Estimates of repeatability and path coefficients on grapes

The objective of this study was to estimate the repeatability coefficient, the minimum number of evaluations to which a trait should be subjected and the effect of the inter-relationships of five characters on grapevine (Vitis spp.) yield, aiming at getting useful information for breeding strategies of this fruit crop. Repeatability coefficients were estimated for the following characters: total soluble solids (TSS); total titrable acidity (TTA); TSS/TTA ratio; berry length, diameter and weight; bunch length, width and weight, and number and yield of bunches per plant on eleven seedless grape varieties in five yield cycles (1997 and 1998) in Petrolina-PE. The repeatability estimates were obtained by the main components method from the correlation matrix. The simple correlation coefficients were calculated and they were partitioned into direct and indirect effects by the path analysis. The estimated repeatability coefficients ranged from 0.4750 to 0.8372 associated to the coefficients of determination from 81.9% to 96.26%. The traits TSS, TTA and bunch length presented low repeatability coefficients, meaning a low regularity of performance from one measurement to another. The other characters showed regularity on the repetition of the behavior of the genotypes. The results of the path analysis showed that the studied variables satisfactorily explain the character yield per plant.


INTRODUCTION
are one ofthe most important fruit cropsin the agribusiness of the São Francisco River Valley. The cultivated area of 5,300 hectares positions the region as the major exporter of table grapes in Brazil(Agrianual, 2002). The economic and social importance of this crop is the greatest reason for carrying out research studies on grape breeding programsfor the Brazilian semi-arid region. ln any breeding program the selection for superior genotypesmust be accomplished in the most efficient waypossible and for this it is necessary to know the phenotypic and genetic parameters such as heritabilities,repeatabilities, and path analyses ofthe characters.Cruz (2001) pointed out the importance ofbiometricprocedures as auxiliary tools for decision making at the different stages of the breeding programo lna breeding program aiming at parent crossing and cultivarrelease, it is important to select genotypes withgood agronomic potential and that their superior performancebe maintained across evaluations. Thus, whenchoosing a genotype, it is expected that its initial performancebe permanently maintained (Cruz and Regazzi,1994). This expectation can be confirmed Based on that, repeatability studies are very important tools for helping breeders achieve precise results, and also for saving time and labor in trait evaluations. High values of the repeatability coefficient indicate that it is possible to predict the real value of the individuais using a relatively small number of measurements (Cornacchia et al., 1995), suggesting that there wi 11be little gain in precision with increase of the number of repeated measurements (Falconer, 1987). When the repeatability is 10w, a large number of repetitions will be necessary in order to get a satisfactory determination value.
Repeatability studies are essential for perennial crops breeders, since they represent the maximum value that the heritability of a character in a wide sense can reach (Falconer, 1987;Cruz and Regazzi, 1994). They are also used to determine the number of phenotypic observations to be made in each individual so that the discrimination or phenotypic selection among genotypes is efficiently carried with reduced costs. ln this context, repeatability coefficients have been estimated in fruit crops like coconut (Siqueira, 1982), "cupuaçu" (Fonseca et al., 1990;Costa et al., 1997), cashew tree (Cavalcanti et al., 1999) and barbados cherry (Gonzaga Neto et al., 1999;Paiva et al., 2001;Lopes et al., 2001).
The knowledge of the association among characters is another tool of great importance for breeding works, mainly if the selection for one of them is difficult due to low heritability and/or if there are problems measuring the traits. However, although being of great use toward quantifying the magnitude and direction of the influence of factors on determination of complex characters, this association does not give the relative importance ofthe effects ofthese factors. The path analysis (Wright, 1921(Wright, , 1923 consists of studies concerned with direct and indirect effects of characters on a basic variable whose estimations are obtained through regression equations where the variable is previously standardized. Among the fruit crop species this technique has been utilized on guarana (Nascimento Filho et aI., 1993), cocoa (Almeida et aI., 1994), umbu tree (Santos and Nascimento, 1998) and "açaí" tree (cabbage-palm) (Oliveira et al., 2000).
In spite of the importance and the non-requirement that the data be originated from experimental designs, the two techniques have not been used by grape breeders.
This study had the objective of estimating the repeatability coefficient and the minimum number of evaluations to be taken for a precise prediction ofthe real value of individuals and quantifying the direct and indirect effects among agronomically important characters on grapevine crop.
According to Kõeppen classification, the climate of the area is classified as Bswh type, which corresponds to a very hot semi-arid region. The mean annual rainfall is 571.5mm. The mean annual temperature is 26.4°C, with minimum of 20.6°C and maximum of 3 1.7°C.

2003, Brazilian Society of Plant Breeding
The vineyard where the experiment was run was a seedless grape variety collection established on September 1994, using the cultivar lAC 572 'Campinas" as rootstock. The study period was in the years 1997 and 1998, the evaluations being made during five yield cycles.
Due to the cyclical behavior of the yield in many grapevine cultivars, the estimate of the repeatability coefficient was accomplished by the analysis of the main components proposed by Abeywardena, (1972) and modified by Rutledge (1974). Accordingly, the estimates of repeatability coefficients are obtained by the method of the main components (CP), based on the correlations coefficient among each pair of measured traits, from which normalized eigenvalues and eigenvectors are determined. The eigenvector, whose elements present same sign and close value, is the one that expresses the tendency ofthe genotypes in maintaining its relative positions in several intervals of time, acordding Cruz and Regazzi (1994). The proportion of the eigenvalue, associated to the eigenvector, is the estimator of the repeatability coefficient, given by: The determination coefficient for the analysis of the explanatory variables on the main variable is given by: R~123 =polrol +P02r02 +P03r03 +···+Po,,fOI1· The residual effect was expressed by: All estimations for repeatability, determination coefficient, minimum number of evaluations, phenotypic correlation coefficients and path analysis were carried using the GENES computer program (Cruz, 2001).

RESULTS AND DISCUSSION
The estimates ofthe repeatability coefficient and the respective determination coefficients can be found in   For characters assaciated with berries (length, diameter and medium weight), the obtained estimates present reasonable regularity on the repetition ofthe character frorn one evaluation to another. Two measurements, on the average, were sufficient to obtain coefficients of determination of 90% in these characters.
In general, except for bunch length, TSS and TTA, the predictian of the real value, expressed by the coefficient of determination, was higher than 88%, suggesting that the superiority or inferiority of the behavior ofthe varieties can be maintained from one It can also be found that five cycles of evaluations for all studied traits should be necessary in order to reach a confidence levei above 81%. Camarga (2000) pointed out that three ta five vegetative cycles should be enough to enable selection. However, the number of necessary evaluations will depend on the variable and on the defined precision leveI. In the present study, the necessary number af measurements for selection regarding to yield varied from 6 ta 13 to get precision between 90 and 95% ( Table 2).
The breakdown of the phenatypic carrelation coefficients between yield per plant and the explanatory variables can be found on Table 3. The influence of the variables berry diameter and bunch number, expressed by the path coefficients (direct effects) ofthe same sign and extent of those showed by the correlation coefficients, indicated these variables as determinant of the behavior of the basic variable (yield per plant).The coefficient of total determination of 94.97% indicates that the variables used explain satisfactorily the behavior of yield.
According path analysis and repeatability coefficients, it can be concluded that the most favorable situation for grapevine breeding to increase yield per plant was observed with the character berry diameter, that presented high repeatability estimate, and relatively high and positive values on the correlation and on the direct effect ofyield. Thus, the indirect selection for yield can be accomplished through berry diameter, with a reduction of 50% of the time that would be necessary for accomplishing direct selection with the variable yield.

CONCLUSIONS
TSS and TTA showed low values for repeatability coefficient, requiring eight and nine evaluation cycles to predict the individuaIs' real values with certainty levei above 90%; The estimates ofthe repeatability coefficient for berry diameter, length and mean weight demonstrate reasonable regularity in the repetition ofthe character from one cycle to another, and that two evaluations are enough to reach a coefficient of determination of 90%; Berry diameter presented the highest repeatability coefficient and high and positive values on the correlation, indicating indirect selection on the trait to increase yield per plant.