Genotype x Environment Interaction for reproductive traits in brazilian Nellore breed cattle

SC550 and AFC respectively. The results obtained in the analysis, indicated that this interaction was not significant for SC at different ages (genetic correlation, rg> 0.8). For AFC, significant effect of GEI was observed for combinations involving the Northern region (rg<0.8), indicating that this interaction should be considered by the genetic evaluation programs in this region.


INTRODUCTION
The Nellore breed stands out in Brazil, because it presents the greatest genetic contribution to the herd, which is estimated in 218.25 million cattle (IBGE, 2016). According to OLIVEIRA et al., (2002), 80% of this population is composed by genes of this breed and its crosses. Because of that, it is considered an important breed for beef cattle breeding in the tropical region and for the meat supply in the world. The Brazilian territory is vast, presenting regions with different climatic conditions and varied production systems. Such scenario lead to different performances of genotypes, which characterizes the genotypeenvironment interaction (GEI).The importance of internal migration of bovine populations was pointed out by McManus et al. (2016). That work highlights the importance of evaluating the GEI to better define the sires to be selected, given the trend of movement between different regions. Among the objectives of the selection for Nellore herds in Brazil, the reproductive traits present economic importance for the success of the activity, as can be observed in the studies developed by Brumatti et al. (2011), Jorge Júnior et al. (2007, and Carvalho & Bittencourt (2015). In beef cattle, the reproductive evaluation of cows is based on the number of calves born annually, leading to the increase in the number of calf/year and the number of calf/cows along the reproductive life (CHUD et al. 2014). Evidences for the presence of GEI in development traits have already been demonstrated for the Nellore breed in Brazil -between different regions of a State, between States or between the different regions of the country (TORAL et al. 2004;PÉGOLO et al. 2009e DIAZ et al. 2011).Carvalho et al. (2013 evaluated the presence of GEI in the Nellore breed for the development traitsW210 and W365 between the Center-West, North, and Southeast regions of Brazil, emphasizing their presence between the North and Southeast regions when W365 was evaluated. Other works have reported similar results, such as those performed by Chiaia et al. (2015), Lemos et al. (2015), and Ambrosini et al. (2016). Due the economic importance of reproductive traits for Nellore, the aim of this study was to evaluate the GEI via Bayesian inference in the scrotal perimeter traits, at different ages and the age at first calving in heifers among herds distributed in the Brazilian Central-west, North, and Southeast.

MATERIAL AND METHODS
For the development of the present study, the phenotypic information of Nellore animals participating in the Nellore Brazil Genetic Breeding Programwere used. This tool was managed by the National Association of Breeders and Researchers (ANCP). The animals used in this work were born between 2001 and 2009The commercialization of animals for slaughter and the production of genetically superior breeds and breeding herds are the main objectives of the production of herds. The animals were kept in pastures throughout the year, receiving mineral supplementation and water ad libitum.Females were submitted to a mating season with duration of 90 to 120 days, submitted to artificial insemination or controlled mating. Weaning was carried out around 6 to 8 months. The database used was constructed using information from herds raised in several regions of Brazil, however, information from the states with the highest number of animalswere used. In order to characterize the breeding environment, the states were grouped according to their geographical location. In this way, the database used in the analyzes was composed by farms distributed between the Central-West (Goiás, Mato Grosso do Sul, Mato Grosso), North (Tocantins, Pará, and Rondônia), and Southeast (São Paulo and Minas Gerais). The scrotal perimeter was adjusted to the following ages: 365 days (SC365), 450 days (SC450), 550 days (SC550), andat first calving of heifers (AFC). The number of animals evaluated in each region is shown in Table 1. The original data were edited usingSAS 9.2 program (SAS Inst., Inc., Cary, NC) that contained information on 146,536 animals. However, in order to set the information necessary for the present study, some restrictions were made: birth seasons (1-December to February, 2 -March to May, 3 -June to August, 4 -September to November), contemporaneous groups (CG) with information on the breeding farm creation, management group (GROUP 365, 450 and 550), season and year of birth. Data from animals that exceeded the mean ± 3 standard deviations for the traits of interest, CG information with less than 3 animals, and information from breeding animals with less than 5 calf were excluded. The genetic connection between the evaluated enviroments was guaranteed. The first database was used in order to estimate the genetic parameters for the traits evaluated. It was composed by the following information: identification of the animal, identification of the bull and cow, CG for the different ages of perimeter scrotal and age at first calving (CGSC365, CGSC450, CGSC550, CGAFC), SC365, SC450, SC550, and AFC. However, to verify the presence of the genotype-environment interaction (GEI)were created separated files, where the studied trait is considered for each breeding environment.That way, other fourfiles containing the following information were created: the identity of the animal, bull and cow, CG for the trait, trait X in the North region, trait X in the Southeast region, andtrait X in the Center-West region. The pedigree file contained the information about the identity of the animal, bull, and cow. Initially, a multi-trait evaluation was performed to estimate the genetic parameters of the traits.After that, the analyzes were performed to verify the presence of the GEI, in this case, a multi-traits analysis was used. In the model used the fixed effects were controlled through the creation of the contemporaneous group (CG for each of the traits) and the random effects are considered additive genetic directstudied for each traits SC365, SC450, SC550, and AFC. The data were analyzed usingGIBBS2F90 program (MISZTAL et al., 2014). In matrix form, the general model can be described as: where, y, β, a and e arethe vector of observations, vector of the systematic effects (would be the fixed ones), vector of direct additive genetic effects, and vector of random errors, respectively. X and Z are, respectively, the incidence matrices that associate β and α to the observations. The vectors β and α are the lease parameters of a conditional distribution y | β, α. It was considered, a priori, that β has a uniform distribution, which reflects vague preliminary knowledge about this vector. Inverted Wishart distributions were assigned to the other components (random effects). Thus, the distribution of y, given the parameters of the location and scale, was considered as: VAN VLECK, 1996).

y | β, a, R ~ N [Xβ + Za, INR] (VAN TASSEL&
A total of 1,000,000 samples were generated with a burn-in period of 300,000, with samples taken every 50 cycles. Convergence was verified using the POSTGIBBSF90 program (MISZTAL, 2014). The means of the a posteriori variances estimated for each trait were used for the estimation of heritabilities and a posteriori mean correlations. According to Robertson et al. (1959), the GEI investigationwas verified when the genetic correlation (rg) between the traitswas less than 0.8. However, to verify this correlation, the same trait as a distinct trait in each of the different breeding environments must be considered.

RESULTS
High heritability estimates (h²) were found in the multi-trait evaluation (Table 2) for the scrotal perimeter adjusted for the ages invastigated (h²> 0.4). So, significant selection gains are expected for this trait, as well as, the additive genetic effects have an important contribution to the performance of the scrotal perimeter in the evaluated herds. However, at the age of the first calving (AFC) the estimated h² was of low magnitude (h² <0.2), proving the low effect of the additive genetic components indicating that nonadditive genetic and environmental effects (management and climate) are more pronounced. Regarding the genetic correlation between the traits evaluated, it can be observed in Table 3 that there is a high correlation in the scrotal perimeter measurements (rg> 0.8), indicating that the same gene groups are acting on the traits at different ages. However, when the genetic correlation between the perimeter measures in males and the age at first calving of heifers was evaluated, it was verified that there was a negative correlation for the combination between all ages of SC and AFC, indicating that the genetic groups that lead to the increase of the performance for a trait act decreasing the performance of the other. In the case studied, the genes that are responsible for the increase of the scrotal perimeter of males at different ages are also responsible for determining the decreasing of the age at the first calving heifers.  In order to verify the existence GEI for scrotal circumference measured at different ages, a evaluation of multitraits was performed and no interaction was observed (Table 4). However, for AFC, the presence of GEI was found between the North and Central-west regions as well as North and Southeast regions (rg <0.8).

RESULTS AND DISCUSSION
The results found in the descriptive analysis (Table 1) BUZANSKAS et al. 2017). These works showed mean values that ranged from 20.13 to 31.88 cm. Although scrotal perimeter measures do not present direct economic benefits, they have been used by the genetic improvement programs. That happens because of their association with the reproductive capacity of bulls and cows, as well as being related to growth traits (FORTES et al. 2012;SIQUEIRA et al. 2013;BUZANSKAS et al. 2017). Heritability values obtained in the multi-trait evaluation (Table 2), for the SC measurements at different ages were of high magnitude, ranging from 0.465 -0.50 that are in line with results published for the same breed by Raidan et al. (2015), Chiaia et al. (2015), andBuzanskas et al. (2017). However, Boligon et al. (2007) estimated h² values for SC365 and 550 equal to 0.25 and 0.37, respectively. In other words, the values found were lower than those present in the literature for the Nellore breed. According to the same author, low estimates of h² for the scrotal perimeter may be caused by the inadequate adjustment of the perimeter by the age of the animal at the time of measurement. SC heritability values for animal at different ages found in this paper, and also observed in other works, pointed out that h 2 is from moderate to high magnitudes. Also, SC is highly correlated for theses ages with correlation values greater than 0.85. Therefore, the selection of males for this trait can be performed at younger ages, which would increase the genetic gains and reduce the maintenance cost of young bulls that are candidates for selection. According to Siqueira et al. (2013), genetic evaluation programs have adopted the standard age of selection for SC at 18 months. The Nellore breed is considered sexually late. In an attempt to anticipate the age of puberty as well as to reduce the age at first calving, by increasing its useful life in the herd, selection works have been intensified. The identification of earlier animals enables cows having a greater number of progenies during their life produced. Thus, AFC has been included as a selection criterion for the Nellore breed in Brazil. Despite having low heritability, it presents genetic variability and potential to be improved with the use of selection, mainly due to the greater selective intensity applied to the females (MATOS et al., 2013). Genetic variability is confirmed by h² value estimated to be 0.117 (Table 2). Other studies corroborated the low magnitude of h² for this trait in the Nellore, as the results showed by Sousa et al. (2015) with animals raised in the middle northern region of Brazil. In that work, an estimate of h² equal to 0.026 was obtained, evidencing that the additive genetic effects are not very pronounced for the performance of this trait. The estimated h 2 value found in the present study is higher than that one presented by Sousa et al. (2015). This finding may be related to the fact that the animals were submitted to different environmental and management factors of the herds, combined with the fact that the management and age at which females were introduced in reproduction are directly related to age at the first birth. However, other studies obtained estimates with similar magnitude found in the present work, for instance, Boligon et al. (2008) found estimates of h² ranging from 0.14 -0.15, Pereira et al. (2010) evaluated animals of the same breed in which values between 0.06 -0.10 were presented, Chiaia et al. (2015) verified that the h² for the AFC varied between 0.09 -0.50, depending on the environmental gradient to which the animals were submitted, and Ambrosini and collaborators (2016) who found h² equal to 0.06 ± 0.02. These values are due to the locations and management adopted in the herds, and some of the animals evaluated in these studies were distributed among the Southeast, Central-west and Northeast regions of Brazil. Buzanskas et al. (2017) found h² values equal to 0.25 ± 0.02 for Nellore animals found in Brazil, which is of moderate magnitude and is higher than that one found in the present study. However, low estimates of h² for different birth ages, especially for the age at first calving, may be a consequence of the criteria adopted for the entry of the heifers in the reproduction, especially those related to weight and age. Normally, it is expected that the heifers reach a satisfactory body condition to be exposed to the bull or to be inseminated, initiating the reproductive activity (BOLIGON et al., 2007;MELLO et al., 2016). For Chiaia et al. (2015), the variation of variance components and estimates of h² in different breeding environments can be explained by many reasons. The h² parameter is a property of the population and the environment, while the environmental variance is dependent on the general management conditions and climate. In general, greater variations of environmental conditions reduces h², while greater environmental uniformity increases heritability (TORAL et al., 2004). The identification of females that have the capacity to gestate at younger ages is one of the priorities of selection and breeding programs in the Nelore breed (FARIA et al., 2009). Studies to determine genetic correlations between SC and reproductive traits of cows have been developed, in order to overcome the greatest difficulty in determining easily measurable traits that are