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Estimation of genetic parameters for probability of calving up to 39 months of age, stayability and scrotal circumference in Nelore cattle

S Kluska, L O C Silva1, F M Costa Maia, D L Lourenco2, T E Stivanin, F Baldi3, E Peripolli3 and E N Martins

Departamento de Zootecnia, Universidade Tecnológica Federal do Paraná, Dois Vizinhos, PR, Brazil
1 Embrapa Gado de Corte, Campo Grande, MS, Brazil
2 University of Georgia – UGA. Rhodes Center for Animal and Dairy Science, Athens, GA, EUA
3 Departamento de Ciência Animal, Faculdade de Ciências Agrárias e Veterinárias, Jaboticabal, São Paulo, Brasil


Improving reproductive indexes is of extreme importance in beef cattle production systems, as well as investigating new methodologies and traits in order to increase genetic gains for reproduction. Reproductive efficiency directly affects the profitability and productivity of herds, being an important criterion in breeding programs. The objective of this study was to estimate genetic parameters in a Nelore cattle population for probability of calving up to 39 months of age (PC39), stayability, using two measures of age (STAY64 – 64 months of age; and STAY 76 – 76 months of age), and for scrotal circumference at weaning (SCW) and 550 days of age (SC550). Genetic parameters were estimated using 2,287,827 records collected from 1901 to 2015 in Nelore cattle belonging to the Geneplus beef cattle breeding program (Campo Grande, MS, Brazil) database. Bayesian procedures were applied in single- and two-trait analyses using the GIBBS2F90 and THRGIBBS1F90 software, for linear and threshold analysis, respectively.

Heritabilities from single-trait analysis were 0.15, 0.23, 0.20, 0.28, and 0.36 for PC39, STAY64, STAY 76, SCW, and SC550, respectively. The correlation between PC39 and scrotal circumference were of low magnitude, 0.20 and 0.25 with SCW and SC550, respectively, suggesting that the selection for SC550 in sires would possibly lead to higher changes in PC39 occurrence than selection for SCW. The reproductive traits comprised in this study should be included in Nelore cattle breeding programs. Especially PC39, STAY64, and SC550 because its traits would increase the indexes reproductions of the production system.

Key words: bos indicus, heritability, reproductive traits, threshold model


The low reproductive efficiency is one of the major limitations that affects beef cattle production systems (Azevêdo et al 2006), mainly in zebu cattle breeds due to the late sexual puberty (Costa et al 2015). Reproductive efficiency traits measured in females are not widely used as selection criteria in breeding programs because they are difficult to measure, their response to selection tend to be slow as they have a low heritability, and they are evaluated only in one sex and later in the life, which results in weak selection intensities (Boligon and Albuquerque 2010). Hence, exploiting appropriate methodologies and ways to measure and to include those traits in the analysis, when genomic selection is not possible is of great importance for the increase in accuracy of selection (Borba et al 2011).

Age at first calving (AFC) is one of the most studied traits in zebu cattle and has been used as selection criteria in several breeding programs (Dias et al 2004; Boligon et al 2010; Borba et al 2011) , because it is easy to measure and serves as a good indicator of female sexual precocity. However, AFC may be misunderstood in most of the evaluations as animals that do not have AFC records are included in the evaluation of their relatives as missing information. This misinterpretation leads to biased values regarding the average age of first calving of the sire’s daughters. Thus, females with potentially high AFC values could be removed from the evaluation. In addition, when a sire with many daughters with missing records is compared to a sire with a large number of daughters with AFC records and high AFC average, the first sire is erroneously assessed as superior. One way to overcome this problem is penalizing the animals without AFC records or categorizing them, which can be performed through the probability of calving (PC), so all animals can be included in the evaluation.

According to Bormann and Wilson (2010), removing those animals without AFC records from the dataset leads to a bias in the evaluation, due to the variability reduction in the studied population. Furthermore, it underestimates the genetic parameters and overestimates the genetic value of sires with large amounts of missing information (Notter 1988). Studies for the inclusion of animals without calving date whereby it is possible to calculate the AFC, or the inclusion of penalized/categorized animals with missing AFC records have been proposed (Dias et al 2004; Johnston and Bunter 1996; Meyer et al 1990), however, none of them have been widely used in genetic evaluation programs.

Another indicator of the reproductive efficiency in herds is stayability, proposed as a measure of longevity in dairy cattle (Van Vleck, 1980). Stayability can be defined as the probability of a female to remain in the herd up to a given age with a minimum number of calvings (Hudson and Van Vleck 1981). Hence, the selection for stayability leads to the selection of animals with higher fertility indexes, which increases the birth rate in the herd, consequently improving the reproductive indexes. Estimated heritabilities for stayability were reported ranging from 0.06 to 0.35 (Jamrozik et al 2013; Marcondes et al 2005; Nieto et al 2007), suggesting that satisfactory gains can be achieved by direct selection, however, heritability is specific for the population, time and place. Additionally, the economic value of stayability is directly related to the acquisition cost of replacement heifers, and it has a 3.27-fold greater impact than sexual precocity (Formigoni et al 2005).

In animal breeding programs, besides the study of target traits for selection, such as probability of calving and stayability, the knowledge about correlated traits is of great importance. This is especially true when the target traits have low heritability, are difficult to measure and presented high correlation to other traits; in this case, gains can be obtained by indirect selection. Therefore, the objective of this study was to estimate genetic parameters for probability of calving up to 39 months using penalized information of AFC, stayability up to 64 and 76 months of age, and for scrotal circumference at weaning and 550 days. Additionally, we aimed to study the relationship between probability of calving up to 39 months and scrotal circumference. The results of this study should provide information for the use of new traits as indicators of reproductive efficiency in beef cattle breeding programs.

Materials and methods

The dataset used in this study was provided by the Geneplus-Embrapa beef cattle breeding program (Campo Grande, MS, Brazil), and comprised only information about the Nelore breed. Age at first calving (AFC) was used to estimate the probability of calving up to 39 months of age (PC39). Stayability up to 64 (STAY64) and 76 (STAY76) months of age, scrotal circumference at weaning (SCW) and 550 days of age (SC550) were also evaluated. Animals with less than 20 months of age, with an AFC higher than 1640 days, missing birth date and breeder/farm information, and contemporary groups with less than two animals were excluded from the dataset. The edited dataset consisted of phenotypes measured on 857,566 females and 2,287,827 animals in the pedigree.

The threshold of 39 months was established aiming to select animals capable of calving when exposed to a second mating, considering a mating season system with the first exposure to reproduction between 14 and 18 months and the second one between 26 and 30 months of age. In this regard STAY 64;76 were appointed too; i.e STAY64 was choose in order to select animals that calved when exposed to the first or second mating season and had at least three calves up to 64 months of age (animals with regular calves), and for STAY76 followed this same reason, however, the females could have a failure and then they should be had three calves up to 76 months of age. These two approaches for STAY were used to identify which one would respond better to the selection.

The contemporary group (CG) at birth (CGB) was used for PC39 and STAY 64;76; CG at weaning (CGW) for SCW, and CG at yearling (CGY) for SC550. The CGB included herd, year and season of birth, and sex; the CGW included farm, date of weighing, sex, and feeding management at maternal and weaning phases; the CGY included farm, date of weighing, sex, and feeding management at maternal phase and up to 550 days of age.

Table 1. Descriptive statistics, number of animals (N), phenotype mean, number of animals in contemporaries groups (GC) and number (n) and percentage of animals whithin each category (2 for success and 1 for failure).





Categories (n, %)







213,552 (34.9)

397,879 (65.1)





21,606 (21.6)

78,277 (78.4)





60,053 (64.4)

33,155 (35.6)









PC39: probability of calving up to 39 months of age; STAY: stayability up to 64 (STAY64) and to 76 (STAY76) months of age; SC: scrotal circumference at weaning and 550 days (SCW and SC550).

In the analysis of PC39, a threshold model was used and the animals were categorized as success (2) if their age at first calving (AFC) happened when they were up to 39 months old (1185 days or 3.3 years) or failure (1) otherwise (Table 1). For the estimation of PC39 a total of 398,439 females (65.2%) did not have first calving (AFC) recorded and, were penalized. The penalization consisted of ordering the animals by the date of the first calving within each CG. Then, the largest AFC of the CG was taken and 21 days were added into this value, assuming that all females with missing calving date gave birth 21 days after the last one in the group (Borba et al 2011; Pereira et al 2000). To obtain the AFC, the calving date was subtracted from the female’s birth date.

The stayability until 64 months of age with at least three calvings (STAY 64) without the opportunity of failure was also analyzed using threshold models. For STAY64, females with 64 months of age and at least three calvings were given the phenotypic value of 2. Females that reached 64 months but did not have three calvings were phenotyped as 1, and females younger than 64 months old and with less than three calvings were assigned missing records. The stayability up to 76 months of age with at least three calvings (STAY76) was analyzed as a categorical trait in threshold models, where the animals were classified as follows: i) females with 76 months of age with at least three calvings had their phenotype for STAY76 described as 2, ii) females that did not reach three calvings at 76 months of age had their phenotype described as 1, and iii) females that were younger than 76 months old and had less than three calvings were assigned missing records.

The model used for PC39, STAY64, and STAY 76 analyses was proposed by Mrode and Thomson (2005), given the model for the threshold analysis:

y = Xβ + Zu + e

Where is the vector of phenotypes in the observed scale, β and u are vectors of fixed (contemporary groups) and ran dom effects, respectively; X and Z are incidence matrices for fixed contained in β and additive genetic effects contained in u, respectively. The prior distributions for residual effect (e) is assumed to follow normal multivariate distributions

e ~ N(0, I σ2 e)

However, in the threshold model it was assumed that the underlying scale for the binary traits has a normal distribution as follows:

Uǀ0 e ~ N(W 0, I σ2 e)

Where U is the vector of the base scale with order r; 0ˊ= (βˊ, aˊ) is the parameter vector; β is a vector of fixed effects with order , where is animal numbers with records, and is the additive genetic effect; W is the incidence matrix with order by ;I is the identity matrix with order by , and σ2 e is the residual variance. Since the variable in the underlying distribution is not observable, for binary models it is admitted σ2 e =1 (Sorense and Gianola 2002), which is the standard for analyzing binary/categorical data under threshold models (Van Tassell et al 1998).

According to Gianola and Foulley (1983) after establishing the parameters of the model, categorical and continuous scales are linked, thus the probability of an observation being in the first category is proportional to:

Where: yr is the response variable for the r-th observation, with values equal to 1 or 2 if the value belongs to the first or second category (failure or success), respectively;t is the threshold vector fixed as arbitrary; Ur is the value of the underlying variable for the observation; Ø is the cumulative distribution function of the standard normal variable; r is the incidence vector that unites Ø to r-th observation; Ø = (b´, ɑ´) is the parameters vector with order by b (fixed effects) and ɑ (random effects).

The scrotal circumference at weaning (SCW) and 550 days of age (SC550) were measured in centimeters and adjusted for the age of measurement. These measures were performed in this age because in this moment are realized weighing of animals, and thus management is reduced. The SCW and SC550 were analyzed separate in single-trait linear models, and were also analyzed in a two-trait linear-threshold model with PC39. For SCW and SC550, the animal model was used as follows:

y = Xβ + Za + e

Where is a vector of observations; X is the incidence matrix of fixed effects contained in β; Z is the incidence matrix of the additive genetic effects contained in a; e is the random residual vector.

The joint distribution of y, a, and e is multivariate normal, as described below:

For the single-traits analysis, G is the covariance matrix given by A σ2ɑ whereA is the pedigree-based relationship matrix and σ2ɑ the additive genetic variance; R is the residual variance matrix given by where I σ2 e is the identity matrix with order equal to the number of animals evaluated and σ2e is the residual variance of the analyzed traits. For the two-trait analysis, under a threshold-linear model, it was assumed that the prior distributions of the genetic and residual effects follow a normal multivariate distribution, as follows:

Where G0 are genetic variance-covariance matrices; R0 is the residual variance-covariance matrix; is the direct product operator; A is the relationship matrix, and I is the identity matrix.

The variance components for PC39, STAY64 and STAY76 were estimated in single-trait threshold analyses using the TRHGIBBS1F90 software (Misztal et al 2002). The SCW and SC550 were analyzed considering a single-trait linear animal model using the GIBBS2F90 software (Misztal et al 2002). For the two-trait analysis between PC39 and scrotal circumference (SCW and SC550), a linear-threshold animal model was used in the software TRHGIBBS1F90. All the analyses were carried out under a Bayesian approach; therefore, Gibbs chains of 550,000 iterations were generated, with an initial burn-in of 50,000 and a sampling interval of 1,000.

Heritabilities in the liability scale and genetic correlations were calculated based on the posterior distribution of variance components; therefore, credibility intervals and high density regions were constructed for all the genetic parameters at 90% level of credibility. As the high density regions were very similar to the credibility intervals, only the latter will be reported. The convergence was tested using the Geweke and the Heidelberger and Welch diagnostic tests, available at CODA (Convergence Diagnosis and Output Analysis), implemented in R software

Results and discussion

Phenotype average and SD, number of animals, number of contemporary groups and percentage of animals in each category for traits evaluated in this study, are presented in Table 1. In the PC39 analysis, only 34.9% of the evaluated females calved up to 39 months (Table 1), which is consistent with the results reported by Borba et al (2011) for the Canchim breed. For Nelore breed, Terakado et al (2015) showed a percentage of success lower than this study (10.8%) for occurrence of calving up to 26 months of age. However, the results of the present study are considered unsatisfactory, since a high proportion of the calves (65%) were born from females older than 3.3 years of age. Hence, these females remained for approximately three unproductive years in the herd, and were no longer generating profit for the breeder. The higher percentage of success for STAY76 than STAY64 showed here should be related to the late age at first calving, observed as a consequence of failure percentage in PC39. Additionally, results of STAY64 and STAY76 showed that these females did not have calves every year (Table 1).

The posterior mean of heritabilities were low for PC39 (0.15), and moderate for STAY64 (0.23), STAY76 (0.20), SCW (0.28) and SC550 (0.36) in a single-trait analyses (Table 2). The intervals of credibility were small, indicating that the estimate of variance components and genetic parameters were accurate. Phenotypic variance was calculated as the sum of genetic and residual variance. For PC39, STAY64 and STAY76 traits the residual variance was fixed at 1.0 (Table 2 and 3). Heritabil­ity estimates in this study indicated that a low proportion of the phenotypic variance of the traits evaluated in this population may be explained by genetic variance. However, for the STAY higher proportion of variance additive was obtained for evaluation until 64 months of age, and for scrotal circumference, the evaluation at 550 days enable detecting higher proportion of additive variance (Table 2) too.

Table 2. Posterior mean and respective credibility interval for the additive genetic (σ2a), residual ( σ2e) and phenotypic ( σ2y) variance components, and heritability ( h2), in a single-trait analysis for probability of calving up to 39 months (PC39), stayability (STAY64,76), scrotal circumference at weaning (SCW) and 550 days (SC550) in Nelore cattle.




h 2


(0.16 – 0.18)1


(1.17 – 1.19 )

(0.14 – 0.15 )


(0.27 – 0.35)


(1.29 – 1.37)

(0.21 – 0.25)


(0.20 – 0.30)


(1.25 – 1.34)

(0.16 – 0.22)


(0.39 – 0.49)

(1.10 – 1.18)

(1.56 – 1.60)

(0.25 – 0.31)


(1.85 – 2.14)

(3.50 – 3.70)

(5.54 – 5.66)

(0.33 – 0.38)

1- Credibility intervals at 90%

The heritabilities estimates for PC39 in single and two-trait analyses (Tables 2 and 3) were lower than reported by Boligon and Albuquerque (2011) (0.45) for pregnant heifers, in which precocious had to calve up to 31 months of age. And then showed by Bormann and Wilson (2010) for the AFC penalized (0.35, 0.31 and 0.27). According to Bormann and Wilson (2010) an increase in the number of days by penalization would lead to a decrease in heritability estimates, since they observed estimates described above for age at first calving (AFC) penalized in 30, 60 and 90 days, respectively. According to Yokoo et al (2012), the reduction in the AFC, in this case PC39 has a great influence on the productivity of the herd, since it is related to the number of calves produced during the full life cycle of the dam, to the increase in the selection intensity, and to the reduction in the generation interval, factors that contribute to the genetic progress in the herd.

There is still no consolidated methodology in analyzing AFC with the inclusion of missing data, however some authors have considered this information when setting up the dataset (Borba et al 2011; Malhado et al 2013). Moreover, the penalization and categorization proposed in our study has not yet been reported in the literature. Malhado et al (2013) tested five alternatives for evaluating datasets with missing information and obtained heritabilities for AFC ranging from 0.13 to 0.26. The binomial model (success or failure) proposed by them resembles the approach used for PC39 analysis in this study. With this model, the authors had the lowest estimate of heritability (0.13) for AFC, which is similar to the estimates described for single and two-trait analysis for PC39 (Tables 2 and 3). The low posterior mean heritability for PC39 described in the present study might be highly related to the reduced number of classes applied in the categorical approach, since a restricted number of classes result in a reduction in the variability of the population.

For STAY64 and STAY76 (Table 2) the posterior mean heritabilities showed in this study were higher than those presented by Nieto et al (2007) for Canchim breed (0.06 and 0.08). For Nelore and composite breeds similar heritabilities for STAY up to 6 years when a cow calved every year were described by Santana Jr et al (2013) (0.25 and 0.20, respectively). Additionally, the lower heritability observed for STAY 76 than STAY64 (Table 2) in this research can be explained by Jamrozik et al (2013), whose studies have found that the heritability for stayability tends to decrease over time. The authors reported a value of 0.35 for stayability at the second calving and 0.13 for the eighth calving in Simmental cattle, indicating that the magnitude of the heritability is linked to the order of calving.

The posterior mean heritability for STAY64 and STAY 76 suggesting than selection for these traits would result in a low genetic gain, although STAY64 showed an increased heritability when compared to STAY76. This increase might stand for the largest additive genetic variance detected for STAY64, since the residual variance for both of them was set as 1.0. Additionally, as STAY64 is measured earlier than STAY76, this would allow selection decisions to be taken earlier, reducing the generation interval, and thus leading to a greater genetic gain per generation of selection. In addition, the selection of animals for STAY64 allows the breeder to select the females capable of calve the same three calves as in STAY76 in one year less, therefore, reducing the calving intervals. This selection would dilute the production costs and the average intervals between calvings, besides, it would also increase the reproductive indexes of the herd.

The main factor that limits the detection of the genetic variability in reproductive traits of females, in this research also, is the definition of the weights or ages to initially expose the animals to reproduce when considering a mating season system (Boligon et al 2010). Late evaluations tend to decrease variability among animals. The pregnancy of animal very young is not recommended since the heifer is still in development, which can prevent the female from weaning heavier calves, especially when it is associated with feeding restrictions.

However, second Bormann and Wilson (2010), heifer's daughters of two-year-old dams were older at first calving than those born from 3 to 10-year-old dams, indicating that the anticipation of the mother's AFC may result in the late daughter's AFC. Beside, with regard to the longevity of the females, Terakado et al (2015) reported that daughters of precocious heifers (AFC up to 26 months) were 33% more likely to remain in the herd by age 5 and 6, and a further chance of 28% of remaining in the herd until age 7 when compared to daughters of non-precocious heifers (AFC calving between 31 and 35 months of age). Hence, the heifer’s AFC anticipation may result in greater daughter longevity.

For scrotal circumferences to weaning and at 550 days the results in a single and two-traits analyses are presented in Table 2 and 3, respectively. The intervals of credibility were small, indicating that the estimate of variance components and genetic parameters were accurate. The residual variance for PC39 was fixed at 1.0 (Tabela 3). We observed a slight increase in heritability and variance components for SC550 compared to SCW in a single and two-trait analysis (Table 2). The posterior mean heritability for SCW (0.28 and 0.27) are similar to the results reported by Borba et al (2011) in a two-trait analysis with the inclusion of reproductive traits to estimate the scrotal circumference at 420 days (0.25 - 0.26), and lower than the estimates for SC550 in a single and 2-traits analysis (Table 2 and 3).

Table 3. Posterior mean with respective credibility interval for additive genetic (σ2a) residual (σ2e) and phenotypic (σ2y) variance components, heritability ( h2) and genetic correlations (ra ) in a 2-trait analysis for probability of calving up to 39 months (PC39) and scrotal circumference at weaning (SW) and to 550 days (SC550) in Nelore cattle.




h 2



(0.16 - 0.18) 1


(1.17 - 1.19)

(0.14 - 0.15)

(0.13 - 0.25)


(0.38 - 0.45)

(1.12 - 1.18)

(1.56 - 1.59)

(0.24 - 0.29)


(0.16 - 0.18)


(1.16 - 1.19)

(0.14 - 0.15)

(0.15 - 0.33)


(1.91 - 2.28)

(3.19 - 3.55)

(5.43 - 5.51)

(0.35 - 0.42)

1- Credibility intervals at 90%.

The posterior heritability averages for SCW and SC550 were lower than those described by Lopes et al (2011) for scrotal circumference measured between 17 and 24 months of age (0.45), and smaller than those reported by Marques et al (2013) (0.55), both in Nelore cattle. Despite the variation in the heritabilities for scrotal circumference, it can be observed that in all the studies its magnitude was moderate, indicating genetic gains are possible by direct selection. How SCW and SC550 are not economic important traits to be improved by selection, thus, we aimed to investigate genetic correlations among SC550 and PC39, a trait which presented a larger heritability (Table 2).

For PC39 and SCW or SC550 the posterior mean heritabilities and variance components in two-trait analysis were similar to those described in a single-trait analysis (Table 3). With the inclusion of SCW or SC550 in the PC39 evaluation, it was not possible to detect a greater proportion of the additive genetic variance. Grossi et al (2009) using the maximum likelihood method obtained heritabilities higher than those described for SC550 in a single and two-trait analysis (Tables 2 and 3). The authors described a heritability of 0.64 for SC500 and a genetic correlation between SC550 and AFC of -0.13. Hence, the number of genes that affect SC550 and AFC is very small, revealing that there is a rare or no association between these traits.

The genetic correlation between PC39 and scrotal circumference was greater in a combination with SC550 than SCW (Table 3). Thus, the estimated genetic correlation between PC39 and SC550 (0.25) indicates that the selection of sires with greater SC550 can increase the PC39. A similar correlation is described by Borba et al (2011) for the probability of calving up to 38 months of age and scrotal circumference (0.37). Results of correlations between PC39 and scrotal circumference are limited in the literature. In this way, the use of SC550 as an indirect selection criterion for PC39 can be had gains higher than SCW and perhaps greater gains than direct selection for PC39 depending on population. Additionally SC550 had higher heritability than SCW increasing the genetic gain.

The heritabilities for reproductive traits measured in females and males indicate that these traits would be improved to a small extent. However, genetic gains are cumulative and depend on other factors too. Therefore, the economic importance of those traits can justify their selection. The decreasing of PC39 and increasing in reproductive indexes has a great influence on the productivity of the herd, since are related to the number animals produced in the year, to the increase in the selection intensity due to a greater number of animals available for selection, and to the reduction in the generation interval, factors that contribute to increasing the genetic progress in the herd.



To Geneplus-Embrapa breeding program for providing the data for this research. SK received a scholarship from Coordination for the Improvement of Higher Education Personnel (CAPES)

Conflict of interest

The authors have no conflict of interest to declare.


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Received 1 March 2018; Accepted 23 April 2018; Published 1 May 2018

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