3-Title: Bayesian Using Gibbs Sampling (BUGS) Algorithm for Life Time Traits in Sahiwal Cattle

3-Title: Bayesian Using Gibbs Sampling (BUGS) Algorithm for Life Time Traits in Sahiwal Cattle

Authors: Nistha Yadav, Sabyasachi Mukherjee, Shivam Bhardwaj, Oshin Togla, Shilpa Gujral and Anupama Mukherjee

Source: Ruminant Science (2022)-11(1):15-20.

How to cite this manuscript: Yadav Nistha, Mukherjee Sabyasachi, Bhardwaj Shivam, Togla Oshin, Gujral Shilpa and Mukherjee Anupama (2022). Effect of vaccine modality for foot and mouth disease on immunogenicity and efficacy in Hallikar calves. Ruminant Science 11(1):15-20.


Variance and covariance components for life time traits, such as life time milk yield (LTMY), productive life (PL) and herd life (HL) measured on Sahiwal cattle were estimated using a Bayesian application of the Gibbs sampler. Data came from the Livestock farm unit of ICAR-NDRI Karnal, Haryana, India for animals born between 1990 and 2019. There was 802 life time recorded data (raw) for Sahiwal cows for milk production as well as for survival in the herd. Multivariate/trivariate analysis was conducted for all three variables of life time traits by considering a mixed model which includes sire as a random effect, period and season of calving as fixed effects, age at first calving as a covariate and residual variances for the LTMY, PL and HL and the covariance between sire effects for different trait combinations. Although most of the densities of estimates were slightly skewed, they seemed to fit the normal distribution well, because the mean, mode, and median were similar. Direct heritabilities for PL in were relatively high with the marginal posterior mode of 0.51. Direct genetic correlations between all life time traits were found to be positive. Higher estimates for genetic and environmental correlations for LTMY-PL and LTMY-HL were observed. Marginal posterior estimates for heritability for LTMY, PL and HL were found as 0.13±0.018, 0.51±0.017 and 0.33±0.017 respectively along with its Monte Carlo Error for Sahiwal.


Abbas M and Sachdeva GK (2008). Effect of genetic and non-genetic factors on productive herd life and longevity in a herd of Sahiwal cows. Indian Journal of Animal Research 42(2):136-138.

Casella G and George E (1992). Explaining the Gibbs sampler. American Statistical 46:167-174.

Gelfand AE and Smith AFM (1990). Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association 85:398-409.

Gelman A and Rubin DB (1992). Inference from iterative simulation using multiple sequences. Statistical Science 7(4):457-472.

Geman S and Geman D (1984). Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images. IEEE Transactions on Pattern Analysis and Machine Intelligence 6(6):721-741.

Geweke J (1992). Evaluating the accuracy of sampling-based approaches to the calculations of posterior moments. Bayesian Statistics 4:641-649.

Geyer CJ (1992). Practical Markov chain Monte Carlo. Statistical Science 7:473-483.

Gianola D, Rodriguez-Zaz S and Shook GE (1994). The Gibbs sampler in the animal model. INRA, La Colle sur Loup 47-56.

Harvey WR (1990). Mixed model least squares and Maximum likelihood computer program.

Kriese LA, Bertrand JK and Benyshek LL (1991). Age adjustment factors, heritabilities and genetic correlations for scrotal circumference and related growth traits in Hereford and Brangus bulls. Journal of Animal Science 69:478-489.

Link WA and Eaton MJ (2012). On thinning of chains in MCMC, Methods in Ecology and Evolution 3(1):112-115.

Misztal I and Perez-Enciso M (1998). FSPAK90A Fortran 90 interface to sparse-matrix package FSPAK with dynamic memory allocation and sparse matrix structure.  Proc 6th World Cong 27:467-468.

Sewalem A and Johansson K (2000). Egg weight and reproduction traits in laying hens: Estimation of direct and maternal genetic effects using Bayesian approach via Gibbs sampling. Animal Sciences 70(1):9-16.

Singh Jaswant and Singh CV (2015). Genetic evaluation of Sahiwal cattle for lifetime production performance traits. Indian Journal of Animal Genetics and Breeding 33-34.

Sorensen D, Andersen S, Gianola D and Korsgaard I (1995). Bayesian inferences in threshold models using Gibbs sampling. Genetics Selection Evolution 27:229-249.

Sturges H (1926). The choice of a class-interval. Journal of the American Statistical Association 21:65-66.

Tiao GC and Box GE (1973). Some comments on “Bayes” estimators. American Statistician 27(1):12-14.

Tsuruta S and Misztal I (2006). THRGIBBSF90 for estimation of variance components with threshold and linear models. Proc 8th World Congress Belo Horizonte, Brazil. CD-ROM Communication 27-31.

Upadhyay A, Sadana DK, Gupta AK, Singh A and Shivahre PR (2015). Effect of genetic and phenotypic parameters on lifetime performance traits in Sahiwal cattle. Indian Veterinary Journal 92(1):58-61.

Van Tassell CP and Van Vleck LD (1996). Multiple-trait Gibbs sampler for animal models: Flexible programs for Bayesian and likelihood-based (co)variance component inference. Journal of Animal Science 74:2586-2597.

Wang CS, Rutledge JJ and Gianola D (1993). Marginal inference about variance components in a mixed linear model using Gibbs sampling. Genetics Selection Evolution 21:41-62.

Williams T and Kelley C (2004). GNUPLOT version 4.0: An Interactive Plotting Program.

Yadav B, Singh G and Wankar A (2014). Adaptive capability as indicated by redox status and endocrine responses in crossbred cattle exposed to thermal stress. Journal of Animal Research 5(1):67-73.