Bayesian inference of genetic parameters for reproductive traits in Sistani native cows using Gibbs sampling

Introduction

Cow fertility is an important trait in profitability of cattle enterprises, and is considered as the most important objective in cattle breeding (Cammack et al., 2009). Early indices for improving the cow reproduction were mainly calving interval (CI), days open (DO), and gestation length (GL) (Jansen, 1986). However, accessibility to data on insemination and calving date has allowed the  use of other traits such as age at first service (AFS), age at first conception (AFC), interval from calving to first service (CTFS), first service to conception (FSTC), non- return rate (NRR), and number of inseminations per conception (NSPC) in breeding programs (Jamrozik et al., 2005).

Reproduction in domestic animals is a complex character with low heritability that is influenced by many environmental factors. However, it has been reported that the average heritability of reproductive traits for beef cattle are higher than those for dairy cattle suggesting that high genetic variation in reproductive traits of beef cattle may lead to better genetic improvement in these breeds (Koots et al., 1994). Cows that do not wean a live calf cannot compensate the cost of several months rearing and management (Heaton et al., 2013). However, research on reproductive traits in beef cattle have been limited due to inaccessible of records (hard to measuring) and their low heritability (Buzanskas et al., 2013; Johnston, 2014). Low heritability, longer generation intervals, low selection intensity, and low numbers of correlated traits are amongst the factors that result in low level of reproductive performance and genetic progress in female fertility (Johnston et al., 2014). Accurate estimates of (co)variance components for economically important traits, such as reproductive ones, are pre-requisites for efficient designing of breeding strategies (Falconer and Mackey, 1996).

Iranian native breeds have valuable traits that differentiate from their Western counterparts (Mohammadabadi et al., 2011). Sistani cattle (Bos indicus), an important native meat type breed in Iran, are well adapted to the tropical region of Sistan (located in east of Iran). Such characteristic has become a biotype of great interest for meat production industry within the last few years. One of the most distinctive features of Sistani cattle is its great capability to resist diseases which makes it a potential reservoir of germplasm useful for future crosses (Mohammadi et al., 2009). In recent years, the population of Sistani breed has been decreasing, therefore, effective strategies should be implemented to prevent the extinction of this breed. Identifying superior animals for the next generation requires the comprehensive knowledge on the variance-covariance components and genetic parameters of the traits. Bos indicus heifers have a higher age at puberty, indicating the importance of maturity in indigenous breeds and selection programs for reproductive traits under local systems in tropics (Carvalheira et al., 1995; Buzanskas et al., 2013; Chud et al., 2014; Diskin and Kenny, 2014). The objective of this study was to estimate the genetic parameters for CI, GL, DO, CTFS, FSTC, CR, PR, and NSPC traits in Sistani cattle using Gibbs sampling.

Materials and methods

A total of 1489 insemination and calving dates of 346 Sistani cows, recorded from 1999 to 2013, were used to estimate the genetic parameters for the reproductive traits. Reproductive traits including the calving interval (CI), gestation length (GL), days open (DO), calving to first service (CTFS), first service to conception (FSTC), conception rate (CR), pregnancy rate (PR), and number of inseminations per conception (NSPC) were calculated. Calving interval was measured as the number of days between two consecutive calving (Berry and Evans, 2014). Gestation length was calculated as the interval between the last insemination and subsequent calving date, and ranged between 250 to 300 days (Eghbalsaied, 2011). An interval of calving date to last observed insemination date was considered as days open and outlier records (i.e., out of range of 15 to 390 days) were omitted (Eghbalsaied 2011). Conception rate was defined as the percentage of successful insemination, and calculated as: CR= (1/NSPC)*100 (Zambrano and Echeverri, 2014). The NSPC is the number of inseminations per conception. Pregnancy rate was the success rate for getting pregnant; 1 for successful pregnancy, and 0 for other cases (Rust and Groeneveld, 2001). Pregnancy rate was calculated as PR = 0.25 × (233 - DO) (Kuhn et al., 2004). A summary of the data is shown in Table 1.

Table 1. Descriptive statistics for reproductive traits

¹CI: calving interval; GL: gestation length; DO: days open; CTFS: calving to first service; FSTC: first service to conception; CR: conception rate; PR: pregnancy rate; NSPC: number of inseminations per conception

²SD: standard deviation

The data were edited and the significance of fixed effects were checked using the R program. Variance components of traits were estimated via Gibbs sampling in a single- traits analysis using the following models:

where, y was the vector of observed traits, X was the incidence matrix associating data to the fixed effects (year- season of calving, lactation, sex, year – season of insemination, birth weight of calf, linear and quadratic effect of age at first calving), b was the vector of fixed effects, Z and Z₁ were the incidence matrices associating data to the additive genetic effects, Z₂ was the incidence matrix associating data to the sire effects (service sire), W was the incidence matrix associating data to the permanent environmental effects, and a, s, pe, and e were the vectors of additive genetic, service sire, permanent environmental, and residual random effects, respectively. The models were compared using the deviance information criteria (DIC) as follows:

where, PD was the effective number of parameters, and calculated as follows:

and D̅  was the posterior expectation of the deviance ,  

y and θ were the data and unknown parameters of the model, respectively,  was the likelihood function, and C was a constant that was deleted in all calculations that compare different models (Berg et al. 2004; Gelman et al., 2013).

Genetic and environmental correlations between traits were estimated by Gibbs sampling in a multi- traits analysis and best model for each trait. The matrix model used was:

in which, y_i = vector of observations for i^th trait; bi= vector of fixed effects (year- season of calving, lactation, sex, year – season of insemination, birth weight of calf, linear and quadratic effect of age at first calving) for i^th trait; a_i = vector of random animal effects i^th trait; s_i = vector of random effects of service sire for i^th trait; pe_i = vector of random permanent environmental effects i^th trait (only considered for CI, FSTC, CR and NSPC); e_i = vector of random residual effects for a_i = vector of random animal effects i^th trait; X_i, Z_i, SS_i and W_i are incidence matrices which relate the data to the fixed and random effects, respectively. The expectations of the vectors and (co)variances of random effects for models are as follows:

Direct genetic, service sire, permanent environment, and residual variances are represented by σ²_a, σ²_s, σ²_pe and σ²_e, respectively. A is the numerator relationship matrix of all animals, I is an identity matrix equal to the number of observations.

Gibbs chains for single-trait analysis were generated with 300000 iterations, an initial discard of 30000 samples, and a sampling interval of 100 iterations. The same chains for multi- trait analysis were generated with 1000000 Gibbs chain, 100000 samples as burn in and sampling interval of 50. The convergence checking of the chains generated by the Gibbs sampler was done using graphical analysis and diagnosis tests (Geweke algorithm) available in Bayesian output analysis program (BOA) (Smith, 2007). Credible intervals and high density regions for all estimates of covariance components and genetic parameters were determined at 95% level. Geweke method was used for diagnosis (Geweke, 1992), which was assessed by comparing the sample mean in early segment of the chain and the mean in subsequent segments.

Results

The P-value obtained from Geweke algorithm supported convergence for all chains. After convergence, 3000 and 20000 samples were used for the estimation of posterior means of genetic parameters in single-trait and multi-trait analyses, respectively. Figures 1 and 2 show the trace plots and marginal posterior densities of heritability for reproductive traits in the best models for single- traits. The plots indicated that the algorithm mixed well, despite of differences among traits. Variance components, heritability, and DIC of different models are shown in Table 2. According to DIC of the models, the best model for CI, FSTC, CR, and NSPC was model 4 whereas the best model for GL, DO, CTFS, and PR was model 3. The posterior mean of heritability for GL and NSPC was higher than those for other traits (> 0.1). The lowest heritability was for FSTC and CTFS (

Table 2. Variance components, heritability, and DIC of different models for reproductive traits

¹ CI: calving interval; GL: gestation length; DO: days open; CTFS: calving to first service; FSTC: first service to conception; CR: conception rate; PR: pregnancy rate; NSPC: number of inseminations per conception

²  : Additive variance; : error variance; : permanent environmental variance; : heritability; DIC: deviance information criteria; SE: standard error

Table 3 shows the posterior mean of genetic and environmental correlations between reproductive traits. The genetic correlation between CI with DO and NSPC was close to 1, thus the effected genes for these traits are the same as expected. High negative associations were observed for CI×CR, DO×CR, DO×PR, and CTFS×CR indicating that selection for one of these traits could lead to decrease in others. Genetic correlations for CI×CTFS, CI×FSTC, GL×DO, GL×CTFS, GL×FSTC, GL×CR, GL×NSPC, DO×PR, CTFS×FSTC, and CTFS×PR were moderate. Low genetic correlations were found for CI×GL, CI×PR, GL×PR, DO×CTFS, DO×FSTC, DO×NSPC, FSTC×PR, CR×PR, and CR×NSPC (Table 3). The genetic correlations for CTFS×NSPC, FSTC×CR, FSTC×NSPC, and PR×NSPC were less than 0.1. The highest environmental correlations were recorded for CI×DO, CI×PR, DO×PR, and CTFS×PR (>0.88); however, most reproductive traits had environmental correlations of less than 0.1. The high positive and negative genetic correlations between traits indicate that improving the additive genetic level in one trait may lead to either partial genetic improvement or genetic suppression in other traits, respectively (Pantelić et al., 2011).

Table 3. Genetic and environmental correlation between reproductive traits

¹CI: calving interval; GL: gestation length; DO: days open; CTFS: calving to first service; FSTC: first service to conception; CR: conception rate; PR: pregnancy rate; NSPC: number of inseminations per conception

²r_g: Genetic correlation; r_e: environmental correlation; SE: standard error

Discussion

In this study, several important indices of reproductive performance in Sistani cattle were analyzed. The model  consisting of the additive, sire, and permanent environment parameters (i.e., model 4) was the most appropriate model for CI, FSTC, CR, and NSPC, indicating that sire and environment effects should be considered together in the model for accurate estimation of the genetic parameters. On the other hand, model 3 was the most suitable model for other traits so that including sire effect in the additive effect as random effect produced unbiased estimation. In reported studies, comparisons of model had not been done for estimation of genetic parameters of reproductive traits and most studies used model 1 (additive and residual) or model 2 (additive, permanent environmental and residual). The model 1 was used for CI (Van der Westhuizen et al., 2001; Gutiérrez et al., 2002; Bernardes et al., 2015; Do Amaral Grossi et al., 2016; Martínez et al., 2016), PR (Bormann et al., 2006; Johnston et al., 2014), CR (Johnston et al., 2014) and DO (González-Peña et al., 2010). Eghbalsaied (2011) used simple animal model for estimation of 13 reproductive traits in Iranian Holstein cattle. The animal model with additive and permannet environmental random effect was used for estimation of genetic parameters of the reproductive traits in UK Holstein- Friesian (Kadarmideen et al., 2000), Spanish dairy cattle (González-Recio and Alenda, 2005), Chinese Holstein (Guo et al., 2014), Holstein and Jersey (Zambrano and Echeverri, 2014), Brahman cattle (Cavani et al., 2015), Mexician Brown Swiss (Colli et al., 2015), Nellore cattle (Ulhôa Magnabosco et al., 2016), Canadian Holstein (Jamrozik and Kistemaker, 2016), and Tunisian Holstein (Zaabza et al., 2016). Fitting of service sire effect in the model as random effect was reported for CTFS traits (Andersen-Ranberg et al., 2005) and GL (Jamrozik and Kistemaker, 2016). In this study, three models as well as combination of three models (model 4) were compared and the best model was selected for each trait.

The very low heritability for CI (0.032, Table 2) is in agreement with other reports (Olori et al., 2002; Berry et al., 2013; Berry and Evans, 2014; Colli et al., 2015, Cavani et al., 2015). The reported heritability of CI in beef and dairy cattle ranged from 0.04 to 0.39 (Roughsedge et al., 2005; Veselá et al., 2013; Bernardes et al., 2015; Do Amaral Grossi et al., 2016; Martínez et al., 2016). Gestation length certainly varies among individual cows which is reflected in CI. The estimated heritability for GL (>0.1) in our study was close to the values reported in the Nellore cattle  (Azevêdo et al., 2006; Ulhôa Magnabosco et al., 2016) but smaller than in other studies (Crews, 2006; Mujibi and Crews, 2009; Johanson et al., 2011; Chud et al., 2014). Selection for this trait might result in genetic improvement and indirectly result in genetic gain for CI. The discrepancy between our findings and other reports could be due to differences in genetic variation among the populations, statistical models used for genetic analysis, or environmental conditions.

Days open (DO) and CI are usually influenced by the same factors because GL is a fixed interval (Jainudeen and Hafez, 2000). Estimated heritability of 0.096 for DO in the present study was close to the values in Australian beef cattle (0.11; Berry et al., 2014), Colombia Jersey (0.09; Zambrano and Echeverri, 2014) and Australian beef cattle (0.09; Goyache et al., 2005) but higher than reported range of 0.03- 0.07 in other studies (Demeke et al., 2004; Oseni et al., 2004; Goodling et al., 2005; Chang et al., 2006; Ulhôa Magnabosco et al., 2016). The reported heritability value of 0.01 to 0.136 for CTFS (Kadarmideen et al., 2000; Morris et al., 2000; Biffani et al., 2005; Guo et al., 2014; Zaabza et al., 2016) was higher than our estimate (0.002). The estimated heritability for FSTC in the present study (0.01) was higher than for Iranian Holstein (0.003; Eghbalsaied, 2011). The reported heritability of FSTC for Spanish (0.02; González-Recio and Alenda, 2005), Canadian dairy cattle (0.03- 0.055; Koeck et al., 2014; Jamrozik and Kistemaker, 2016), and Tunisian Holstein (0.024; Zaabza et al., 2016) were higher than findings in the present study.

The heritability of CR for Sistani cattle in the present study (0.084) was higher than that for Australian composite breed and Colombia Holstein (0.01 and 0.03, respectively) but smaller than that for Australian Brahman and Colombia Jersey (0.11 and 0.147, respectively) (Johnston, 2014; Zambrano and Echeverri, 2014). The heritability of PR was estimated at 0.023 that was close to (0.02) in composite cows as reported by Johnson et al. (2014), and smaller than those (0.03 to 0.33) reported in other studies (Evans et al., 1999; Bormann et al., 2006; MacNeil et al., 2006; Cushman and Perry, 2012).

The NSPC is an indirect measure of reproductive cycle showing large variations between animals. This trait requires the record of each service, which is rarely available under natural service conditions. The heritability of NSPC was estimated at 0.12. NSPC is related to FSTC and CTFS and any improvement in NSPC could indirectly influence the latter traits. The estimate of heritability value of NSPC was higher than the recorded heritabilities (0.009- 0.093) in other breeds (Kadarmideen et al., 2000; Demeke et al., 2004; Azevêdo et al., 2006; Guo et al., 2014; Koeck et al., 2014). Because of the low heritability and repeatability of the reproductive traits, their improvement through mass selection may be slow; however, it is essential because of economic value of these traits. The heritability of fertility traits in hot climates was reported to be smaller than in temperate climates (Zaabza et al., 2016). Hansen et al. (2011) also reported that the major cause of the decrease in reproductive performances was heat stress that occurred through physiological adaptations ensuring a better thermoregulatory potential. Improvement in NSPC could impact on CR due to its inverse relationship with NSPC. On the other hand, lower NSPC could decrease DO and increase PR.

Genetic correlation between reproductive traits varied from 0.001 (between CTFS and NSPC) to - 0.999 (between CI and CR). Genetic correlation between CI and other traits was very high, except for PR and GL. Residual correlations of CI with DO and CTFS were highly positive, and highly negative for CI × PR. Genetic correlation between GL and other traits was moderate (

The estimated genetic correlation of -0.23 between CI and GL in Sistani cattle was higher than 0.12 for Iranian Holstein (Eghbalsaied, 2011). The genetic correlation of 0.97 between CI and DO was within the range of values (0.58- 99) in previous reports (González-Recio and Alenda, 2005; Guo et al., 2014; Zambrano and Echeverri, 2014; Zaabza et al., 2016). Selection for fewer days open would contribute towards shorter calving intervals because the genes that act on one trait also act on the other. The recorded genetic correlation of 0.51 between CI and CTFS was close to 0.55 reported by Guo et al. (2014), higher than 0.33 found by Eghbalsaied (2011), and smaller than (range 0.67 t0 0.80) in other reports (Biffani et al., 2005; Berry et al., 2014; Zaabza et al., 2016). According to González-Recio and Alenda (2005), Berry et al. (2014) and Zaabza et al. (2016), genetic correlation between CI and FSTC was within the range of 0.79- 0.98, which is higher than our estimate (-0.59). Genetic correlation (0.25) for CI×PR in the present study was smaller than that (0.94) found by González-Recio and Alenda, (2005). The estimated genetic correlation between CI and NSPC (0.90) was close to the reported values (0.96- 1) for several cattle populations (González-Recio and Alenda, 2005; Eghbalsaied, 2011; Zambrano and Echeverri, 2014), but higher than the heritabilities in Chinese (0.49), Italian (0.61), and Tunisian (0.77) Holstein (Biffani et al., 2005; Guo et al., 2014; Zaabza et al., 2016), and in beef cattle (0.50; Berry et al., 2013).

The genetic correlations of GL×DO, GL×FSTC, GL×NSPC, GL×CTFS were estimated at -0.55, -0.53, 0.44 and -0.44, and higher than 0.02 (GL×DO), -0.19- (-0.28) (GL×FSTC), -0.22- (0.23) (GL×NSPC) and 0.14 (GL×CTFS) for Iranian (Eghbalsaied 2011) and Canadian Holstein (Jamrozik and Kistemaker, 2016) cattle. Genetic correlation between DO and CR was almost identical to the value reported by González-Recio and Alenda (2005). Genetic correlations of DO with CTFS (0.22), FSTC (0.22), PR (-0.79), NSPC (0.16) in the present study were higher than those reported in other studies (González-Recio and Alenda, 2005; Berry et al., 2014; Guo et al., 2014; Zaabza et al., 2016). The genetic correlation of CTFS×FSTC (-0.49) was in line with the values (-0.40 to -0.50) reported by others (González-Recio and Alenda, 2005; Eghbalsaied, 2011; Berry et al., 2014), whereas lower values were reported for Canadian Holstein (-0.26) and Tunisian Holstein (-0.13) (Zaabza et al., 2016; Jamrozik and Kistemaker, 2016). The estimated genetic correlations of CTFS with PR (-0.46) and NSPC (0.001) in the present study were lower than other reports (Kadarmideen et al., 2000; Biffani et al., 2005; Zaabza et al., 2016; Jamrozik and Kistemaker, 2016). However, the reported genetic correlations of FSTC×PR, FSTC×NSPC, CR×PR, CR× NSPC (González-Recio and Alenda, 2005; Eghbalsaied, 2011; Johnston et al., 2014; Zambrano and Echeverri, 2014) were higher than those recorded in the current study.

In general, differences between our results with other reports could be related to the management and climatic variations that may affect both the genetic and environmental variances, using of different methodology to estimate of variance- covariance components, size and structure of data sets and breed differences.

Conclusions

Genetic parameters for 8 reproductive traits were estimated by Gibbs sampling. The results showed that the sire effect as the second random effect should be included in analysis of all traits, and the effect of permanent environment should be used in the models for CI, FSTC, CR, and NSPC along with additive and sire effects. The estimates of heritability for all traits were smaller than 0.1, except for GL and NSPC. Strong genetic correlations were observed for CI×DO, CI×CR, CI×NSPC, DO×CR, DO×PR, and CTFS × CR suggesting that these traits have the same genetic structure with the same gene controls. Therefore, CI, CR and PR could be improved by selecting for GL, DO and NSPC. The results showed that Sistani cows had genetic variations for some reproductive traits in their natural habitat (warm and dry climate with diet shortage) and these traits may be included in their breeding programs.