bayesian method

So far, several methods have been used to identify genetic factors affecting polygenic traits. Common methods are least squares regression analysis, maximum likelihood regression analysis, and Bayesian. The superiority of Bayesian methods over other methods is that it is possible to use all SNPs in the model simultaneously.  The simultaneous presence of markers can prevent overestimation of marker effects and increase the probability of identifying true positive SNPs. Therefore, in the present study, the BayesCpi method was used to identify SNPs related to body weight at early stages of growth (i.e. body weight at week 2) in an F2 population of mixed chickens. For this purpose, the Illumina 60K SNP bead chip was used to genotype the present population, including 312 chickens from the F2 population. According to the results of the analysis, 16 SNPs with a Bayes Factor (BF) between 20 and 150 were known and suggested as markers for body weight at early age. Results of post-GWAS showed that these SNPs were distributed across 4 chromosomes and were located close to, or inside the 16 genes. Among the identified genes, 12 genes were protein-encoding and 4 were noncoding RNAs. To identify genes associated with each SNP in candidate regions, 0.5 Mb around each significant SNP was considered.

In order to evaluate cytoplasmic inheritance of growth traits (including birth weight, 3, 6, 9 and 12 month weight), the total number of 19717 Arabic sheep records which was collected by Agricultural Organization of Khuzestan province was used during1989 to 2010. Following the cytoplasmic lines from progeny to the parents, cytoplasmic primary sources were identified. Environmental factors affecting these traits were analyzed by SAS statistical software. Genetic parameters were estimated using Bayesian statistical method and MTGSAM software. Significant effect (P <0.01) on traits including lambs sex, birth type, maternal age and birth year were found. Based on the lowest acacia criteria in Bayesian statistical method, models 5, 5, 3, 4, 3 for birth weight, 3, 6, 9 and 12 months were the best models respectively. The cytoplasmic inheritance for birth weight, 3 months of age was 0.02, 0.03, and for the weights at 6, 9 and 12 months age, there was no cytoplasmic inheritance. However, the observed cytoplasmic variance for birth weight and 3 months old weight in Arab sheep were 0.004, 0.410, respectively, while no cytoplasmic variance for 6 to 12 months old was observed. Generally, although for the weight trait the share of cytoplasmic inheritance was low, but considering maternal effects and cytoplasmic heritages would result in a more accurate estimation of the genetic parameters of the growth traits of all ages.

Complete information of relationship matrix is ​​an important principle to achieve reliable results in genetic evaluations. Two kinds of pedigree errors, including incorrect pedigree information and missing pedigree information, reduce the capability of the livestock model in traditional methods. The purpose of this study was to investigate the different levels of missing pedigree information such as sire, dam and both parents (sire and dam together) on heritability, accuracy of prediction and estimation of breeding value in threshold traits.

Sex-limited traits with heritability of 0.05, 0.1, and 0.2, were simulated. In order to create threshold phenotypes of litter size, 20% of the top-phenotypes were considered as two and the rest were considered as one. Different ratios of missing sire information (zero, 5, 10, 15 and 20), missing dam information (zeros, 5 and 10) and a combination of both missing information (sire and dam together) were created. A threshold model was considered. Heritability, breeding values ​​and accuracy of prediction were calculated by Bayesian statistical method.

With the introduction of different levels of missing pedigree information to the complete pedigree, the amount of heritability decreased. The lowest values ​​of heritability were 0.018, 0.084 and 0.16 for heritability of 0.05, 0.1 and 0.2, respectively. In the complete pedigree, the lowest and highest accuracy of prediction were 0.375 (h2 =0.05) and 0.521 (h2 =0.2), respectively. The lowest values of accuracy of prediction for heritability of 0.05, 0.1, and 0.2 were 0.309 (30% in paternal pedigree defects and 10% in maternal pedigree defects), 0.353 (paternal pedigree defects 20% and maternal pedigree defects 10%), and 0.459 (5% defect in paternal pedigree and 10% defect in maternal pedigree), respectively. Furthermore, missing pedigree information led to a decrease in the average breeding value.

The results showed that, compared to the paternal or maternal missing pedigree information separately, paternal and maternal missing pedigree information together, further reduces the estimation of genetic evaluations.

The goal of genome-wide association (GWA) studies of quantitative traits is to identify genomic regions that explain a substantial proportion of the genetic variation for the trait, with the ultimate goal to identify causal mutations underlying the genetic basis of the trait. The standard GWA approach is to genotype a population that has been phenotyped for the trait(s) of interest and genotyped for many genetic markers across the genome and to analyze these data by estimating and testing the effects of marker genotypes on phenotypes using a regression-type of analysis for each single nucleotide polymorphism (SNP), one at a time. Bayesian methods such as Bayes A and Bayes B assume a heavy tail prior distribution for SNP effects and use Markov Chain Monte Carlo (MCMC) to sample from the posterior distribution. Although the objective of these methods was to predict the breeding value of selection candidates (genomic breeding values), they do that by estimating the effects of all SNPs. The estimated SNP effect, the proportion of variance explained by a SNP, or the number of times the SNP fits in the model with non–zero effect can be used as criteria to identify locations or genomic regions that affect the trait of interest. Results have shown that these Bayesian methods can effectively detect QTL in simulated and real data. Recently, a new methodology has been developed to address this limitation and allow for a better understanding of the genetic architecture of complex traits through a gene network analysis. For this purpose, to identify genomic regions and candidate genes associated with egg weight (EW), a genome-wide association study (GWAS) was performed in the present study using Affymetrix 600 K high density SNP array in 1,078 hens of 11th generation of Rhode Island Red. Data available for 1,078 pedigree-recorded hens were used to collect phenotypic EW-related data. Seven traits, including egg weight at the first laying of hens, and egg weight at 28, 36, 56, 66, 72, and 80 weeks of age were collected for each bird.  The analyses were performed using GenSel v4.73R, by fitting covariates for haplotype alleles in BayesA and BayesB models. A single Markov chain Monte Carlo (MCMC) chain of length 41,000, including burn-in of 1,000 first iterations, was computed for each analysis to obtain posterior estimates of covariate effects. These were used to obtain a direct genetic variance for animals. The primary analysis showed that correlations and regression coefficients had converged at this chain length. Annotation terms and pathway analyses were conducted using protein analysis through evolutionary relationships of PANTHER software version 10.0. The results showed that the BayesA method performed better in explaining additive genetic variance compared to BayesB method. Nine markers obtained from BayesA with the highest additive genetic variance were located on chromosomes 1, 3, 5, and 20. Genes that overlap in regions of interest were identified with the Ensembl BioMart data mining (http://www.ensembl.org/biomart/) based on the Galgal6 assembly and the Ensembl Genes 96 database. The detected SNPs were located close to 35 genes, among which, the candidate genes of BPIFB2, OCX36, CPT1A, TCF15, CECR2, SIAH3, FADS1, FADS2, and SGK1 play important functions in the egg production process through the albumen protein formation, fatty acids metabolism, and eggshell formation. It is noteworthy that the present study has detected an association in regions different from that reported by previous studies. This can be because of flock particularities, such as the extent of linkage disequilibrium, allelic frequencies, and statistical approaches. The results of the present study showed that when the genetic architecture of studied traits follows infinitesimal model assumptions, the BayesA method usually performs better than BayesB. Moreover, considering the identification of new genome regions and the key role of the mentioned genes on the development of egg weight, the efficiency of the BayesA method can be confirmed for GWAS in egg weight traits.

In structural equation modeling, it is possible to create hidden variables that cannot be directly measured by the researcher. The aim of this study was to model the structural equations of hidden genetic constructs of production, reproduction and longevity of Holstein dairy cows in Iran using breeding value of the traits that make up these constructs. Accordingly, the breeding value of the traits of the age at first calving, calving interval and the open days made up the hidden genetic construct of reproductive production; the adjusted milk, fat, and protein production traits formed the hidden genetic construct of the product and the lifetime traits in the herd and the productive lifespan constituted the hidden genetic construct of longevity. Estimation of single-trait and multi-trait animal model of genetic variance components, breeding values of each of the above traits was performed using Bayesian method conducted in GIBBS3F90 software. For this purpose, 500,000 rounds were performed and 50,000 initial samples – as burnt-in were removed from analysis. Then, using the variance-based method implemented in SMARTPLS software, 4 conceptual models of structural equation modeling (SEM) were created using the breeding value of the mentioned traits. Using the single animal model, the heritability of milk, fat and protein productions, age at first calving, calving interval, open days, lifetime in herd and production lifespan were 0.36, 0.55, 0.56, and 0.0250, 0.24, 0.07, 0.07 and 0.011, and using the multi-animal model, these values were 0.21, 0.52, 0.42, 0.48, 0.38, and 08, 0.0, 0.74 and 0.51, respectively. The estimated genetic correlation between the traits varied from -0.87 (milk production-fat production) to 0.98 (lifetime in herd and productive lifespan). The report root means square residuals (RMSR) on different SEM models fitted to breeding values of the traits that made up the various structures showed that the best fit was obtained when reproduction and production constructs had causative effect on longevity construct. This type of modeling approach has been used for the first time in the animal sciences which is rooted in social science researches. Therefore, adapting SEM modeling assumptions to the reality of animal sciences data can be a new field for breeding specialists, especially managers of production farms, because researchers in breeding sciences can ask many questions and hypotheses in the form of different constructs and create appropriate and establish a better management for the breeding farm due to the significant causal relationship between the extracted constructs.

The present study was conducted to estimate the genetic and phenotypic parameters of productive and reproductive traits of Holstein cows in Mazandaran Holstein dairy cattle. To this purpose, data 39792 records of Holstein cows collected at Mahdasht Milk and Meat Company in sari during 1986 to 2015 were used. Productive traits included corrected 305 days milk records, fat and protein production, and reproductive traits were age at first calving, calving interval, dry period and days open. Genetic parameters were estimated by THRGIBBS1F90 software under single trait animal model using Bayesian statistical method based on Gibbs sampling approach. A total of 200000 cycles were implemented among which the first, 20000 cycles were considered as burn-in period. Heritabilities obtained as 0.34, 0.68, 0.65, 0.17, 0.007, 0.07 and 0.07 for milk production, fat production, protein production, age at first calving, calving interval, dry period and days open, respectively. The genetic correlation between milk production and fat production was 0.48. Genetic correlation between milk production, fat production and protein production with age at first calving was -0.003, 0.14 and 0.39, respectively, Genetic correlation between milk and protein production with calving interval was estimated to be 0.23 and 0.55, respectively. According to the results, correlations between production and reproduction traits could be considered in breeding programs.

In this study for prediction of the (Co)-variance components and genetic and phenotypic parameters for growth traits of Moghani sheep, data from birth weight (7368 records), weaning weight (5892 records), 6-month weight (5110 records), 9-month weight (2912 records) and yearling weight (2893 records) were used.  Data was collected during 1995-2017 from Moghani sheep breeding station in Jafarabad of Moghan. (Co) variance components and genetic parameters were estimated by Bayesian statistical method based on Gibbs sampling technique, because of high accuracy of bayasian method. Environmental factors such as birth year, birth season, Sex of lamb, birth type and mother's age were significant on all traits (P<0.01 and as fixed effects in the mode. Age of lamb during weaning was used as covariate in the model. Based on lowest AIC for birth weight, weaning weight, 6-month weight, 9-month weight and yearling weight the direct heritability was found to be 0.35±0.003, 0.20±0.004, 0.23±0.002, 0.36±0.004 and 0.24±0.003 for the traits, respectively. Maternal heritability of birth weight and weaning weight were 0.26±0.002 and 0.11 ±0.002, respectively. The results revealed by increasing lamb's age and reducing lamb's dependence on mother, the contribution of maternal effects to direct genetic effects decreases. Therefore, the importance of this effect was reduced by increasing age due to decreased dependenc if lamb to mother. Low to moderate heritability of the traits indicated that selection for these traits will result in a low to moderate genetic improvement.

Accurate estimation of variance components using pedigree and genomic data plays a key role in prediction of breeding values. Since SNP markers in genomic selection are distributed across the genome, they may cover all quantitative traits loci and potentially explain all of genetic variation. In this study, genotype data from Merino sheep, genotyped by 50k Illumina SNP chip were used. Staple length and Fibre diameter traits were studied in this research. To study the association between allele frequency spectrum and captured additive genetic variance, all SNPs were partitioned in five MAF bins with the equal numbers of SNPs. Two statistical models including separate analysis for each category of MAF SNPs or joint analysis of all MAF groups were fitted. The analysis were performed using REML (parametric) and a Bayesian method implemented via Gibbs sampling and RKHS (semi-parametric) model. Using all common SNPs in REML approach, estimates of genomic heritability were 0.72 and 0.48 for Staple length and Fibre diameter, respectively. In Bayesian approach, genomic heritability for mentioned traits were 0.74 and 0.47 respectively. In the separate analysis, estimates of genomic heritability using REML and Bayesian approaches for each MAF class were similar, but in joint analysis estimates of two approaches were different. Overall, when the model is simple both approaches perform similarly while when model is complicated as joint analysis in present study, two approaches work different. Therefore, to determine which approach is more reliable, further research is required

Introduction Egg quality related traits are economically important in laying hens Egg quality is one of the important factors in the process of hatching. So, economical success of commercial and local flocks of hens depends on the quality of eggs produced. Increased egg quality results in higher marketability of the egg. Having eggs with higher quality is possible through improving nutrition, management and genetics. Understanding genetic structure of these traits with high accuracy will help us to design a desirable breeding program. Maternal effects can be caused by genetic or environmental differences between mothers or by the combination of the genetic and environmental differences. Advantages of Bayesian technique as a method of choice would be a promising method for providing high accurate genetic parameters estimations and having eggs with higher quality in next generations.
The purpose of current study was to estimate and compare variance components and heritability for egg quality traits in Khorasan Razavi native fowl using different animal models.
Materials and Methods The records for egg quality traits were collected from native fowl of Khorasan Razavi breeding center located in east north of Iran. In this experiment, 1000 eggs from 775 hens of 9th generation at the age of 28 to 29 weeks were collected and measured for internal and external traits. An electronic scale with an accuracy of 0.01 g was used to weigh the eggs (EW). The short and long lengths of each egg (SL and LL, respectively) were measured using Egg Form Coefficient Measuring Gauge. The eggs were broken using an Egg Shell Strength Tester to measure shell strength (SS). The height of yolk and albumen (YH and AH, respectively) were measured using a tripod micrometer (calibrated in mm) and a dial caliper to the nearest 0.01 mm was used to measure albumen and yolk diameters (AD and YD, respectively). Subsequently, yolk and albumen were carefully separated and yolk weight (YW) and albumen weight (AW) were measured. Shell weight (SW) was measured after 72 hours’ exposure to dry air. Shell thickness (ST) was measured with a Shell Thickness Meter (calibrated in mm) at the pointed end, equator and blunt end of shells and average values were used. These traits were evaluated by six different animal models through Bayesian method using Gibbs3f90 software. The most suitable model was determined by deviance information criterion (DIC) for each trait.
Results and Discussion The mean value of egg weight in this local breed was 49.66 gr. The mean value for specific gravity in present study was 1.089. Specific gravity is an important indicator to determine the quality of shell and the amount of shell to the other members. The mean values of shape index, shell strength, shell weight and shell thickness obtained in this study were 76.92, 4.24 kg/cm2, 5.19 g and 0.43 mm, respectively. The mean values of albumen weight, albumen height, yolk weight and yolk height were 28.11 g, 6.41 mm, 14.07 g, and 17.53 mm, respectively. For egg weight, specific gravity, egg length, shape index, yolk diameter and Haugh unit, a model consisted of maternal permanent environmental effects in addition to direct genetic effects was the most suitable. For egg width, shell strength, shell thickness, shell weight, yolk weight and yolk height, model including maternal genetic and permanent environmental effects in addition to direct genetic effects was the optimal model. For albumen index and albumen diameter, only direct genetic effects were affective. The estimates of direct heritability were from 0.08 (albumen height) to 0.28 (egg weight and shell weight) and maternal heritability ranged from 0.03(yolk index) to 0.13 (yolk height and albumen height). Observed differences in genetic and non-genetic parameters estimations determined by different models indicated that model choice is an important aspect for obtaining accurate estimates, which are going to be used when deciding on a breeding scheme. Generally, this study indicated that considering maternal effects in the models resulted in unbiased estimations of direct genetic variance and heritability for most of the studied traits.
Conclusion It can be concluded that all egg quality traits in Khorasan Razavi native fowl are influenced by maternal genetic and environmental effects. Therefore, including maternal effects in statistical models is essential for estimation of genetic parameters; the models included direct and maternal effects result in more accurate genetic parameters estimations for most of the studied traits.

This research was carried out to estimate genetic and phenotypic parameters for growth traits of Mehraban sheep. The data included the birth weight (BW، n=6645)، 3-month weight (3MW، n=3685)، 6- month weight (6MW، n= 2406) and 9-month weight (9MW، n=1684) records that were collected from 1994 to 2010 at Mehraban Sheep Breeding center under supervision of Agriculture-Jahad Organization of Hamedan. The pedigree file consisted of the information of animals from 1987 to 2010 years of birth. The effects of herd-year، season، sex، type birth and age of dam at lambing were fitted in the model as fixed effects. Due to the variation between ages at weighting of lambs this effect considered as a covariate in the model. The significant of fixed effects were determined using general linear model (GLM) procedure of SAS software. Bayesian analysis was carried out for traits، using the GIBBSS3F90 program. The most suitable model for each trait was determined based on deviance information criterion (DIC). The estimated direct heritabilites with most appropriate model were 0. 24، 0. 43، 0. 43 and 0. 23 for BW، 3MW، 6MW and 9MW traits، respectively. The estimated maternal heritabilites were 0. 04، 0. 43 and 0. 19 for BW، 3MW and 9MW، respectively. The results of this research show that a fair rate of genetic progress seems possible by selection for all traits، but negative genetic correlation was observed between direct and maternal genetic effects for all the traits، indicating antagonistic pleiotropy، which needs special care while formulating breeding plans.

Genetic parameters for litter size trait in Makuie sheep were estimated using Bayesian method and different models. For this purpose, six threshold models were fitted. Different models with direct genetic effects, maternal and permanent environmental effects were implemented. Effects after significance test (P<0.05) by logistic procedure of SAS software were included in these models (herd and year of lambing). Variance components of litter size trait were estimated by Thrgibbs1f90 software. The most appropriate model was determined based on deviance information criterion (DIC). Model 4 was recognized as the best model for the genetic analysis of litter size trait in Makuie sheep. The meanof the posterior distribution of estimated additive and maternal heritability for best model (model 4) were 0.03% (0.004) and 0.109(0.017), respectively. Estimated genetic parameters of litter size in this studyshowed that for genetic gain in this trait more attention should be paid to maternal effect and improve environmental condition.

The variance components and genetic parameters of body weight at 8 weeks of age, ageat sexual maturity, egg weight and egg number of native fowls for three provinces: Mazandaran (1991 to 2010), Isfahan (1995 to 2011) and Yazd (2001 to 2010) were estimated based on data collected by the provincial native fowls breeding centers. Genetic parameters were estimated by six different animal models with Bayesian method based on Gibbs sampling technique using GIBBS3F90 software. For the test of significance of models, the Deviance information criteria were used. Fitting of additive genetic effect without considering maternal effects resulted in overestimation of direct heritability. Results showed that considerable part of phenotypic variance was attributed to maternal additive genetic effects. Estimated heritability for average egg weight, body weight at 8 weeks old, egg number and age at sexual maturity according to the appropriate model were 0.54, 0.23, 0.15 and 0.41 for Mazandaran center and 0.31, 0.12, 0.10 and 0.28 for Esfahan center and 0.33, 0.13, 0.16 and 0.19 for Yazd center, respectively.

The present study was carried out to estimate genetic and phenotypic parameters for litter size trait in Mehrabani sheep by threshold model. Data file included the litter size of 5069 ewes which collected from 1994 to 2010 at Mehrabani sheep breeding center under supervision of Agriculture-Jahad Organization of Hamedan. The pedigree file consisted of the information of animals burned which were born from 1987 to 2010. The number of lambs per ewe were used as, repeated records. The effects of herd, year, and lambing time were fitted in the model as fixed effects. The significance of fixed effects was examined using Logistic procedure of SAS software. The analysis for trait was carried out, using the Thrgibbs1f90 program. Estimates of direct heritability, maternal heritability and repeatability were 0.039, 0.11 and 0.057, respectively. The low estimations of direct heritability, maternal heritability and repeatability were obtained in the current study for litter size trait. It indicates that selection based on the ewe’s own performance may result in slow genetic improvement.