INTERRELATIONSHIPS OF CANE YIELD COMPONENTS AND THEIR UTILITY IN SUGARCANE FAMILY SELECTION: PATH COEFFICIENT ANALYSIS

Orlando De Sousa-Vieira and Scott B. Milligan

Orlando De Sousa-Vieira. Ph.D., Louisiana State University, USA. Researcher, Instituto Nacional de Investigaciones Agrícolas (INIA), Venezuela. Address: INIA Yaracuy, Apartado 110, San Felipe, Estado Yaracuy 3201, Venezuela. e-mail: odesousa@inia.gov.ve

Scott B. Milligan. Ph.D., Louisiana State University, USA. Former Professor, Louisiana State University and Researcher, United States Sugar Corp. Address: 684 Turtle Lane; LaBelle, FL 33935, USA. e-mail: scottbmilligan@earthlink.net

Resumen

El programa de desarrollo de variedades de caña de azúcar de Louisiana, EEUU, (LSVDP) utiliza, en su etapa inicial de selección, pruebas de progenie para identificar familias superiores y estables. Para optimizar esta metodología se examinó la importancia relativa de las familias y la distancia entre individuos dentro de cada familia en términos de la efectividad del procedimiento. El conocimiento de la interrelación entre los caracteres considerados importantes en el proceso de selección es parte fundamental para el éxito del LSVDP. El análisis de coeficiente de sendero fue utilizado para medir la influencia directa e indirecta de los componentes del peso de la cepa de caña de azúcar en la estimación del peso de la cepa. Para ello los coeficientes de correlación genética y fenotípica se expresaron en términos de componentes de efecto directo y de efecto indirecto. Los efectos directos, tanto fenotípicos como genéticos, fueron todos positivos, indicando que la selección que se realice para cualquier componente del peso de cepa se traduce en un aumento del peso de la cepa de caña de azúcar. El coeficiente de determinación indica que los componentes número de tallos por cepa, diámetro de tallo y altura de tallo explican la mayor parte de la variación existente en el peso de cepa. Independientemente de la distancia entre cepas, los coeficientes de sendero revelaron que, relativo a los valores de coeficientes de correlación, los componentes diámetro de tallo y número de tallos por cepa mostraron los mayores efectos positivos sobre el peso de cepa, tanto al nivel fenotípico como genotípico.

Summary

Progeny testing is used to identify sugarcane families with superior, stable performance at the first selection stage of the Louisiana Sugarcane Variety Development Program, USA (LSVDP). Research to optimize the current progeny-testing methodology examined the relative importance of family and intra-row plant spacing in terms of effectiveness of the testing procedure. Knowledge of the interrelationship among the various traits considered important in selection plays an important role in the success of the LSVDP. Path coefficient analysis was used to measure the direct and indirect influence of plant weight components on the estimation of plant weight by partitioning phenotypic and genotypic correlation coefficients into components of direct and indirect effects. Phenotypic and genotypic direct effects were all positive, indicating that selection for any of the plant weight components should translate into an increase in plant weight. Number of stalks per plant, stalk diameter, and stalk length accounted for almost all of the variation in plant weight as indicated by the coefficient of determination. Irrespective of plant spacing, path coefficients revealed that, relative to the correlation coefficients values, stalk diameter and number of stalks per plant had the largest direct positive effect on plant weight at both phenotypic and genotypic levels.

Resumo

O programa de desenvolvimento de variedades de cana de açúcar de Louisiana, EEUU, (LSVDP) utiliza, em sua etapa inicial de seleção, provas de progênie para identificar famílias superiores e estáveis. Para melhorar esta metodologia examinou-se a importância relativa das famílias e a distância entre indivíduos dentro de cada familia em termos da efetividade do procedimento. O conhecimento da inter-relação entre os caracteres, considerados importantes, no processo de seleção é parte fundamental para o êxito do LSVDP. A análise do coeficiente de Sendero foi utilizada para medir a influência direta e indireta dos componentes do peso da cepa de cana de açúcar na estimação do peso da cepa. Para isto os coeficientes de correlação genética e fenotípica se expressaram em termos de componentes de efeito direto e de efeito indireto. Os efeitos diretos, tanto fenotípicos como genéticos, foram todos positivos, indicando que a seleção que se realize para qualquer componente do peso da cepa se traduz em um aumento do peso da cepa de cana de açúcar. O coeficiente de determinação indica que os componentes: número de caule por cepa, diâmetro de caule e altura de caule, explica a maior parte da variação existente no peso da cepa. Independentemente da distância entre cepas, os coeficientes de Sendero revelaram que, relativo aos valores de coeficientes de correlação, os componentes diâmetro de caule e número de caules por cepa mostrou os maiores efeitos positivos sobre o peso de cepa, tanto ao nível fenotípico como genotípico.

KEYWORDS / Genotypic Correlation / Phenotypic Correlation / Saccharum spp. / Sugarcane Breeding /

Received: 07/01/2004. Modified: 01/17/2005. Accepted: 01/21/2005.

Introduction

Since 1992 the Louisiana Sugarcane Variety Development Program (LSVDP) has been using progeny appraisal data to identify sugarcane families with the most potential to produce superior individuals. Chang and Milligan (1992) reported expected selection gains to be consistently larger for an initial 50% family selection and subsequent 20% individual selection within the best families than for simple individual selection at 10% selection intensity (mass selection). The research demonstrated considerable potential benefits of family selection to the LSVDP.

Knowledge of the interrelationship among the various traits considered to be important in selection can be useful in devising proper selection strategies in a sugarcane breeding program. For example, this type of information affects planning strategies for breeding for a particular objective, as the strategy will vary according to the nature and importance of these relationships.

Breeding decisions based only on correlation coefficients may not always be effective since they provide only one-dimensional information while neglecting important and complex interrelationships among plant traits (Kang, 1994). Path coefficient analysis has been extensively used by plant breeders to enhance the usefulness of the information obtained from correlation coefficients and to obtain precise information on those interrelationships to better assess the consequences of selecting for one or more traits (Furtado et al., 2002). Correlation coefficients simply measure mutual association without regard to causation, whereas the path coefficient analysis identifies causal relationships and measures their relative importance (Bhatt, 1973). The purpose of the path coefficient analysis method is to partition a correlation coefficient into unidirectional pathways o r direct and indirect effects through alternative pathways.

De Sousa-Vieira and Milligan (1999) examined intra-row plant spacing as a source of variation affecting the efficacy of progeny testing and family selection. The effect of intra-row plant spacing on direct and indirect path coefficients, however, has not been examined. Therefore, the aim of this article is to assess the effect of intra-row plant spacing on estimates of path coefficients among five agronomic traits, which should help optimize selection of sugarcane families within the LSVDP.

Materials and Methods

Twenty-five randomly selected biparental families from the 1993 crossing series in the Louisiana Sugarcane Variety Development Program (LSVDP) were used in this study. Seeds were germinated in flats under greenhouse conditions in Jan 1994 at the St. Gabriel Research Station of the Louisiana Agricultural Experiment Station. Approximately three weeks after germination, seedlings were transplanted to Speedling^TM trays with 3.8cm² cells and allowed to continue to grow in the greenhouse. The progeny were then transplanted to the field on Apr 21, 1994 to the USDA Ardoyne Farm near Chacahoula, Louisiana, and on Apr 28, 1994 at the St. Gabriel Research Station. Seeds from the same crosses were again germinated in flats in Jan 1995 and transplanted to the field on Apr 25, 1995 at the Ardoyne Farm. Individual plants from each cross were planted in a randomized complete block design with two blocks and a split plot treatment arrangement. Intra-row plant spacings of 41cm (standard at LSVDP) and 82cm were main plots and families were sub-plots. Each subplot consisted of two rows with 16 seedlings in each row and 1.8m spacing between rows.

Millable stalk number per plant, stalk length, and mid-stalk diameter were recorded during 1-14 Aug 1995 from the progeny planted in 1994, and during 13-20 Aug 1996 from the progeny planted in 1995. Data were collected in first ratoon cane. Stalk length (from the stalk base to the first visible dewlap or leaf collar) was measured from two randomly selected stalks per plant. Internode diameter at mid-stalk level of the same two stalks was recorded using a caliper. Stalk weight was estimated as the volume of the stalk assuming a perfect cylinder with specific gravity of one (Miller and James, 1974; Gravois et al., 1991; Chang and Milligan, 1992) as  

Stalk weight = dpr²L

where the density d= 1.0 gm·cm^-3, r: stalk radius (cm), and L: stalk length (cm). Plant weight was estimated as stalk weight multiplied by stalk number per plant.

Genetic and phenotypic correlations

Using family mean data, covariance components between all possible pairs of traits were estimated. Mean-product expectations are analogous to the mean-square expectations for the analysis of variance. Thus, estimates of phenotypic and genetic covariance components were derived in the same fashion as for variance components by using product moment method.

Genetic and phenotypic correlations on a family mean basis, for pairs of traits, were computed as

 r_ij = s_ij / s_i s_j

where s_ij: genetic or phenotypic covariance between traits i and j, s_i: genetic or phenotypic standard deviation for trait i, and s_j: genetic or phenotypic standard deviation for trait j.

Path analysis

Phenotypic and genetic path coefficient analyses were obtained from the simultaneous solution of the equations

P_{1 4} + r_{1 2} P_{2 4} + r_{1 3} P_{3 4} = r_{1 4}

r_{1 2} P_{1 4} + P_{2 4} + r_{2 3} P_{3 4} = r_{2 4}

r_{1 3} P_{1 4} + r_{2 3} P_{2 4} + P_{3 4} = r_{3 4}

where P_ij: path coefficients, and r_ij: correlation coefficients between the pairs of the following traits: stalk number per plant (1), stalk length (2), stalk diameter (3), and plant weight (4). Expressed in matrix form, the above equations can be written as

r P = c

and the direct path coefficients P_{i 4} (i = 1, 2, 3) can be estimated as

P = r^-1 c

where P: the vector of direct path coefficients, r^-1: the inverse of the correlation matrix of the traits, and c: the correlation vector of traits one to three with trait four.

Indirect path coefficients were calculated as described by Dewey and Lu (1959) using an a priori defined set of cause-and-effect relationships. The unaccounted for direct residual effect (P_X4) that influenced plant weight was calculated as

P_{X 4} = [1 - coefficient of determination (R²)]^½

and the coefficient of determination was calculated as

R² = P²_{1 4} + P²_{2 4} + P²_{3 4} + 2P_{1 4}r_{1 2}P_{2 4} + 2P_{1 4}r_{1 3}P_{3 4} + 2P_{2 4}r_{2 3}P_{3 4}

Results and Discussion

The proper estimation of genotypic and phenotypic correlation coefficients is of little value unless some application can be made of these associations (Robinson et al., 1951). The knowledge of associations of plant weight with other traits helps breeders select suitable, desirable plant types. In these correlations, when the indirect associations create complexity, path analysis has been found useful in finding the direct and indirect causes among associations (Dhagat et al., 1977).

Path-coefficient analyses were performed in accordance with a predetermined casual relationship (Figure 1) using phenotypic and genetic correlation coefficients for each of the two intra-row plant spacings. Stalk number, stalk diameter, and stalk length (independent or predictor variables) constituted the component traits of plant weight (dependent or response variable). Plant weight was obtained as the product of stalk number and stalk weight. This method of estimating plant weight may cause spurious correlations between plant weight and stalk number, and between plant weight and stalk weight (Kang et al., 1989). Kang et al. (1985) indicated that involvement of mathematically derived traits, as is the case with plant weight, might inflate in correlations the relative importance of a variable estimated at the phenotypic level, but might not have an appreciable effect at the genetic level. To minimize effects of spurious associations produced by artificially created relationships (Kang et al., 1991), path-coefficient analyses were carried out using only the three components that were measured directly. Stalk weight was considered as an intermediate variable and was not used in these analyses.

Smith et al. (1977) indicated that in a path-coefficient analysis, the direct effect (P) of a component refers to its effect with all other components held constant, and that the indirect effects arise since the components themselves are correlated in such a way that a change in one trait will cause a change in another trait. Phenotypic and genetic direct effects of stalk number, stalk length and stalk diameter on plant weight were positive, indicating that selection for any of the components would cause an improvement in plant weight (Table I). Irrespective of plant spacing, variables with the highest correlations did not produce the largest direct effects. Stalk diameter had the largest proportion of its correlation with plant weight reflected as direct effect, making it an important factor directly influencing plant weight. The largest phenotypic direct effect was that of stalk number at both narrow and wide intra-row plant spacings (0.507 and 0.650, respectively). The direct effect of stalk number was of the same magnitude as the direct effect of stalk diameter at wide spacing (0.501), but was much larger than the direct effect of stalk diameter at narrow spacing (0.402), reflecting the negative effect of competition on stalk diameter. The direct effects of stalk length were the lowest and approximately of the same magnitude at both spacings (0.348 and 0.319, respectively).

Compared with direct effects, indirect effects of the phenotypic path analyses were small, except for the indirect effect of stalk length on plant weight. Indirect effects of stalk length on plant weight via stalk number were of the same magnitude as direct effects. The negative indirect effect of stalk diameter via stalk number and that of stalk number via stalk diameter arose because the correlation between those traits was negative. However, the relative importance of these effects can be considered negligible. This negative association between stalk number and stalk diameter has been shown to be important when working with selected clonal populations (James, 1971; Miller and James, 1974; Kang et al., 1983). This fact makes it more important to improve selection techniques at the seedling stage where, as shown in this study, this negative association is not significant.

For the genetic path analyses, the value of the direct effects of the three plant weight components were, relative to each other, closer in importance, but indirect effects played a more important role than they did in phenotypic path analyses. In addition, indirect effects were different depending on the intra-row spacing. For example, at wide intra-row plant spacing, the indirect effect of stalk number on plant weight via stalk length was higher than the direct effect, whereas, at narrow intra-row spacing, the indirect effect of stalk length on plant weight via stalk number was more important than its direct effect.

Correlation coefficients between stalk length and plant weight were high in all four analyses, which suggested that an increase in stalk length should cause a corresponding increase in plant weight. However, path analyses showed that when stalk number per plant and stalk diameter were held constant, stalk length was not the factor with the highest influence on plant weight and that both stalk number per plant and stalk diameter had a higher direct effect on plant weight than stalk length.

The coefficients of determination (R²) represent the percentage of variation in plant weight that was accounted for by the three plant weight components, number of stalks per plant, stalk length, and stalk diameter. In general, the R² values were relatively high, which indicated that the three components of plant weight accounted for almost all the variation in plant weight. In addition, the relatively small residual effect (P_{x 4}) further reinforced the above conclusion. The R² values were lower when data relative to the narrow intra-row spacing were used in the path coefficient analysis, the difference being primarily the result of competition effects.

ACKNOWLEDGMENTS

The authors thank the personnel at St. Gabriel Research Station and USDA Ardoyne Farm, Louisiana, USA.

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