Morfometría geométrica aplicada al estudio de la hoja de Theobroma cacaoGeometric morphometric applied to the study of Theobroma cacao leafFrank Ernesto Soto Gómez; Igor Bidot MartínezUniversidad de Guantánamo, CubaCorreo(s) electrónico(s) frankernesto@cug.co.cuibidot@cug.co.cuORCID: https://orcid.org/0000-0002-4379-4395 https://orcid.org//0000-0002-1262-7674 Recibido: 19 de abril de 2021 Aceptado: 6 de junio de 2021ResumenEl propósito consiste en analizar los patrones de variación de la forma de la hoja de cacao mediante la morfometría geométrica para identificar los genotipos tradicionales, dada la necesidad de identificar los genotipos tradicionales de cacao basado en la forma de la hoja. Se fotografiaron 490 hojas de siete genotipos y se colocaron 14 puntos clave, se les realizó análisis Procrustes, un ajuste con el análisis de componentes principales y un análisis canónico. Se observó variabilidad morfológica distintiva en cuanto a la forma del cacao tradicional y los genotipos comerciales analizados, lo cual permite una diferenciación preliminar entre ellas.Palabras clave: Componentes principales; Análisis canónico; Morfometría geométrica; Puntos clave.AbstractThe problematic analyzed was: How to identify traditional cacao genotypes based on leaf shape? And the objective was: Analyze the variation patterns of the cacao leaf shape through geometric morphometry to identify traditional genotypes. A total of 490 leaves of seven genotypes were photographed and 14 key points were placed. Procrustean analyzes, principal component analysis and canonical analysis were performed. The distinctive morphological variability in leaf shape of traditional Cuban cacao and commercial genotypes analyzed, allowing a preliminary differentiation between themes.Key words: Principal component; Canonical analysis; Geometric morphometry; Key pointIntroducciónCon el empleo de la morfometría geométrica se evalúan, desde una nueva perspectiva, los caracteres más variables en la sistemática de plantas, según plantean Siegel &Benson (1982). El desarrollo de la morfometría en las últimas décadas alcanza aéreas de la Biología tradicionalmente dedicadas al estudio descriptivo, como las ciencias morfológicas. La morfología, con las nuevas herramientas morfo métricas geométricas, permitió la evaluación cuantitativa objetiva de los cambios morfológicos, según postulan Zelditch, Swiderski, Sheets &Fink (2004). Esto fue posible con técnicas biométricas, instrumentos y programas computacionales que capturan y analizan datos de matrices de morfo coordenadas que representan la geometría de un espécimen. Estas técnicas no se limitan a la obtención de medidas lineales, que carecen de la precisión y el nivel de información de los datos geométricos, según plantean Adams, Rohlf & Slice (2004).La morfometría geométrica es el conjunto de métodos y procedimientos, con base geométrica, para el análisis de los patrones de forma, donde las mediciones usualmente derivan de contornos y puntos morfológicos claves. El análisis morfo métrico geométrico consta de tres etapas fundamentales: (1) obtención de los datos morfo métricos, (2) obtención de la información de la forma pura y (3) análisis exploratorios y confirmatorios de covariación de la forma y factores causales. El conocimiento de la morfometría geométrica permite su aplicación a la solución de problemas en los que la morfología juega un rol esencial. La capacidad de extraer información sobre la localización espacial de la variación morfológica, su magnitud, posición y extensión espacial en el organismo, es uno de los beneficios más importantes de la morfometría geométrica, según describe Bookstein (1991).Sin embargo, a pesar de sus amplias potencialidades, la aplicación de la morfometría geométrica en plantas de cultivo de importancia económica es aún poco extendida. En la sistemática de plantas uno de los principales puntos de ubicación y análisis que se tiene en cuenta, es la morfología foliar, la cual se estudia, principalmente mediante morfometría tradicional. En el caso de la forma de la hoja, esta ofrece un número de variantes a considerar para hacer un análisis biométrico de las partes con mayor variabilidad. Ejemplo de ellas son el ápice, la base, el margen o las dimensiones lineales (ancho y largo), algunos caracteres cualitativos y cuantitativos empleados con mayor frecuencia en la clasificación de especies, subespecies y variedades de las plantas, según plantea Henderson (2006).Uno de los cultivos que tiene una amplia variabilidad morfológica, por lo que potencialmente se puede aplicar la morfometría geométrica es el cacao, Theobroma cacao L. Este es un árbol de cultivo que se utiliza fundamentalmente para producir chocolate a partir de las semillas fermentadas. La diversidad de las hojas y la compleja distribución en los cultivares del cacao constituyen la evidencia fundamental de variación de las hojas, es una hipótesis para comprobar con dichas técnicas y análisis multivariados. A pesar del probable valor fitogeográfico de estas, estudiado en otras especies mediante morfometría geométrica, resulta notable que no se identificaron estudios publicados en cacao donde se analice el alcance de las diferencias entre genotipos de cacao o en regiones con características edafoclimáticas variables, aunque existen estudios similares en otras especies de plantas. Basado en estos antecedentes, la presente investigación se centra en la manera de identificar los genotipos tradicionales de Theobroma cacao basado en la forma de la hoja. A partir de esta problemática se plantea la siguiente hipótesis: Si se analizan los patrones de variación de la forma de la hoja de Theobroma cacao mediante la morfometría geométrica sería posible identificar los genotipos tradicionales. Para evaluar dicha hipótesis se planteó como objetivo general: Analizar los patrones de variación de la forma de la hoja de cacao mediante la morfometría geométrica para identificar los genotipos tradicionales.Para lograr el objetivo se cumplieron los objetivos específicos que siguen:Definir los puntos clave a ubicar en la hoja de Theobroma cacao para el análisis de las formas.Obtener la forma consenso de las hojas de Theobroma cacao de los genotipos evaluados del banco de germoplasma.Confirmar las diferencias entre los genotipos de Theobroma cacao evaluado del banco de germoplasma.La investigación tiene como novedad científica, que por primera vez se evalúa en Cuba el alcance de la variación de la forma de las hojas de Theobroma cacao y se utiliza la morfometría geométrica para comprar su variabilidad morfológica.DesarrolloObtención de los datos morfo métricosLas muestras analizadas se tomaron en el banco de germoplasma de cacao que se localiza en el Instituto de Investigaciones Agroforestales, Unidad de Ciencia y Técnica de Baracoa. La zona tiene elevados acumulados de lluvia anual, con un promedio superior a 2200 mm, el más alto del país. Las características topográficas tienen un 95 % del relieve montañoso.Se tomaron dos grupos de plantas: dos genotipos tradicionales (K 250 y K 251) y cinco genotipos comerciales (UF 12, UF 29, UF 221, UF 613 y UF 296). Al azar, fueron seleccionadas 75 hojas por individuos de hojas maduras sin daños en el margen, las cuales se digitalizaron con una cámara con resolución de 18 Mpx, sobre un fondo con papel milimetrado y una regla como referencia para el tamaño. Las hojas se orientaron con la parte axial hacia el observador y el ápice hacia la parte inferior de la imagen, según Hearn (2009).El procesamiento de las imágenes se realizó con los programas de la serie TPS, según Rohlf & Marcus (1993). Con el programa TpsUtilsse creó el proyecto y con el programa TpsDigs se ubicaron en la imagen los puntos clave y se determinaron sus coordenadas cartesianas. En cada imagen de las hojas se colocaron 14 puntos clave, dos de tipo anatómicos correspondientes al ápice y a la base de la hoja y 12 del tipo 2, según Bookstein (1991), distribuidos de manera uniforme en el borde de las hojas (Figura 1).Figura 1: Ubicación de los puntos clave en las hojas de cacaoFuente: Elaboración propiaObtención de la información que describe la forma puraPara obtener la forma consenso de las hojas de cacao y el conjunto de puntos que representan la tendencia central de los puntos clave de las hojas de cacao se utilizó el análisis de Procrustes. En este análisis, los puntos claves dispuestos en el borde, base y ápice de las hojas de cacao se ajustaron por el método de mínimos cuadrados y de sus respectivas coordenadas matriciales.Posteriormente, se redujo la dimensionalidad de los datos mediante un análisis de componentes principales, lo cual permitió obtener la forma consenso de la hoja de cacao. Los resultados se representaron mediante una figura con los vectores de movimiento entre la forma consenso y la media del cambio de la forma de las hojas, una figura con la media del análisis de componentes principales de los puntos clave de las hojas de cacao y un gráfico de dispersión de dos dimensiones con los componentes principales que explicaron el mayor porcentaje de la varianza. A partir de los resultados del análisis de componentes principales, se maximizó la separación entre los genotipos mediante el análisis canónico. Los resultados obtenidos se representaron mediante dos gráficos de dispersión de los grupos genéticos diferenciados según la forma de la hoja y una figura para comparar la forma consenso de la hoja de cacao con el ajuste del análisis canónico. Todos los análisis de realizaron con el programa MorphoJ, según refieren Zelditch et al. (2004).Análisis exploratorios y confirmatorios de covariación de la forma y factores causalesPara maximizar las diferencias, se calculó la media de los análisis de Procrustes, componentes principales y análisis canónicos obtenidos en el epígrafe anterior, mediante 10000 permutaciones de cadenas de Markov y la distancia de Mahalanobis, según Jolliffe (2002). La media de estos análisis se comparó con los resultados de los mismos análisis y los resultados se representaron como se explicó en el epígrafe Obtención de la forma pura. Todos los análisis se realizaron con el programa MorphoJ, según Zelditch et al.(2004).Discusión de la obtención de los datos morfo métricosSe obtuvo la forma consenso de la hoja de cacao de los genotipos analizados y el conjunto de puntos que representan los puntos clave utilizados, según expresaron Rohlf & Slice (1990) y Robinson, Blackwell, Stillman & Brook (2001).En el análisis de componentes principales, los primeros componentes mostraron un alto porcentaje de correlación que muestran los valores de correlación de Pearson. En los componentes principales del 1 al 10, el grado de correlación fue superior al 0,7; valor a partir del cual se consideran altamente correlacionados, según Zelditch et al. (2004). Con estos diez primeros componentes principales se obtuvieron los vectores de movimiento entre la forma consenso de la hoja y formación de los vectores de movimiento obtenidos en el resultado del análisis de componentes principales y el desplazamiento de los puntos de tipo 1 y 2 de la muestra de las hojas analizadas, como argumenta Lattin, Carroll, & Green (2003). Este resultado permite estimar el desplazamiento horizontal y vertical de cada región en la imagen.El análisis de componentes principales permite comparar la forma consenso obtenida (línea azul) con la media del cambio de la forma de la hoja (línea roja) (Figura 2).Figura 2: Media de análisis de componentes principales de los puntos clave de las hojas de cacaoFuente: Elaboración propiaLos resultados obtenidos en el análisis de componentes principales se representaron mediante un gráfico de dispersión de los diferentes genotipos evaluados con respecto a la forma de la hoja (Figura 3).Los resultados obtenidos muestran un grado elevado de similitud entre grupos, con algunas diferencias entre grupos, por ejemplo, el grupo K 251 con respecto a los demás. Se observó un solapamiento entre las formas de las hojas de cacao, aunque con un bajo nivel de variabilidad entre los genotipos.Debido a las pequeñas diferencias observadas, se realizó un análisis canónico de las variables según analiza Lele & Richtsmeier (2001). Los seis componentes principales que más aportaron a la variación, tuvieron una significación superior al 0,05. Los resultados del análisis canónico con estos seis componentes (línea azul) se compararon con la forma consenso (línea roja) (Figura 4).Figura 3: Gráfico de dispersión obtenido mediante el análisis de componentes principalesFuente: Elaboración propiaFigura 4: Forma consenso de la hoja de cacao obtenida con el análisis canónicoFuente: Elaboración propiaDiscusión de análisis exploratorios y confirmatorios de covariación de la forma y factores causalesLa comparación de la media del análisis procrustes (línea roja) con la media del análisis procrustes (línea azul) se muestra en la Figura 5.ab Figura 5: Análisis de los vectores de movimiento de la media Procrustes (a) comparados con la media procrustes (b)Fuente: Elaboración propiaEl promedio de la matriz covarianza de los seis componentes principales que más aportan a la varianza se muestra en la Tabla 1.Componentes PrincipalesValores PropiosPorcentaje de Varianza10,0010549257,25320,0004201822,80430,0002412313,09240,000078664,26950,000028301,53660,000019271,046Tabla 1: Valores promediados de la matriz covarianzaFuente: Elaboración propiaCon los dos componentes principales que más aportan a la varianza se realizó un gráfico de dispersión de los genotipos de cacao analizados (Figura 6).Figura 6: Comparación entre los dos componentes principales y las separaciones por gruposFuente: Elaboración propiaEstos resultados resaltan las diferencias significativas entre los genotipos. Estas diferencias, aunque existentes, no son completamente evidentes hasta realizar análisis exhaustivos. Los resultados indican que, aunque baja, existe variabilidad en la forma de las hojas, que potencialmente pueden utilizarse para la identificación de genotipos. Sin embargo, se requieren tomar muestras mayores y combinarlos con análisis de otros órganos de la planta, como el fruto por su alta variabilidad e importancia en la clasificación de la especie.El comportamiento solapado de la forma de las hojas de los genotipos se evaluó nuevamente, para demostrar diferencias no evidentes entre los grupos. Los resultados indican que existe variabilidad en la forma de las hojas, más evidente con un nuevo análisis de la media Procrustes, ajuste de la varianza y del análisis de la media de componentes principales (Figura 7).abcFigura 7: Variación del tamaño de las hojas basada en la media del ajuste ProcrustesFuente: Elaboración propiaLos resultados indican que la forma presenta alta variabilidad. Esto podría responder a que los genotipos estudiados se encuentran diferenciados no solo por sus características genéticas, sino también por caracteres morfológicos asociados a factores adaptativos, según Krzanowski (1988). Respecto al tamaño foliar, los genotipos analizados presentaron marcadas diferencias observadas en la figura por la forma consenso de K 250, K 251, presentaron hojas más grandes, mientras los otros genotipos comerciales se agruparon con una forma consenso de hojas de menor tamaño.El hecho de que el tamaño de la hoja se asociara positivamente con la longitud de las hojas de sus genotipos, apoya la idea de que el tamaño es variable por cada grupo genético. Los resultados indican la importancia de los caracteres morfo métricos como apoyo a los estudios interespecíficos de cacao. La investigación combina por primera vez el análisis de puntos anatómicos mediante morfometría geométrica utilizando caracteres morfo métricos. Este estudio permitió una comparación entre el cambio de forma establecido por ordenación del análisis canónico de la variable para inferir el cambio de forma, según analizan Kaliontzopoulou, Carretero & Llorente (2007).Este trabajo documenta que la estimación del cambio de forma es más apropiada para enfoque filogenético, para el análisis de las configuraciones de coordenadas después de la superposición Procrustes y el cálculo de las deformaciones relativas, como aseveran Viscosi, Lepais, Gerber & Fortini (2009). Los resultados descritos, indican que la morfometría geométrica de las hojas de cacao es una herramienta idónea en la discriminación de genotipos, además de un método de fácil aplicación y con validación estadística. Con 14 puntos anatómicos en las hojas, se diferencian los genotipos de cacao comercial y tradicional, aunque las diferencias no son grandes. Debido a este resultado, aún es necesario realizar análisis adicionales que incluyan otros grupos genéticos, con el fin de evaluar los cambios de forma de las hojas para los 10 genotipos existentes de cacao.Aunque se han publicado estudios con métodos morfo métricos en las hojas de varias especies vegetales, hasta la fecha no se ha hecho nada con hojas de cultivares de cacao, los resultados obtenidos representan un paso para la identificación de genotipos por medios morfo geométricos. Por primera vez se mostró la aparición de diferencias en las formas de las hojas mediante la morfometría geométrica.Estos resultados constituyen una primera aproximación a la utilización de la morfometría geométrica para la identificación de cultivares de cacao. Esta técnica presenta ventajas debido a la obtención de resultados de forma rápida y con bajo coste, de esta manera puede ser una primera aproximación para caracterizar la biodiversidad de un grupo de especies. Puede constituir una herramienta útil para este objetivo, teniendo en cuenta las dificultades para identificar los cultivares, debido a las semejanzas que existen entre ellos. Además, pueden ampliarse para utilizarse a otras especies de interés agrícola o forestal.ConclusionesLos 14 puntos claves identificados en las hojas de cacao de los genotipos evaluados permitieron realizar el análisis de la forma de las hojas. A partir de estos puntos clave se obtuvo la forma consenso de las hojas de cacao evaluadas, donde se resumió la información de la forma. Estos resultados permitieron mostrar variabilidad morfológica distintiva en cuanto a la forma del cacao tradicional, distintivo en comparación con los genotipos comerciales analizados, lo cual permitió una diferenciación preliminar entre ellos. Referencias bibliográficasAdams, D. C., Rohlf, F. J. & Slice, D. E. (2004). Geometric morphometrics: ten years of progress following the ‘revolution’. Ital. J. Zool. 71: 5-16.Bookstein, F. L. (1991). Morphometrics tools for landmark data: geometry and biology. Nueva York: Cambridge Univ. Press.Hearn, D. J. (2009). Shape analysis for the automated identification of plants from images of leaves. Taxon 58: 934–954.Henderson, A. (2006). Traditional morphometrics in plant systematics and its role in palm systematics. Bot. J. Linn. Soc. 151: 103-111.Jolliffe, I. T. (2002). Principal Component Analysis. (2daed.). New York: Springer Verlag.Krzanowski, W. J. (1988). Principles of Multivariate Analysis: A User’s Perspective. Oxford: Clarendon Press.Lattin, J., Carroll, J. & Green, P. (2003). Analyzing multivariate data. Pacific Grove: Thomson Learning, Inc.Lele, S. R. &Richtsmeier, J. T. (2001). An invariant approach to statistical analysis of shapes. Florida: Chapman & Hall/CRCRobinson, D. L., Blackwell P. G., Stillman E. C. &Brook A. H. (2001). Planar Procrustes analysis of tooth shape. Arch. Oral Biol. 46: 191–199Rohlf, F. J. & Marcus, L. F. (1993). A revolution in morphometrics. Trends Ecol. Evol. 8: 129– 132.Rohlf, F. J. & Slice, D. E. (1990). Extensions of the Procrustes method for the optimal superimposition of landmarks. Syst. Zool. 39: 40–59.Siegel, A. F. & Benson, R. H. (1982). A robust comparison of biological shapes. Biometrics 38: 341–350. Viscosi, V., Lepais, O., Gerber, S. & Fortini, P. (2009). Leaf morphological analyses in four European oak species (Quercus) and their hybrids: A comparison of traditional and geometric morphometric methods. Plant Biosystems 143 (3): 564-574.Zelditch, M. L., Swiderski, D. L., Sheets, H. D. & Fink, W. L. (2004). Geometric Morphometrics for Biologists: A primer. London: Elsevier Academic Press.PAGE \* MERGEFORMATIIVol. 7, No.15, enero-abril, año 2022152401905000-12446000Ciencia y Progreso Publicada en línea: enero, 2022, RNPS: 2477, ISSN: 2707-7098 http://cienciayprogreso.cug.co.cu15240872934500Vol. 7, No.15, enero-abril, año 2022 PAGE \* MERGEFORMAT2815240871982000Vol. 7, No.15, enero-abril, año 2022 2615240190500Frank E. Soto, Igor Bidot: Morfometría geométrica aplicada al estudio de la hoja de Theobroma cacaoiVBORw0KGgoAAAANSUhEUgAAAQEAAAG3CAYAAAC0f+CVAAAAAXNSR0IArs4c6QAAAARnQU1BAACx jwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAD55SURBVHhe7Z0N2G1zmf/v8+ecMKac8A9pvKaj KHQMigtFdSbExETI+6CY4YopkwahdBG6aGjoophUNDRpVF4OIa/ltTTyGuZk0l8d8hb2//7s3+9+ zjr7rP3ynGfv59l7re/nuu6z1tr7eThn77Xu3/3+m9ZwTAhRW/5PPgohaoqUgBA1R0pAiJojJSBE zZESEKLmSAkIUXOkBISoOVICQtQcKQEhao6UgBA1R0pAiJojJSBEzZESEKLmSAkIUXOkBISoOVIC QtQcKQEhao6UgBA1R0pAiJojJSBEzZESEKLmSAkIUXOkBISoOVICQtQcKQEhao6UgBA1R0pAiJoj JSBEzZESEKLmSAkIUXOkBISoOVICQtQcKQEhao6UgBA1R0pAiJojJSBEzZESEKLmSAkIUXOkBISo OdMaTj4XNeSBB8xuv91s2WXNNt/cbLnl8huiNkgJ1JQ//MFszz3NLr88v+CssILZF75gtv/++QVR C6QEasizz5ptvLHZr36VX2jhrLPMDjooX4jKo5hADfnWt9orADjuOLOXX84XovJICdSQH/0on7Th t781u/POfCEqj5RADcEd6MYLL+QTUXmkBGrIllvmkzYstZTZ7Nn5QlQeKYEassceZsssky9KIDuA IhD1QEqghqy0ktnyy+eLFqZPNzvggHwhaoFShDXkyCPNTjnFbN11zQ491OznP09FQhyvucZsvfXM 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