgAAAAAFAAAAAgEB AAAABQAAAAEC////AAUAAAAuARgAAAAFAAAACwIAAAAABQAAAAwC4AOgGBIAAAAmBg8AGgD///// AAAQAAAAwP///7X///9gGAAAlQMAAAsAAAAmBg8ADABNYXRoVHlwZQAAwAAIAAAA+gIAABAAAAAA AAAABAAAAC0BAAAFAAAAFAIAAhgEBQAAABMCAALaCBwAAAD7AoD+AAAAAAAAkAEBAAAABAIAEFRp bWVzIE5ldyBSb21hbgC88BIAeUh7dUCRfnVvFmZEBAAAAC0BAQAIAAAAMgqJAxYGAQAAAEx5CAAA ADIKcQFOBwEAAABEeQgAAAAyCnEBPgQBAAAARHkJAAAAMgpgAi4AAwAAAENvbmUcAAAA+wIg/wAA AAAAAJABAAAAAAQCABBUaW1lcyBOZXcgUm9tYW4AvPASAHlIe3VAkX51bxZmRAQAAAAtAQIABAAA APABAQAIAAAAMgrRAUIIAQAAADFvCAAAADIK0QFLBQEAAAAybxwAAAD7AoD+AAAAAAAAkAEAAAAC 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