computer simulation

 According to the FAO in 2017, Iran, with 40 milion head of sheep and 291200 ton sheep meat, is the eighth country in the world of sheep production(http://www.fao.org/faostat/en/#data). One of the most important factors influencing accuracy of the estimated breeding value is complete sire pedigree information. Registration of father's number in sheep flocks of Iran is a big problem, through not having  any program for the control of matting program and artificial insemination. Therefore, the information of sire pedigree is not complete in sheep flocks. Incomplete pedigree causes incorrect relationship matrix and reduces accuracy of the selection and estimation of the genetic parameters of the traits and increases errors in the estimates(Clement et al., 2001). So, the existence of false and missing father’s information reduces genetic gain that this decrease in traits with low heritability have steeper slope. Imperfect sires pedigree data increase standard deviation between different repetitions of estimating variance components and cause bias estimation of genetic and phenotypic parameters(Sanders et al., 2006). Therefore, increase of unknown father's will be decreased direct and maternal heritability and breeding value, but the phenotypic variance will not be affected(Senneke et al., 2004).The estimation of heritability in complete and unbiased pedigree is similar to its actual value. But, random excluding of  50% of father’s ID led to bias estimation of heritability. If 50% of parent’s ID removed  from pedigree, the estiomation of heritability will be incorrect(Cantet et al.,2000). Generally, incomplete pedigree increases the standard error of estimations(Dong et al., 1988). Comparing random and consecutive exclusion pedigree methods (consecutive From zero to the last generation) for a trait with heritability of 0.15 showed random exclusion method leaded to a slight reduction in genetic variation, which consequently declined estimation of heritability. But for other trait with heritability of 0.30 different estimation of variance components leaded to significant decrease in estimation of heritability. In the consecutive exclusion method, the reduction of heritability was not significant with an increase  missing in pedigree of sires(Abbasi et al., 2011). Our objective in this study was investigation of influence of incomplete sire's pedigree on estimation of (co) variance components, genetic parameters and accuracy.

In this study we simulated a population with weaning weight (WW) and average daily gain(ADG) records. Heritability for weaning weight (WW) and average daily gain(ADG) were 0.15 and 0.30 respectively and genetic, environmental and phenotypic correlation for two traits were 0.5. Average of weaning weight was 22.29 kg, genetic variance was 1.7525, environmental variance was 9.759, phenotypic variance was 11.5, and heritability was 0.15. The average amount of  genetic variance,  environmental variance, and  phenotypic variance for daily weight gain were 190 g, 1078.2 , 2515.8, 3594, respectively and heritability was 0.3. The pedigree file and performance data were included of animal ID, father and mother ID, phenotypic variance, breeding value, and environmental effects for two traits. Visual Basic 6 program was used for simulation. Mating was random in both populations and the maximum maintenance age of sire and dam was 3 and 6 years, respectively. The ratio of female to male was15:1. In the generated data file, the sire numbers were eliminated asrandom and sequential with proportions 0 to 100 perecnt.The resulted data file were analyzed based on  two traits animal model. The accuracy of selection calculated from correlation between actual and predicted breeding values.

The simulation of data file consist of 20625 head of sheep and base population was 2075 head in this study. Data file included animal ID, sire ID, dam ID, phenotypic value for weaning weight and daily weight gain. Random 10% deletion  of father’s ID increaed unknown fathers from 2750 to 4490 ,while unknown fathers for random 80% deletion  was  equal to 16973. In random and consecutive deletion method, phenotypic variances for two traits were slightly constant. The variance of daily weight gain for random deletion in diferent levels was stable. But the genetic variances were decreased and the environmental variances were slightly increased. The heritabilities of two traits were significantly (P<0.05) reduced in random deletion method.  These results were almost contrary to the results of the randomization method in analysis of a trait with heritability of 0.15, in which the reduction of heritability was not significant(Abbasi et al., 2011). Standard error of heritability in final removal percentage with increase in defect of father's ID slightly increased. In randomization method, variation of variance components led to decrease estimated heritability in 0-80% exclusion of father's ID. In exclusion of father's ID estimated heritability slightly increased by 90 and 100 percent,  which were significant compared with base population (P<0.05). The reduction of genetic variances and heritabilities with increasing in deletion proportion of sire pedigree were only significant(P<0.05) for 50 to 90 percent of sire pedigree sequential deletion. The accuracy of selection were reduced from 0.767 to 0.493 and 0.933 to 0.614 for WW and ADG, respectively. Genetic correlations were reduced with increasing in missing proportion of sire number in random deletion method. But in sequential deletion method, the reductions of genetic correlations were only significant for the proportions of 60 and 80 percent in deletion of sire ID.

 Incomplete pedigree generates incorrect relationship matrix and bias in the estimation of variance components, genetic parameters of traits and the accuracy of selection. so that , the percentage of  father's ID deletion had a slight influence on phenotypic variance, phenotypic, and environmental correlation. The effect of random deletion of father’s ID on pedigree information had more influence than consecutive deletion method; then, this effect depends on the actual heritability, kind of traits, and the structure of simulated data. Generally, genetic variances, heritabilities, the accuracy of selection and genetic correlation between two traits were reduced with inceasing the proportional deletion  of sire number. The reduction of accuracy associated with genetic progress of traits; then, it is necessary to develop artificial insemination and others control mating method in order to record father's ID.

Modeling of breeding programs is useful to predict and compare the results before a strategy is implemented.
In order to compare of the genetic trend of growth traits and inbreeding in Zandi sheep with real condition, a simulation program was designed.
To design the simulating program, the R software of 2.13.0 version was used. Management parameters and average of traits in rural sheep production system for Zandi breed were used as input of the model. Economic values estimated for Zandi breed were used in selection index equations.
The results of a 15-year selection by the simulation method indicated that in the Zandi rural sheep production system, genetic improvement was positive for the traits under study. The accumulative genetic gain after 15 years for BW0, BW3, BW6 and BW9 were estimated to be 0.504, 3.008, 4.433 and 5.509 Kg respectively. The genetic trend of BW0, BW3, BW6 and BW9 were estimated to be 34.08 ±0.0007, 218.12±0.0057, 326.03 ±0.0086 and 395.20 ±0.0097 g per year respectively. The inbreeding coefficient average after 15 years was 1.411% and the aggregate genotype after 15 years of selection based on multi-traits index was 249883.7 Rls.
The genetic simulation results showed that with genetic evaluation by the convenient methods and selection intensity, it can be expected that the performance average due to genetic improvement in Iranian breeds is more changed compared with the current report is published.

In order to study the effect of incomplete sire's pedigree on genetic trend (bBv,y) and gain (R) of quantitative trait, two population were simulated with the heritability 0.15 and 0.30. For each population, information resulted from ten years of selection were saved in different files. In generated data files, the sire numbers were eliminated from pedigree file with 0, 10, 20, …, 100 percentage by two randomly and sequentially methods. The data files were analyzed using animal model. In two populations and the sire numbers deletion method, genetic trend were significantly reduced with increasing the sire number deletion proportions. Reduction of estimated genetic trends in no sire numbers data file rather than complete pedigree's and simulated base population, were 86.18% and 89.1% in population 1 and 88.42% and 90.16% in population 2 respectively. Reduction of bBv,y and R in lower deletion proportions were higher than the later one in random deletion method while were uniformly in the sequential deletion method. Annually genetic gains were significantly decreased based on growing sire missing proportions. Then, it is necessary for breeders to increase accuracy of sire numbers recording in breeding flocks.

In order to study on the effect of incomplete sire''s pedigree on the prediction of breeding value and estimation of genetic trend، two quantitative traits such as weaning weight and average daily gain with heritabilities 0. 15 and 0. 30 were simulated. Phenotypic، genetic and environmental correlations were assumed 0. 5. Resulted data files with different proportion of missed sire pedigree (0-100) were analyzed using bivariate animal model. Breeding value means for WW and ADG reduced from 1. 61 to 0. 55 and 69. 48 to 24. 68 with 10 percent random deletion of sire pedigree. This parameter was also decreased to 1. 47 and 63. 67 for WW and ADG respectively، with 10 percent sequential deletion of sire pedigree. Decreasing genetic trend of ADG were 61. 32 and 0. 66 percent for 10 percent random and sequential deletion of sire pedigree، respectively. This reduction for WW was also 63. 43 and 0 percent. Generally، the incompleteness of sire pedigree affected the accuracy of breeding value prediction and genetic trend and based on the rate of sire pedigree deletion، the part of accuracy of breeding value prediction were lost. Then، the genetic tend estimated using real data should be analyzed based on the rate of completeness of sire pedigree.