The adaptation of animals to a given environment is associated with morphological and functional changes. Thus, selection of Hereford and Braford cattle morphologically adapted to tropical conditions is a way to improve the herd productivity, given the expansion of their use in these environments.

Visual scores have been evaluated in some breeding programs and used to obtain morphologically desirable animals, well adapted to the conditions under which they will be kept. Limb conformation trait is related to the ease of locomotion and comfort, since deficient limbs can compromise not only the pursuit for food and water, but also the mating (Rosa et al., 2003). Breed trait score has been evaluated in beef cattle aiming at identifying the animals that best fit the breed profile, as well as indicating the absence of defects and conferring prepotency. On the other hand, sexual trait score is used in the selection to identify males with masculine attributes and females with feminine attributes, with particular attention given to the functionality of external genitalia (Cardoso and Lopa, 2017).

In Hereford and Braford breeds, eye pigmentation is relevant due to the predisposition of these animals to ocular carcinoma, besides being a mandatory attribute for the breed standard and registration of Braford cattle. Thus, the selection of animals with higher eye pigmentation is an important tool to decrease ocular carcinoma, allowing a better adaptation to regions of high solar irradiation (Cardoso and Lopa, 2017).

The size and positioning of the navel are used in the identification of more functional animals, especially when kept in extensive production systems. In general, cattle with very long or pendulous navel and foreskin are more susceptible to trauma and injury due to the heterogeneous composition of the pastures, which can lead to reproductive problems, especially in natural mating (Boligon et al., 2016).

One relevant aspect of traits related to morphology and functionality in beef cattle is the fact that they are visually obtained, thereby presenting a discrete distribution. While linear models offer ease of application and shorter processing time compared with threshold models (Faria et al., 2008), they may be inadequate for quantifying the discrete nature of categorical data that does not follow a normal distribution. However, comparing the results obtained in analyses using linear and threshold models can help determine the more appropriate model for genetic evaluations of traits measured by scores.

The objective of this research was to compare genetic parameters and breeding values, obtained using linear and threshold animal models, for scores of limb conformation, breed traits, sexual traits, eye pigmentation, and navel size in Hereford and Braford breeds. Additionally, principal component analysis was applied to investigate the relationship among the estimated breeding values (EBV).

Visual scores obtained at weaning and yearling did not show a phenotypic normal distribution in this study (Figure 1). For LCW, BTW, STW, LCY, BTY, and STY, the largest proportion of animals received score 3 and few received score 1. On the other hand, for EPW and EPY, the most frequent scores were 3, 4, and 5. In the visual assessment of NSW and NSY, the least frequent scores observed were 3, 4, and 5.

For all evaluated scores, higher values of direct and maternal heritability were estimated with threshold compared with linear models (Table 2). Low direct heritability values were estimated for LCW and LCY using linear (0.086±0.010 and 0.042±0.008, respectively) and threshold models (0.134±0.021 and 0.084±0.019, respectively). Direct heritability values estimated for BTW and BTY were of 0.111±0.012 and 0.038±0.008, respectively (using linear model), and 0.194±0.023 and 0.099±0.002, respectively (using threshold model). Similarly, higher direct heritability was obtained for STW rather than STY, for the linear model (0.089±0.011 and 0.011±0.005, respectively) and for the threshold model (0.141±0.025 and 0.039±0.015, respectively). On the other hand, lower direct heritability was estimated for EPW and NSW compared with EPY and NSY, using one model or another. Using both models, null maternal heritability were obtained for all weaning visual scores studied.

Rank correlations obtained between breeding values predicted with linear and threshold models for visual scores (Table 3) indicate that different animals would be selected for LCW, LCY, BTW, BTY, STW, and STY, especially when greater selection intensity is applied. These scores showed a lower percentage of animals coinciding with the use of these two different models. However, for EPW, EPY, NSW, and NSY, few changes would occur in the rank, as the correlations and the percentage of coincident animals showed high values.

Considering sires which are parents of animals with phenotypic measures and sires that were parents of animals with phenotypic measures and with accuracy above 0.40, the ranking differences found with the use of the evaluated models (linear and threshold) were more evident for LCW, LCY, BTW, BTY, and STW, which are obtained with scores varying between 1 and 3 (Table 3). These scores showed a lower percentage of coincident animals and lower correlation values, in accordance with the selection intensity applied. This indicates that the choice of model would cause changes in the classification of sires. On the other hand, few changes are expected in the classification of sires for STY, EPW, EPY, NSW, and NSY traits (Table 3).

Similarly, the cross-validation showed that the criteria used to compare the goodness of fit of the models indicated that the threshold model best fits the data for limb conformation, breed traits, and sexual traits. There was only a small difference among these criteria for eye pigmentation and navel size, suggesting that the genetic evaluation of these traits could be performed with both linear and threshold models (Table 4).

The first five components explained 79.91% of the total variance of breeding values for the studied visual scores, which is considered sufficient to capture most of its variation (Figure 2). Breeding values for all traits studied showed a negative association with the first principal component (Table 5), with higher magnitudes observed for scores obtained at weaning (LCW, BTW, STW, and NSW), with values ranging from −0.61 to −0.71. Relating to the second principal component, LCW, BTW, STW, LCY, BTY, and STY were negatively correlated. On the other hand, EPW and EPY showed greater discrimination power, with a correlation of 0.87. Both NSW and NSY were negatively correlated to the third principal component, with a linear correlation of −0.66 and −0.71, respectively. For the fourth principal component, positive and high linear associations were estimated with LCY and STY, with correlation of 0.74 and 0.51, respectively. The fifth principal component was more closely associated with breeding values of LCW, with a higher discriminatory power of 0.62.

The phenotypic distribution observed for the studied visual scores, both at weaning and yearling, possibly occurred because the attribution was made considering pre-established standards for each trait in both breeds. Most of the animals in this population did not show problems of limb conformation and presented traits specific to their sex. For EPW and EPY, the most frequent scores indicate that most of the cattle showed reasonable to excellent pigmentation. On the other hand, most animals had ideal NSW and NSY for the Hereford breed (scores 1 and 2), but not so much for the Braford breed, since scores 2 and 3 were its ideal.

Higher values of direct and maternal heritability were obtained with the threshold model, suggesting that the model was able to better capture the genetic variability of studied traits. The fact that the scores did not present a normal distribution (Figure 1), possibly because they were measured considering pre-established standards and not in relation to the average of the CG to which the animal belongs, could explain the differences observed in the genetic parameters estimated with the use of both models.

Similar to the results obtained in the present study, Campos et al. (2019) reported higher heritability for navel score at yearling using threshold model (0.42±0.02) compared with linear model (0.22±0.02) and recommended its use in genetic evaluation for the trait. On the other hand, in Nelore breed, no differences were reported between linear and threshold models in obtaining genetic parameters for scores of limb conformation, breed characterization, sexual traits, and navel (Passafaro et al., 2013; Boligon et al., 2016).

The heritability estimated for LCW and LCY suggests limited genetic progress with selection for these traits due to reduced variation attributed to additive genetic effects. It is worth noting that good limb conformation is relevant especially in extensive production systems, due to the need for animals to have good mobility skills, which can be obtained by selecting based on that score or by discarding animals with defects. Similar to that obtained in the present study, Lima et al. (2013) reported low heritability (0.05±0.01) for score of posture in Nelore cattle, with visual attribution ranging from 1 to 4 and using a linear model. On the other hand, higher heritability was obtained in other studies. Koury Filho et al. (2002) estimated heritability of 0.35 for limb conformation at weaning in Nelore breed, with visual assignments ranging from 1 to 5 and using a linear model. A similar result was reported by Gutiérrez and Goyache (2002) for Asturiana de Los Valles breed, with heritability of 0.33±0.02 for legs line score ranging from 1 to 9 and using a linear model. Using linear and threshold models, Passafaro et al. (2013) reported heritability of 0.20 and 0.30, respectively, for limb conformation attributed to sires kept in pasture-based weight gain trials and ranging from 1 to 4. Santana Jr. et al. (2013) estimated moderate heritability (0.26) for bone structure score (legs and hocks) at yearling in Nelore animals, ranging from 1 to 3 and evaluated with a threshold model. For Guzerá breed, Abreu et al. (2018) reported higher heritability (0.39±0.04) for limb score (solidity of legs and feet), with scores ranging from 1 to 4 and using a threshold model.

Evaluating the yearling leg and feet score considering values of 1 (animal with defects) or 0 (animal without defects) in Nelore cattle, Vargas et al. (2017) reported higher heritability (0.18±0.04) in relation to that obtained for LCY in the present study. Subsequently, for score of legs and feet, however ranging from 1 (less desirable) to 5 (more desirable) and attributed to the 20% higher animals according to the selection index adopted by the program, the authors estimated a higher heritability (0.39±0.07). It should be noted that those animals that had a defect at yearling were not candidates and, consequently, were not evaluated in the second phase. According to the authors, the strategy of discarding animals based on score of legs and feet, aiming to reduce disturbances of locomotion that can lead to productive and reproductive losses, contributed to the genetic progress of the trait in the Nelore breed. In general, it is common to use different methodologies to obtain scores related to support and locomotion in beef cattle, with few studies conducted using the same attribution for the score of limb conformation considered in the evaluated population, which may explain the differences in the heritability estimated.

Low genetic variability was estimated for breed traits in the studied population, especially when evaluated at yearling. Similarly, low heritability was reported for scores related to breed standard in Nelore cattle, ranging from 0.18 to 0.24 (Faria et al., 2009; Lima et al., 2013; Passafaro et al., 2013; Boligon et al., 2016). In the studied herds, animals that do not conform to the breed standards do not receive certification from breed organizations, leading to a decrease in their commercial value. Therefore, selection for this trait, especially at weaning, is expected to gradually increase the proportion of animals that meet the standards of the Hereford and Braford breeds.

Higher heritability (0.34) in relation to those obtained in the present study was reported by Koury Filho et al. (2002) for breed aspects measured at weaning, using a linear model and score ranging from 1 to 5. For breed traits score in Guzerá cattle, assigned from 1 to 4 and evaluated with a threshold model, Abreu et al. (2018) also estimated heritability of 0.34. For breed standard of Hereford and Braford animals, evaluated by scores ranging from 1 to 5, Reimann et al. (2018) reported heritability of 0.33±0.02, using threshold model. In general, BTW and BTY in the studied population showed low variability in its phenotypic expression, which may justify, in part, the reduced genetic variability estimated for the trait and, consequently, the low heritability.

Limited genetic gains are expected for STW and STY traits when used as selection criteria in Hereford and Braford population. No studies evaluating sexual traits were found for those breeds or even crossbreeds. Different heritability magnitudes were reported in the literature for sexual traits score in Zebu cattle. For Nellore cattle, values ranging from 0.18 to 0.34 were obtained (Koury Filho et al., 2002; Lima et al., 2013; Passafaro et al., 2013). For sexual traits score in Brahman animals, that were obtained with scores from 1 to 10 and using a linear animal model, Fair et al. (2014) estimated heritability close to zero (0.06). On the other hand, higher genetic variability was estimated with a threshold model for sexual traits score in Guzerá breed, with a value of 0.46±.(Abreu et al., 2018). In general, different heritability values may be due to methodologies applied in obtaining phenotypic traits related to sexual aspects in beef cattle, in addition to the common variations expected between the different populations studied.

Eye pigmentation is one of the phenotypic traits of great relevance for the adaptation of Hereford and Braford breeds, being generally assessed visually by score. For this score, low heritability was obtained, thus moderate genetic gains for the trait are expected, even if in the long term, once the selection of animals with better genetic potential for eye pigmentation is a simple and viable alternative to reduce the incidence of ocular carcinoma in cattle, especially those intended for reproduction, as they remain for a longer period in herds. Similar to that obtained in the present study, Teixeira et al. (2015) and Piccoli et al. (2017) reported heritability of 0.18 and 0.20, respectively, for eye pigmentation score at yearling in Hereford and Braford cattle, ranging from 1 to 5 and assessed using a linear model. On the other hand, for the same breeds, Reimann et al. (2018) estimated a higher heritability (0.46±0.02) for eye pigmentation score at yearling, however attributed by scores ranging from 1 to 3 and using the threshold model.

Despite the low genetic variability, selection based on NSW and NSY can lead to genetic gains in the long term, providing satisfactory correction of the trait in the studied population and, consequently, reducing the risks of injuries that can compromise the reproductive performance of animals used in reproduction. For Angus and Angus × Nelore crossbred cattle, Viu et al. (2002) reported similar heritability to that obtained in the present study, with values of 0.09 and 0.10 at weaning and 0.06 and 0.20 at yearling, for foreskin and navel scores, respectively, with visual assignments ranging from 0 to 5. Higher heritability for navel score, compared with that obtained in the present study, was also reported in the literature. Using linear models, Gordo et al. (2012) and Neves et al. (2014) estimated heritability of 0.38±0.06 and 0.45±0.15, respectively, for yearling navel size score in Nelore breed. For the same breed, Boligon et al. (2016) reported heritability of 0.16±0.01 and 0.29±0.01 for navel score at weaning and yearling, respectively, using a linear model; and 0.22±0.03 and 0.42±0.03 for the same score and measurement ages using the threshold model. Recently, evaluating the navel score at yearling for Hereford and Braford animals, Campos et al. (2019) reported heritability of 0.22±0.02 and 0.42±0.02 using linear and threshold models, respectively.

Similar to that obtained in the present study, Boligon et al. (2016) reported changes in the classification of sires using linear and threshold models for breed characterization score in Nelore cattle. Differences in the classification of sires using linear and threshold models were also observed for navel size score in Nelore (Boligon et al., 2016) and Hereford and Braford (Campos et al., 2019) breeds, differing from that found in the present research.

In general, the use of the threshold model is recommended in genetic evaluations of LCW, BTW, STW, LCY, BTY, and STY in the population studied, even with the need to explain to producers a new interpretation of the breeding values with the application of this model. On the other hand, for EPW, NSW, EPY, and NSY, both models evaluated can be used, once the choice of the model should have little influence on the ranking of sires and cross-validation analyses.

In the studied population, the first five components are sufficient to explain most of the variation between the breeding values predicted for visual scores at weaning and yearling. Using breeding values predicted for growth and reproductive traits in Nelore cattle, Boligon et al. (2016) reported that the first three principal components were sufficient to explain 79.06% of the total variation. On the other hand, evaluating traits of growth, reproductive, and visual scores of body structure, precocity of finishing, and musculature in Nelore cattle, Viana et al. (2020) reported that the first two principal components were sufficient to explain more than 96% of the cumulative proportion of the total variation.

In the present study, negative correlations obtained between the first principal component and all visual scores indicate a common association among the evaluated traits. Thus, most of the genetic variability found in this population is related to average performance of animals for morphological traits, except for EPW and EPY due the low association with this component. On the other hand, the second principal component was more associated with EPW and EPY, suggesting that this component could be used in the selection for ocular pigmentation. The third principal component contrasted mainly lower breeding values for NSW and NSY with higher breeding values for BTW and BTY. The fourth principal component showed higher association with LCY and STY, and the fifth principal component with breeding values for LCW and STW. Therefore, the results of the principal component analysis allow breeders to construct selection indices considering the correlations among variables (breeding values), aiming to simultaneously improve morphological traits in the studied population. In practical terms, these indices would be used as selection criteria to achieve a particular breeding objective.

Visual scores of limb conformation, breed traits, sexual traits, eye pigmentation and navel size showed low genetic variability in Hereford and Braford population, with higher heritability values estimated using threshold rather than linear models. The threshold model is recommended in the genetic evaluations for limb conformation, breed traits, and sexual traits. For eye pigmentation and navel size scores, both models (linear and threshold) can be used. The traits studied can be genetically analyzed with the first five main components. Furthermore, it is possible to construct selection indices that simultaneously improve the morphology and adaptation of Hereford and Braford animals.