ABSTRACT The use of longitudinal measurements is an essential practice both in Psidium guajava L. breeding and in other perennial crops in which covariance structures can be introduced to explain the form of dependence between measurements. Hence, this study aimed to analyze six covariance structures to identify one that best described the correlation between the repeated measurements in time in traits of guava full-sib families. The repeatability coefficient for each trait was estimated and the minimum number of evaluations required for estimates representing the population was determined. The work was performed based on average data of three yield-related variables from nine harvests of a guava tree population evaluated from 2011 to 2018. The best model was chosen based on the Akaike and Schwarz Bayesian information criterion. The autoregressive covariance structure best represented the dependencies among families between crops for all traits. The number of variables of fruits and total yield per plant presented repeatability estimates higher than 0.5 and may be essential traits for indirect selection of others, such as fruit mass, which had an estimated repeatability of 0.24, proving low regularity in the repetition of the character from one cycle to another. It was also possible to define four harvests as the minimum acceptable number of observations necessary on the same individual for these traits; therefore, the repetitions represented the individuals.

ABSTRACT Methods for genetic improvement of semi–perennial species, such as passion fruit, often involve large areas, unbalanced data, and lack of observations. Some strategies can be applied to solve these problems. In this work, different models and approaches were tested to improve the precision of estimates of genetic evaluation models for several characteristics of the passion fruit. A randomized block design (RBD) model was compared to a posteriori correction, adding two factors to the model (post–hoc blocking Row–Col). These models were also combined with the frequentist and Bayesian approaches to identify which combination yields the most accurate results. These approaches are part of a strategic plan in a perennial plant breeding program to select promising genitors of passion to compose the next selection cycle. For Bayesian, we tested two priors, defining different values for the distribution parameters of effect variances of the model. We also performed a cross–validation test to choose a priori values and compare the frequentist and Bayesian approaches using the root mean square error (RMSE) and the correlation between the predicted and observed values, called Predictive capacity of the model (PC). The model with the post–hoc blocking Row–Col design captured the spatial variability for productivity and number of fruits, directly affecting the experimental precision. Both approaches applied to the models showed a similar performance, with predictive capacity and selective efficiency leading to the selection of the same individuals.

ABSTRACT: The purpose of this study was to conduct selection, genetic parameter estimation, and prediction of genetic values for 18 S1 families of guava trees using mixed model methodology and simultaneous selection of traits by means of the additive selection index, multiplicative selection index, and mean rank adapted from Mulamba. All families analyzed were obtained by means of self-fertilization of superior genotypes (full siblings) from the genetic breeding program of guava trees at the Universidade Estadual do Norte Fluminense. An experimental randomized block design with 18 S1 families, three replicates, and ten plants per plot was used. A total of 540 genotypes (individual plants) of guava tree were evaluated. Genetic parameter estimation and selection of the best genotypes based on the genetic value were performed using the statistical procedure, from the Selegen-REML/BLUP program. The analyses of the additive selection index, multiplicative selection index, and the sum of rank adapted from Mulamba were also performed under the Selegen program. During the evaluation by the individual BLUPs, families 1, 12, 4, 6, and 8 contributed to most of the genotypes selected for the traits under evaluation, suggesting their significant potential to generate high quality and high yield genotypes. In the selection indexes via mixed models, the multiplicative index showed higher values for genetic gains (74 %), followed by the mean rank index adapted from Mulamba (19 %), and the additive index (2 %).

ABSTRACT: Multicollinearity is a very common problem in studies that employ path analysis in agronomic crops, which generates unrealistic results and erroneous interpretations. This study was aimed at assessing the path analysis in data obtained from guava tree full-sib based on modelling multiple regressions applying latent variables to neutralize the effects of multicollinearity. Seven explanatory variables were measured – fruit mass (FM), fruit length (FL), fruit diameter (FD), mesocarp thickness (MT), peel thickness (PT), pulp mass (PM), total number of fruits (NTF) –, plus the main dependent variable, total yield per plant (YIELD). In accordance with the multicollinearity scenario, eleven values were tested with the addition of the constant K to the diagonal of the correlation matrix X’X. Path analysis was applied in two models: all the explanatory variables with direct effect on the dependent one and another model with multiple regression with more than one chain and the presence of latent variables. The path analysis in the multivariate methodology of structural equation modelling (SEM), which uses latent variable prediction, provided better results than the traditional and ridge path analyses.

Abstract The major hindrance to guava fruit (Psidium guajava L.) growing is the low availability of cultivars for use by Brazilian producers, who usually rely on few options of genotypes to implement the crop. In the present study, 11 full-sib families were evaluated in a randomized-block experimental design with three replicates, in order to more efficiently select superior genotypes. Genetic parameters were estimated and the best genotypes were selected based on genetic value by applying the REML/BLUP statistical procedure. Additionally, genetic divergence was estimated based on the mean Euclidian distance between the individuals selected via BLUP. Based on genetic divergence, the best genotypes were selected for use as parents in new crosses aiming at continuity of the guava breeding program. The mean values of the traits of selected individuals surpassed the mean values of their parents, confirming that the strategy of obtaining full-sib families is effective in generating considerable gains.