random regression model

In order to evaluate the effect of genotype by environment interaction on production traits of Holstein cattle of Iran, first lactation test day records of 344170, 135000 and 156840 of milk, fat and protein yield on 34417, 13500 and 15684 cows and SNP markers of 1935 genotyped bulls were used. The production data were retrieved from the Animal Breeding Center and Productions Improvement of Iran’s database which were collected from 2013 to 2018. To consider the interaction of genotype and environment, mean of temperature-humidity index (THI) in three days before each test day records as continuous environmental effect were retrieved from the 35 closest meteorological stations in the vicinity of 139 Holstein herds from 13 provinces. Variance and covariance components were estimated through a single-trait random regression model with orthogonal Legendre polynomials of second order for days in milk and THI using AIREMLF90 software. The results showed that changes in THI across lactation led tofluctuations in additive genetic variance over time. The change in heritability of milk production traits over lactation followed the same trend as additive genetic variance. The results from cross-validation analysis showed that including genomic information into the predictive model, increased prediction accuracy and including THI information increased unbiasedness. Due to the changes in milk production of daughters of bulls across days and THI , genotype by environment interaction should be considered when selecting bulls under different conditions.

The objectives of present study were to estimate the genetic and permanent environmental covariance components and genetic and phenotypic trends of test-day records of somatic cell score (SCS) of the first lactation Iranian Holstein cows. Dataset included the 108995 test day records were collected by the Animal Breeding Center of Iran from 2001 to 2010. The GLM procedure of SAS software was used for fitting the fixed effects in the statistical models of analysis. All analyses were performed using the AIREML algorithm of WOMBAT software. 16 different random regression models were studied and compared based on Akaike’s information criterion. Random regression model with Legendre polynomial functions of orders of 4, 4, 5 were chosen to fit fixed regression, additive genetic and permanent environmental effects, respectively, and residual variance was assumed in 4 heterogeneous levels during the lactation. Estimation of heritability was low (0.022 to 0.032) that indicated this trait mostly affected by environmental factors. Genetic and environmental correlations between daily SCS were high for adjacent tests and low between the beginning and the end of lactation. The estimated environmental correlations were lower than the genetic correlations in all stages of lactation. Annual genetic and phenotypic trends were -0.59±0.103 and -0.08±0.002, respectively, for SCS trait. Both genetic and phenotypic trends for SCS were significant (P

The objective of this research was to estimate the genetic parameters and trend of somatic cell count in Holstein cows of Iran using test day records. The phenotypic the used data consisted of were consisting of 407167 first lactation test day records the which were collected by the center of Animal Breeding and Livestock Production Improvement center of Iran during 2009 to 2013. Somatic cell count was transformed to Somatic cell score using logarithm transformation method. The genetic parameters were estimated using random regression models with Bayesian statistical method based on Gibbs sampling. The results revealed that the observed trend for additive genetic variance and permanent environmental were similar high in early lactation compared to other days. The heritability was estimated between 0.023-0.065 for somatic cell score. Repeatability showed highest changes at the start and the end of lactation. Additive genetic correlations were estimated for days 5 and 305. The result showed high variation in genetic trend of somatic cell score in different years, without an specific trend.

Introduction Productive traits such as milk production and fat and protein percentage have economic importance in the livestock industry. Accurate prediction of breeding value of animals is one of the best tools available for maximizing response to selection program. It is a fact that the main objective of the breeding program, is to achieve the maximum economic benefit. For breeders of dairy cattle, milk, fat, and protein are the main sources of income that are the most important traits in the firm goals. For evaluating the dairy cattle based on these traits (milk production, fat, and protein percentage), prediction of breeding values is essential. The present study was performed in order to estimate the genetic and phenotypic parameters and genetic and phenotypic trends of production traits in the Mediterranean climate of Iran (including; Ardebil, Hamadan, East and West Azerbaijan and Zanjan provinces) using 105118 records for Test Day and 30985 records for 305-day lactation records Related 8808 Herd of first lactation Holstein Cattle calving between 2003 to 2013. All records collected by Animal Breeding Center of Iran.
Materials and Methods Records were edited using Fox ¬pro 8.0 and ACCESS 2010 software and the wrong and unusual records were removed from the dataset. All analyses were performed using the RR (random regression) routine of the WOMBAT software package using AIREML algorithm on Linux operation system. Test day records were analyzed with the following random regression model (RRM): Where; Pk; kth fixed effect of province, YSl; lth fixed effect of year-season of calving, Yklimnptv; test day record i obtained at dimt of cow p calved at the nth age group in herd-test day m, HTDm; fixed effect of mth herd-test date, Cf; The fth fixed regression coefficient for calving age, agen; The nth calving age, k; The order of fit for fixed regression coefficients (k=4), βr; The rth fixed regression coefficient, ka; The order of fit for additive genetic random regression coefficients, kp; The order of fit for permanent environmental random regression coefficients, αpr; The rth random regression coefficient of additive genetic value for pth cow, γpr; The rth random regression coefficient of permanent environmental effect for pth cow, ∅r)dimt (; The rth coefficient of Legendre polynomials evaluated at days in milk t, emnptv; is The residual effect.
Results and Discussion The heritability of milk yield, fat percentage, and protein percentage during days 5 to 305 of lactation were 0.07 to 0.2, 0.019 to 0.041, and 0.019 to 0.217, respectively. The repeatability of milk yield, fat percentage, and protein percentage during this period of lactation were 0.65, 0.09, and 0.16, respectively. The study of production traits suggested that during the last 10 years in the Mediterranean climate of Iran, Genetic trend of Milk production was positive, but the genetic trend of fat and protein percentage, negative or zero. Figures 2 and 3 clearly indicate that using both types of records; test day records and 305-corrected records, genetic trend for milk production compared with fat and protein percentage was positive and increasing. Heritability of production traits in early lactation was low. The great influence of environment on animals and the negative energy balance are the reasons for the low heritability in this period (2). This amount was being increased and reaches its maximum in the second half of lactation. Increased heritability in the second half of lactation is a function of increasing additive genetic variance and sharp decline in the variance of permanent environment. Similar trends for the results of other studies were reported in the country (1, 14).
Conclusion Recent studies showed that the accuracy of test day records using random regression method was higher than 305 days lactation records. The results of random regression method and Test Day records showed that the heritability of milk production is the highest and heritability of fat percentage is. Result of this study showed that, during the last 10 years (from 2003 to 2013) in the Mediterranean climate of Iran, Genetic trend was positive in the amount of milk production, but genetic trend of fat and protein percentage, negative or near zero.

Genetic parameters were estimated for somatic cell score (SCS) in dairy cattle of Iran using test day records. The records of first lactation were extracted from the database of National Animal Breeding Center for cows calved between 2001 and 2010. Data included 222923 test-day records, obtained from 29668 animals distributed in 100 different herds. Estimates were carried out through Gibbs sampling procedures and using a random regression test-day model. Lactation curve were described in the model with orthogonal Legendre polynomials on days in milk. In order to correct for heterogeneity effect of residual variance, lactation period (5 to 365 days in milk) was classified into 10 groups with unequal distances. According to the results, residual variance was highest at the beginning and it was steady and decreased slowly from the second months to the end of lactation. Low residual and permanent environment variances and high genetic variance were lead to increase of heritability at the end of lactation. The lowest and the highest of heritability were at days 68 (0.031) and 365 (0.098), respectively. Genetic correlations between individual test-day records were high for adjacent tests and decreased as the interval between tests increased. Daily breeding values and genetic curve across lactation were produced for all animals using predicted regression coefficients. Estimation of genetic and phenotypic trends for SCS were -0.0025 and -0.1075, respectively (P<0.01). The results show a desirable improvement for somatic cell score at genetic and phenotypic levels.

The main aim of this research was comparison of random regression animal and sire models for estimation of the genetic parameters for production traits of Iranian Holstein dairy cattle. For this purpose, were used the test day records 928513, 788577 and 653317 regarding milk, fat and protein yields, respectively, belonged to first of lactation of cows collected from 2003 to2010, by the animal breeding center of Iran.Number of Cows 108873, 96511 and 79501 and number of herd 1483, 1400 and 1227 for milk, fat and protein yields, respectively. The genetic parameters were estimated using restricted maximum likelihood algorithm by random regression model with legend repolynomials. For comparison of models, -2logL, Akaike’s information criterion, Bayesian information criterion and Residual variances criteria were used. Homogeneous residual variance was assumed throughout lactation. According to that used the records of all animals in the random regression animal model, therefore is high accuracy. Additive genetic variance and permanent environmental variance was higher in end lactation and beginning lactation, respectively. Estimates of heritability milk, fat and protein yields traits for both animal and siremodels were found to be lowest during early lactation. Estimates of heritability in the randomregression animal model for milk yield, fat yield and protein yield ranged from 0.05 to 0.25, 0.04 to 0.13 and 0.07 to 0.21 and in the random regression sire model 0.08 to 0.21, 0.05 to 0.12 and 0.5 to 0.23 in the during lactation were estimated, respectively. Phenotypic variance of the considered traits during lactation was not constant for both random regression animal and sire models, it was higher at the beginning and the end of lactation. Additive genetic correlation between adjacent test days was higher than between distant test days.The random regression animal model, purposed for estimation of the genetic parameters for production traitsof Iranian Holstein dairy cattle.

In this research, a total number of 701212 (milk), 596331 (fat) and 505793 (protein) yields were used to estimate genetic parameters for persistency of lactation. The records were collected by the national animal breeding center of Karaj during 2006 and 2010. (Co) variance components were estimated using REML method and random regression models. Five persistency measures of lactation were evaluated using estimated breeding values. The estimated heritabilities of persistency for milk, fat, and protein yields ranged from 0.06 to 0.16, 0.03 to 0.17, and 0.06 to 0.20, respectively; the heritabilities for 305-d yield were 0.29, 0.28 and 0.28, respectively. Values of Spearman correlations between measures of persistency and EBVs of 305-d milk, fat, and protein yields ranged from 0.02 to 0.76, -0.24 to 0.58, and -0.50 to 0.80, respectively. Genetic correlations between persistency measures and EBVs of 305-d yield were varied; and were higher for milk and protein yields than for fat yield. For milk and protein yields, selection for EBVs of 305-d production identified sires or cows that are genetically superior in regards to persistency of lactation. But for fat yield, high breeding values for 305-d yield does not identify superior cows for yield persistency. Therefore, genetic evaluation for persistency of lactation is important for improving the milk production traits of Iranian Holstein cows and it is applicable in breeding programs for Iranian Holstein dairy cattle.

Although Wood function is of great importance to studying lactation curves because of its coefficients with biological interpretation, it has not been used under a random regression models. The objective of this study was to investigate the possibility of fitting Wood function on the test day records of dairy cows under a random regression model. Data was consisted of 743,205 test day records in first lactation of 81,192 Holstein cows from 46 herds in Iran which have been collected during 1991 to 2008. Linear form of Wood function which was a polynomial of 3 has been used. Three forms of Legendre polynomial functions with third order for additive genetic effects were also applied to evaluate the results of Wood function. Heritability estimates for daily milk yield obtained by linear form of Wood function were higher than those obtained by Legendre functions in most days indicating its advantage for genetic evaluations. Correlation between breeding values of animals predicted by linear form of Wood function and Legendre functions was 90%. In conclusion, Wood function can be employed in random regression models causing exploitation its desired characteristics and the advantages of random regression models to explain the genetic variations of dairy cows’ lactation curve.

A number of 5558 lambing records of 2245 Mehraban ewes، collected during years 1995 to 2010 were utilized to estimate the variance components and heritability for the number of lambs per lambing، making use of B-Spline random regression models. The fixed factors affecting the studied trait were identified using general linear model analysis as well as SAS software، where flock-year-season and the age of ewe at lambing (month) had significant effects. Variance components were estimated as based on linear، quadratic and linear-quadratic B-Spline random regression models with 4 to 6 knots، using WOMBATsoftware. The models were compared using AIC and BIC indices، out of which model QLL4 (quadratic for fixed regression and linear for additive genetic، as well as permanent environmental effects with 4 knots) was found out as more suitable than the others. According to this model، estimates of additive genetic، permanent environmental، and phenotypic variances of a number of lambs per lambing stood in the ranges of 0. 01 to 1. 24، 0 to 4. 09 and 0. 34 to 5. 98، respectively. Moreover، heritability estimate for the studied trait was in the ranges of 0. 02 to 0. 28. The heritability estimates for the number of lambs per lambing at 60 to 72 months of age were higher than those for the other ages.

In this research, milk yield and fat percentage records of Iranian Holstein dairy cattle were used for investigating the existence of genotype by production level interaction via multi-trait random regression model. The records of first lactation were extracted from the database of National Animal Breeding Centerfor cows calved between 2001 and 2010. Herd-years of calving were grouped in low, medium and high production levels based on milk yield and fat percentage. For milk yield, 827295 records from 98136 cows/2146 herds and for fat percentage, 713053 records from 87928 cows/2395 herds remained in the data file. (Co)variance components for milk production traits were estimated by restricted maximum likelihood (REML) method. For milk yield, rank correlations of estimated breeding values for 305-d yield between low and medium production levels and between low and high production levels were 0.77 and 0.78, respectively and for fat percentage, among all levels were higher than 0.90. Genetic correlations between low and high production levels and between low and medium production levels of milk yield in early and late lactation period were less than 0.8; but correlation between medium and high production levels of milk production and between all levels of fat percentage were high. Re-ranking of sires in different production levels led to ratings and genetic correlations lower than 0.8 implying to significant presence between genotype and environment interaction.

In this investigation 13699 data related to milk production from 2716 Holstein first calving and daughter from 167 sire cows were analyzed based on random regression model (RR/CF) and REML Method incomplete lactating (5-90 days) and (5-120 days) in correlations to complete lactating were 0.67 and 0.72, respectively with progress in complete 5-240 day was 0.91 the correlation value for lactating persistency trait for incomplete lactating period (5-150 days) were 0.68 and as increase in milk production period this value reaches to 0.91 for incomplete period (5-240 days). Also this correlation for two months milk production and lactating persistency were 0.88 and 0.59, respectively, and for one month milk production and lactating persistency reached higher than 0.90.