The data used in this study were collected from Kordy sheep breed research station, located in north of Khorasan province. The derivative free restricted maximum likelihood procedure was used from model 8 of DFREML 1997 univariate soft ware to evaluate the mathernal effects. Maternal heritability of traits including birth weight, sucking weight, 6, 9, and 12 months weight and preweaning, post weaning, 6-12 months weights, birth to yearling, average daily gain were evaluated as follows: 0.11, 0.05, 0.01, 0.08,0.01, 0.005, 0.0001, 0.003, respectively and directed heritability of these traits using univariate animal model were: 0.18, 0.06,0.29±0.06, 0.22, 0.31, 0.35, 0.05±0.02, 0.28±0.1,0.37±0.11, respectively. Sex effects, age of mother, birth type, year of birth, insemination method and management for all the traits were significant (P<0.05).

In this research a stochastic method was employed to simulate litter size data under the assumption that the phenotype of the trait of interest is categorically distributed with a liability of normally distributed background effect. Analysis was conducted through DFREML for phenotypic data set. For the phenotypic categorical measurements, normal distribution of liability was assumed. Also MATVEC was employed for the analysis of phenotypic data assuming a threshold model for the trait. In the simulation process, different true background heritabilities were applied in combination with different points of threshold. Results indicated that by a a departure of the points of threshold from the population mean towards the two tails of the distribution and also by increasing the true heritability, the differences become greater between estimated heritability and true heritability. When comparing heritability estimates obtained through MATVEC with those obtained using DFREML it evident that the linear model had always underestimated true heritabilities but, while threshold model of MATVEC not showing a consistent trend. While threshold model may be trusted at higher levels of true heritability, it does not behave consistently at lower heritability levels. It is possible to use estimates to obtain a confidence range for true heritability when there is enough information about approximate location of threshold and aboutestimates of heritability obtained through linear model.

This experiment was carried out based on 5913 records of Baluchi sheep from Abas Abad Animal Breeding Station in North East of Iran. The under study traits were, birth weight, three months, six months, nine months and yearling weights. Six different models of DFREML software were used. Genetic parameters were estimated by REML method with the animal model. Age of dam, sex of animal, birth type, year and month of birth was regarded as fixed factors in analysis data and traits. Number of days between birthday and time of obtaining each trait were used as a covariate for correcting the real data. The estimated heritability for birth weight, three, six, nine and twelve (yearling) months were 0.14 (0.033), 0.28 (0.045), 0.25 (0.05), 0.28 (0.052) and 0.33 (0.055) respectively. It was conduced that increasing the age of animal, direct genetic effects on weight traits also increased significantly.  

Estimation of cytoplasmic effects of Baluchi sheep breed for production traits were studied. The data used in the present study were collected from flocks at the Abbasabad sheep breeding research station in north east of Iran included 13625 animals descended from 275 sire and 3863 dam.Traits were birth weight, waning weight, 6-month weight, 12-month weight and greasy fleece weight at 18 month. Cytoplasmic origin was found by tracing the individual progeny to the earliest ancestor in the pedigree. Genetic Parameters were estimated by Derivative Free Restricted Maximum Likelihood (DFREML) using univariate animal models. For all traits cytoplasmic effects were not important. The evidence is broadly consist with 4% for BW and 2% for GFW of variation in performance due to cytoplasmic effects. However effects in genetic evaluations are likely to be small. Maternal genetic effect contribution on greasy fleece weight was very low.

In this research, a set of 1300 records belonging to 480 Holstein cows reared in dairy herd of agriculture faculty, Mashhad was used. The records were collected from 1985 to 1998 (14 years). For estimation heritability and genetic correlation animal model was fit to the data. The production traits were lactation milk yield, milk yield at peak time and average daily milk yield. The reproduction traits were gestation length, open days and calving interval. Genetic and environmental variances and covariances were estimated by DFREML software. The heritability estimates were 0.276 (SE=0.05), 0.215 (SE=0.05) and 0.311 (SE=0.06) for production traits and 0.173 (SE=0.04), 0.085 (SE=0.02) and 0.059 (SE=0.03) for reproduction traits, respectively. Average daily milk yield had positive genetic correlations with milk yield at peak time (0.13) and lactation milk yield (approximately 1) indicating that average daily milk yield could be used for genetic selection. With respect to low heritability of reproduction traits, environmental improvement could results in increasing fertility performance in the herd under consideration.

In this research 17620 records of growth traits of Moghani sheep breed collected during 1994 to 2005 in sheep breeding station of Jafar-Abad, were used to estimate the genetic and phenotypic trends. The Best Linier Unbiased Prediction (BLUP) from breeding value was estimated by Derivative Free Restricted Maximum Likelihood (DFREML) with univariate and multivariate animal model. The trends were estimated by regression of mean of estimated breeding and phenotypic values on birth year. Phenotypic trends were positive and significant (P<0.05) for birth and 3 months weights and  are negative for 6 months, 9 months and yearling weights. Genetic trends were positive and significant for all traits in both models for lamb weights at birth, 3 months, 6 months, 9 months and yearling of age being 0.0055, 0.0053, 0.0052, 0.0061 and 0.0849 kg per year in univariate analysis (P<0.01) and 0.0107, 0.0968, 0.1311, 0.1613 and 0.1328 kg per year  in multivariate analysis (P<0.01), respectively. Multivariate model offered better results in comparison with univariate models.

In this study, 5608 records of Kordi sheep body weights collected during 21 years (1990 to2010) in Sheep Breeding Station of Shirvan were used to estimate genetic, phenotypic andenvironmental trends. Best linear unbiased predictions (BLUP) of breeding values were obtained byderivative free restricted maximum likelihood (DFREML) using univariate animal model. Genetic,phenotypic and environmental trends were estimated by regression of average estimated breedingvalues, average phenotypic values and average difference between phenotypic and breeding valueson birth year, respectively. Total genetic progress in 21 years for birth weight (BW), weaningweight (WW), body weight at 6 (6W), 9 (9W) and 12 months of age (12W) were 0.017, 0.890,1.319, 0.727 and 1.199 kg, respectively. Genetic trends for BW, WW, 6W, 9W and 12W were4.4±0.5, 64±2, 73±3, 71.56±4 and 98.4±5 gr per year, respectively. The phenotypic trends for BW,WW, 6W, 9W and 12W were 16±2, 328±13, 227±18, 295±23 and 405±28 gr per year, respectively.Estimates of trends were significant for all traits (P < 0.01).

The β-lactoglobulin gene (β-LG) has been considered to be one of the most important genes involved in the milk productin related traits. In the present research, the association of β-LG polymorphism with breeding values for milk production related traits was investigated in Brown Swiss cattle. The data of this study was collected from the Golpayegan dairy farm. In this study, genomic DNA was extracted from 150 blood samples by modified salting out method. Following this stage, a fragment of 247 bp was amplified and used for enzymatic digestion. The HaeIII restriction enzyme was used to digest of 247 bp of gene. The results showed that genotypes AA, AB and BB of the β-LG gene were estimated to have frequencies of 0. 24, 0. 48 and 0. 28, respectively. These Genotypes were distributed according to the HardyWeinberg equilibrium. Genetic parameters were estimated by the restricted maximum likelihood (REML) method using DFREML program. Heritability and repeatability for milk yield traits were estimated to be 0. 154 and 0. 309, respectively. The statistical analysis based on the General Liner Models revealed that there is no significant effect for β-LG genotypes on the milk yield breeding values.

In this study 5025 records from the Lori-Bakhtiari sheep stud were used to predict phenotypic, genetic and environmental change in ewe traits from 1989 to 2004. Best linear unbiased prediction (BLUP) of breeding values was estimated by Drivative Free Restricted Maximum Likelihood (DFREML) procedure using single and multi-trait animal model. Phenotypic, genetic and environmental trends were calculated by regressing of the average phenotypic values, predicted breeding values and environmental values in the year of ewe birth respectively. The estimated phenotypic trends were –0.1223 kg for ewe body weight, -0.0415 kg for greasy fleece weight, 0.6639% for conception rate, 0.0003 for number of lambs born per ewe lambing, 0.0094 for number of lambs weaned per ewe lambing, 0.0380 kg for total birth weight per ewe exposed and 0.4227 kg for total weaning weight per ewe exposed. The estimated genetic trends were 0.0603 kg, -0.0004 kg, 0.0183%, -0.0012, -0.0007, 0.0030 kg and 0.0211 kg from single trait analysis and 0.0549 kg, -0.0006 kg, 0.0089%, -0.0008, -0.0008, 0.0030 kg and 0.0230 kg respectively from multi-trait analysis. The estimated phenotypic and environmental trends were significant but genetic trends were not significant (P<0.05) for often traits.