Repeatability analysis on morphological descriptors in the early stages of development

1 Departamento de Engenharia Agrícola, Universidade Federal de Viçosa – UFV, CEP 36570-900, Viçosa – MG, Brasil. 2 Departamento de Fitotecnia, Universidade Federal de Viçosa – UFV, CEP 36570-900, Viçosa – MG, Brasil. 3 Departamento de Genética e Melhoramento, Universidade Federal de Viçosa – UFV, CEP 36570-900, Viçosa – MG, Brasil. 4 Departamento de Engenharia Civil, Universidade Federal de Viçosa – UFV, CEP 36570-900, Viçosa – MG, Brasil.


INTRODUCTION
One of the major components of the global financial market are the agricultural Commodities, within the soybean (Glycine max (L.) Merrill) stands out, in relation to the volume sold.Brazil is the world's second largest producer of soybeans with 102,110 million tons produced in 2015/2016, in a total planted area of 33,228 million hectares, and presents the greater growth in planted area in the Brazilian agribusiness (Embrapa, 2016).
The genetic improvement programs of the oleaginous have been intensively acted in the development of new cultivars in Brazil, mainly after 1,997, when it was sanctioned the Law of Protection of Plant Varieties (LPC) n o .9,456, April 25, 1,997, regulated by Decree n o .2,366, November 5, 1,997 (Neto et al., 2005).For a cultivar to be protected, it is necessary to prove that it is distinct, uniform and stable.The distinctiveness of a cultivar refers to a clear difference from any other variety whose existence on the date of the period of protection is recognized (Grilli, 2005).
The differentiation of cultivars is performed by a minimum margin of descriptors that are specific to each species (Neto et al., 2005).Currently, about 38 descriptors are used between the mandatory and the additional to differentiate genotypes of soybean, nevertheless, they are still insufficient to distinguish cultivars (Nogueira et al., 2008).Therefore, there is the need of expanding that list.
The identification of morphological descriptors evaluated in the early stages of plant development should be preferred, once it enables to obtain fast results and it is not necessary to wait for adult plants, thereby accelerating the work of the breeder.
Nevertheless, in literature, there is few detailed information about the amount of plants which should be measured to determine the number of evaluations needed in order to estimate the difference between the evaluated materials, in order for the selected genotype maintain its characteristic in future generations.According to Cruz et al. (2004) and Paula Ferreira et al. (2010), this expectation may be proved by the repeatability coefficient of the studied characteristic, and being possible to estimate when the measurement of the character is performed repeatedly in a particular individual.
The concept of repeatability can be stated as the correlation between measurements of a given character in the same individual, whose assessments were repeated in time or in space.It expresses the proportion of the total variance that is explained by the variations provided by genotype and by permanent changes attributed to the common environment (Cruz et al., 2004).Many authors such as da Silva et al. (2014), Lessa et al. (2014), Lira et al. (2009), Ribeiro et al. (2015) have been studying repeatability and morphological descriptors for breeding and preservation of cultivars for different crops, showing that the study has impact and importance worldwide.
In the tests involving regularly evaluated genotypes, it is possible to estimate the repeatability coefficients of the variables studied, that is, the probability that this result will be repeated in future evaluations.Also, it is possible to estimate the number of phenotypic observations required, for a certain character, which must be performed on each individual so that discrimination (or selection) between the genotypes is carried out with a certain degree of reliability and time and labor economy (Cruz and Regazzi, 1997).
There are several methods used to estimate the repeatability, as the variance analysis, principal components and structural analysis (Abeywardena, 1972;Cruz and Regazzi, 2001;Mansour et al., 1981).
The objective of this study was to estimate the repeatability coefficient of some morphological descriptors in the early stages of development of soybean and the minimum number of evaluations necessary to predict the real value of genotypes.

MATERIALS AND METHODS
The experiments were conducted and evaluated in a greenhouse at the city of Viçosa, Minas Gerais -Brazil (20°45'14" S; 42°52'54" W; altitude of 408 m).
Five experiments were conducted in a completely randomized design, in which each experimental unit consisted of a plant, and the experiments one, two and three were conducted with five replicates for each treatment and the experiments four and five were conducted with sixteen repetitions.All experiments were grown in pots containing 3 dm 3 of soil with 1/3 of organic matter and seeding depth standardized at 3 cm.After germination, the plants were conducted according to culture recommendations.
Initially, the variance analysis was performed, in order to identify the existence of genetic variability between genotypes, based on the characters analyzed in each experiment.Only for the characters with significant differences between the genotypes (p < 0.05), the repeatability study was conducted.The repeatability coefficients (r) were estimated by the variance analysis (ANOVA); principal *Corresponding author.E-mail: fcsantossilva-ma@hotmail.com.
It was observed, in general, in the present study, that the greater the repetitions number, greater the results for the repeatability coefficient (r) and lower the numbers of evaluations needed.Nevertheless, this occurred in function of the genetic properties of analyzed genotypes.According to Danner et al. (2010), the repeatability and determination coefficients obtained among the individuals selected from a strawberry guava tree were high in relation to those found in surinam cherry tree, because the genotypes of strawberry guava tree presented greater phenotypic stability, due to the increased selection pressure and management used to plants.
Taking into account the same confidence level (90%), the prediction of real value to the CRFC would be necessary to evaluate 36 individuals by the methods CP (cov) and CP (correl) and 37 individuals by ANOVA and AE(cov).While for the characteristic AIFU would be needed 13 evaluations by ANOVA, 10 by the CP(cov) and AE(cov and 9 by CP(correl) (Table 7).
The results for CH, CE and CRFT corroborate with the obtained values by Matsuo et al. (2012), however they present lower predicted values to CPIN and CPFT, which probably is due to the genetic properties of different genotypes analyzed in the two studies.
The increase in accuracy for 95% implies the need for a greater number of evaluations and this would increase the costs and time for obtaining the results, but if laborintensive enough, these factors do not impede the realization of the test in any of the characteristics studied.
In general, based on estimates of repeatability and reliability of 95%, considering the methods and experiments average, would be necessary 17 evaluations for hypocotyl length, 6 for plant height in V3, 9 for epicotyl length, 7 for the first internode length, 12 for petiole length of unifoliate leaf and petiole length of trifoliate leaf, 36 for rachis length, 18 for opening angle of the petioles of unifoliate leaf.
(2016) also found similar results to the present work.
The results indicate the need for further studies with the aim of better understanding about the effect of genotypes, the influence of environmental conditions and genotype x environment interaction for the additional descriptors, aiming to estimate repeatability and determination coefficients and the number of evaluations needed in order to estimate the difference between the evaluated materials.

Conclusions
The length of the first internode requires a smaller amount of measurements in comparison to other characteristics measured in the early stages of soybean development for the same level of reliability.
With six measurements, reliability levels of 95 and 90% were obtained for plant height in V3 and length of the first internode, respectively, by the methods of the ANOVA, CP(correl), CP(cov) and AE(correl).

Table 2 .
Estimate of repeatability coefficients (r) and determination coefficients (Det), using the different methods for the morphological descriptors of soybean: CH, ALV3, CE, CPIN and CPFU.
For the CRFT, the repeatability coefficients ranged from 0.196 to 0.581, with the lowest one obtained by the method of the AE (cov), in Experiment 3, and the largest by methods CP(correl), AE(correl) and AE(cov), in Experiment 1.The same character had determination coefficients that ranged between 54.931 and 94.977%, in *Estimation methodologies of the repeatability coefficient: ANOVA: Variance analysis with one factor; CP(cov): principal components obtained from the matrix of covariance; CP(correl): principal components obtained from the correlation matrix; AE(correl): structural analysis based on theoretical eigenvalue of the correlation matrix or correlation average; and AE(cov): structural analysis based on theoretical eigenvalue of the covariance matrix.(Table2).The repeatability coefficient estimated for CPFU presented magnitude of 0.849 by CP(cov) to 0.506 by ANOVA, in the fifth and third experiment, respectively.The determination coefficients ranged from 98.898 to 83.678% (Table2).Whereas, for the CPFT (Table3), the

Table 3 .
Estimate of repeatability coefficients (r) and determination coefficients (Det), using the different methods for the morphological descriptors of soybean: CPFT, CRFT, AIFU, COVG and DVG.

Table 4 .
Number of evaluations needed associated with different determination coefficients (R 2 ), estimated for the CH and ALV3 in five experiments based on different methodologies*.

Table 5 .
Number of evaluations needed associated with different R 2 , estimated for the CE and CPIN in five experiments based on different methodologies*. -

Table 6 .
Number of evaluations needed associated with different R 2 , estimated for the CPFU and CPFU in five experiments based on different methodologies*.

Table 7 .
Number of evaluations needed associated with different R 2 , estimated for the CRFT and AIFU in five experiments based on different methodologies.
* R 2 - Estimation methodologies of the repeatability coefficient: ANOVA: Variance analysis with one factor; CP(cov): principal components obtained from the matrix of covariance; CP(correl): principal components obtained from the correlation matrix; AE(correl): structural analysis based on theoretical eigenvalue of the correlation matrix or correlation average; and AE(cov): structural analysis based on theoretical eigenvalue of the covariance matrix. *