The significance (p < 0.0001) of the fixed effects for the RFIpop implies that the environmental effects and animal age were better adjusted for the RFIpop than did for the RFItest. Thus, it is expected that non-genetic differences affecting RFI were better corrected or less biased for RFIpop. It should be highlighted that different regression equations to estimate the RFI was applied for the each individual test (RFItest) whereas a unique regression equation was employed for the whole population (RFIpop). Additionally, the random sire variance effect was higher for the RFIpop (0.017 ± 0.02) than for the RFItest (0.014 ± 0.01), pointing out that differences in the RFI due to the sire effect were more noticeable for such population.
The largest additive genetic variance estimated for the RFIpop implies a greater chance of identifying genetically superior animals, being expected higher response to selection for such population. Hoque and Oikawa (2004) comparing the RFI obtained for each feed efficiency testing stage with that obtained using genetic and multiple regression (ordinary RFI) in Wagyu cattle, suggested that the genetic and ordinary RFI would contribute more for genetic selection than the RFI obtained for each testing stage, as it displayed superior additive variance estimates.
When the RFI was calculated within the population (RFIpop), the prediction of the genetic value is conditioned to the solution of the CG effect (fixed effects) and random effects. On the other hand, this condition is not accomplished for the RFItest, influencing the partition of the variance components, and consequently, a fraction of the genetic variance is absorbed by the pre-adjusted fixed effects. This pattern can be supported by the calculation leading to an increase in the additive variance of the RFIpop. The heritability estimates obtained for RFIpop and RFItest (Table 4) were within the interval described in the literature for beef cattle, with values ranging from 0.13 to 0.28 (Grion et al. 2014; Oliveira et al. 2014; Olivieri et al. 2016; Silva et al. 2016).
Moderate heritability estimates were observed for DMI, which is in accordance with Oliveira et al. (2014) (0.29) and de Moraes et al. (2017) (0.25 to 0.36) in Nellore cattle. Heritabilities for growth, reproductive, longevity, and carcass traits reported in this study were consistent with the literature, ranging from low to moderate (Yokoo et al. 2010; Zuin et al. 2012; Santana et al. 2014; Bonin et al. 2015; Tonussi et al. 2015; Grossi et al. 2016; Lopes et al. 2016; Pires et al. 2017; Kluskaa et al. 2018; Gordo et al. 2018; Bonamy et al. 2019; Sainz et al. 2020). As expected, the lowest heritability estimates were obtained for sexual precocity and maternal heritability related traits, such as AFC and ACP. The heritability estimates for BW, W240, W45, MCW, PP30, STAY, REA, BF, MAR, RF, SC365, and FRAME pointed out that selection for these traits is feasible when phenotypic records are available.
Higher genetic correlations between the RFIpop and some traits (BW, STAY, BF, RF, MAR, and DMI) were obtained when compared with those for the RFItest. Differences in (co)variance decomposition between the RFIpop and RFItest might explain these results. Hypothetically, biased variance components were obtained for the RFItest since the RFI was pre-adjusted for the feed efficiency test. Therefore, it is possible to infer when the RFItest estimation is performed within the feed efficiency tests, and the differences between the CG may not be properly corrected or adjusted. Hence, calculated RFI within the test is adjusted for the CG without considering the random effects. In contrast, for the RFIpop calculate considering all feed efficiency tests, the CG and other fixed effect were estimated simultaneously with random animal effect. It is important to emphasize that in the mixed and animal model, the solution of the fixed effects relies on the random effects and vice versa (Perri and Iemma 1999).
Despite the low genetic correlation estimates between RFItest and RFIpop with the other evaluated traits (BW, W240, MCW, SC365, AFC, ACP, PP30, STAY, REA, BR, RF, MAR, and FRAME), the estimates obtained with the DMI were moderate. Such a pattern may be due to the fact that the RFI is estimated as a function of the DMI. The correlation estimates obtained were in agreement with those presented in the literature (0.33 to 0.95) (Grion et al. 2014; Santana et al. 2014; Ceacero et al. 2016; de Moraes et al. 2017; Polizel et al. 2018). Low correlation estimates between RFI and growth, reproduction, longevity, and carcass traits were also reported in Nellore cattle (Grion et al. 2014; Santana et al. 2014; Ceacero et al. 2016; de Moraes et al. 2017; Ferreira Júnior et al. 2018; Bonamy et al. 2019; Moraes et al. 2019; Brunes et al. 2021).
High genetic (0.72) and phenotypic (0.71) correlation estimates were obtained between RFItest with RFIpop. It has been widely accepted that just traits with a correlation over than 0.80 can be assumed to be genetically the same trait, what doesn't apply here (Robertson 1959). Despite the high genetic and phenotypic association, these values were less than unity, implying that there are some differences between these traits (Table 5). According to Herd and Bishop (2000), differences in the RFI estimation can be attributed to the information used in the estimation. These results pointed out that differences in the genetic progress are expected using RFItest or RFIpop as selection criteria to improve RFI, and changes in sires ranking are also expected using one or another.
The highest inflation of the GEBVp for the RFItest might be attributed to the differences between the CG, which are not properly corrected or adjusted when the RFI calculation is performed within the feed efficiency tests. Differences due to the management, environment, and other non-genetic components would be better corrected for the RFIpop since the adjustment for the fixed effects was performed with the mixed model. As a result, the fixed effect solutions and genetic predictions were less biased in the RFIpop calculation. The implication is that genetic selection based on RFItest might not lead to the identification of the best feed efficient animals since overestimated GEBV’s are expected for them.
Despite the differences in (co)variance decomposition between RFIpop and RFItest, the prediction ability for them were similar. Thus, there is non-advantage or differences in terms of prediction ability between RFIpop and RFItest. The prediction ability observed in this study for the RFIpop and RFItest were similar to those reported in the literature for Nellore cattle (Silva et al. 2016; Brunes et al. 2020). However, the genomic selection main goal is the phenotype approximate prediction, and in this case, the use of RFIpop is the strategy that would guarantee lower inflation. To best our knowledge, no study has been conducted evaluating the GEBVs obtained for the RFI considering each and all feed efficiency tests to corroborate these results.
From a nutritional assessment point of view, it is not recommended to combine tests or exclude the feed efficiency test effect in the RFI regression estimation. The RFI calculation within the feed efficiency test groups may be more suitable for datasets in which the differences between the metabolizable energy concentrations and diet composition or environmental effects are higher (Arthur et al. 2001; Lancaster et al. 2009). For genetic evaluation purpose, to obtain the RFI calculated within the test, initially a pre-adjustment is performed for the feed efficiency test effect, and it influences the variance component estimation and the genetic value solutions. Thus, considering the standardization of environmental and management conditions, the use of the RFIpop is supported, mainly for genetic evaluation purpose.
In conclusion, the RFI estimation influences the decomposition of the variance components and, consequently, the estimation of variance components and genomic prediction. The genetic correlation between RFIpop and RFItest was moderate, implying that both traits have different genetic background and differences in sires ranking and genetic response are expected between both traits. The use of a unique regression equation with all evaluated animals to estimate the RFI (RFIpop) would be more appropriate to adjust or correct non-genetic effects and to decrease the genomic prediction inflation.