random regression

This study aimed to estimate the genetic parameters of body weight traits in Markhoz goats, using B-spline random regression models. The data used in this study included 19549 records collected during 29 years (1992-2021) in Markhoz goat Breeding Research Station, located in Sanandaj, Iran. The model used to analyze data included fixed effects (year of birth, sex, type of birth and age of dam) and random effects including direct additive genetic, maternal additive genetic, permanent environmental and maternal permanent environmental assuming homogeneous and heterogeneous residual variance during the time. Akaike (BIC) and Bayesian (BIC) information criteria were used to compare the models and bspq.4.4.4.4 was selected as the best model. The direct heritability values for birth, 3-month, 6-month, 9-month and 12-month weights were estimated to be 0.14, 0.16, 0.08, 0.28 and 0.26, respectively. Genetic correlation between body weights at birth and 3-month, birth and 6-month, birth and 9-month, birth and 12-month, 3-month and 6-month, 3-month and 9-month, 3-month and 12-month, 6-months and 9-month and 9-month and 12-month were 0.22, 0.38, 0.21, 0.56, -0.26, 0.30, 0.62, 0.86 and 0.77, respectively. The highest phenotypic correlation was between the weight of 9-month and 12-month (0.82) and the lowest correlation was between birth weight and 3-month and 6-month (0.12). The results showed that the 9-month weight is a good criterion for selection in Markhoz goats.

The aim of this research was to estimate (co) variance components, heritability, genetic and phenotypic correlations between different stages of lactation for milk fat to protein ratio (FPR) of Holstein dairy cattle in Iran using a random regression model. The data used included 1302984 test day records of 149440 cows in 307 herds that were calved during the years of 1996 to 2017. Contemporary groups herd-month of recording (herd test day (HTD)), the age at the calving and lactation curve were considered as fixed effects in the model. Additive genetic and permanent environment effects were fitted by the Legendre’s orthogonal polynomial with forth order. The results showed that FPR had an adequate genetic variation, but due to the high environmental variations, the estimates of heritability were low in different stages of lactation and varied from 0.06 to 0.08. Genetic correlations of FPR in different stages of lactation were in the rage of 0.24 to 0.99. The genetic correlations between first and second stage was high (0.84); but its decreased dramatically with other stages and ranged from 0.24 to 0.52. However, the genetic correlation between the other lactation stages was gradual decreased with increasing the interval between them. The phenotypic correlations between lactation stages were lower than the genetic correlation and were observed in the range of 0.02-0.25. Genetic improvement is possible for FPR because of genetic variation; however, more daughters are needed for each sire to achieve appropriate accuracy of breeding values due to low heritability.

Estimates of the amount of milk produced by lactating ewes provide information for the implementation of optimum management and feeding strategies for ewes and their lambs. Lamb survival and subsequent birth weight gains until weaning reflect milk production abilities of ewes. Genetic evaluation of milk yield traits in dairy sheep may be based on whole lactation records (Rahman Ahmad, 2010) or test day records (Horstick et al. 2001; Komprej et al. 2009; Carlos 2014). The random regression method of data analysis seems to be the most appropriated technique to apply in longitudinal data including growth and milk production and the corresponding models have been incorporated in animal breeding for the estimation of breeding values (Schaeffer, 2004). The main objective of this study was genetic analysis of test day milk records for Kurdi ewes of Shirvan Kodri sheep breeding station using fixed and random regression models. Matherial and Kordi sheep is an Iranian fat-tailed native breed developed mainly for meat production but produce milk and wool production as well. This breed is distributed in North Khorasan Province of Iran and is mainly grown traditionally by nomadic people in pastures. Kordi sheep breeding station is located in Shirvan city, North Khorasan Province, Iran. This station was established in 1988. The breeding system in this station is semi-intensive. Considering local weather conditions, lambs and ewes are usually sent to the pastures around the station for daily grazing in late April. Sheep are grazed in the pasture until early July and during the wheat and barley harvest in farm lands of the town. With the onset of the cold season the herd is transferred to the station, and by setting appropriate diets each animal group (pregnant ewes, male and female lambs and rams) is fed separately and manually three meals a day. Mating season is from mid August to late October and the lambing begins in early January and continues until late March (Saghi et al, 2014). Data included 1124 test day records of milk yields collected from 250 Kurdi ewes. Milking was carried out by hand combined with lamb suckling at 14 days intervals starting from May to August 2012. General linear model was used to identify effective fixed effects on the trait by SAS 9.1 software. Fixed effects of litter size, parity and month of recording and random effects of direct genetic and permanent environmental effects were included in the models. Variance and covariance components were estimated using restricted maximum likelihood procedure. Genetic analysis of milk yield was carried out using fixed and random regression models by Wombat software. Average milk yield of studied Kurdi ewes was 0.38 kg. Average heritability estimates of milk yield were 0.04 and 0.07 in fixed and random regression models, respectively. In random regression model, the highest and the lowest heritability estimates were found at 14 (0.18) and 84 (0.006) days, respectively. Heritability of milk yield was higher in the first than in the second part of lactation period. Repeatability of milk yield in different days of lactation was ranged from 0.51 (day 28) to 0.89 (day 126). Genetic correlations between milk yields at different days in milk were ranged from -0.942 to 0.999. Permanent environmental correlations between milk yields at different days in milk were ranged from -0.850 to 0.920. Milk yield additive genetic and permanent environmental correlations between adjacent test days were more than between distant test days. Kominakis et al. (2001) were found low heritabilities for milk yields in different days of lactation for dairy ewes (0.05 to 0.25). Komprej et al. (2013) were also reported estimated heritabilities of milk yields in different days for Slovenian dairy sheep ranged from 0.08 to 0.16. Lower genetic correlations between milk yields at different days with increase in intervals between test day records were also found by other researchers (Zavadilova et al. 2005; Madad et al. 2013). Results indicated that Kordi sheep has a relatively good potential for milk production among Iranian native sheep breeds. For milk yield in the studied population, orthogonal Legendre polynomials of order 2 and 3 for additive genetic and permanent environmental effects, respectively, was found the most appropriate model. Considering low heritability of milk yield, improvements in environmental conditions could result in increasing milk yield performance in the studied flock. Lower genetic correlations with increase in intervals between test-day records may suggest that different genes are involved in milk yield in different days of lactation.

In the quantitative genetics area, random regression model is one of the most accurate models for estimating daily breeding value in dairy cattle. However, because of the higher number records per each cow, application of this model is labor and time consuming. In addition, breeding values of cows at different days of lactation are highly correlated. The main objectives of the current study were to determine the relative importance of each breeding value at different days of lactation and to estimate the genetic principal components for the breeding values of Iranian Holstein dairy cattle for milk production traits. Maternal and methods: records of milk production traits of first-parity dairy cows. Milk yield, fat percentage and protein percentage test-day records of 73839, 65165 and 46881 cows, respectively, from 230 herds with 176390 cows in their pedigree were used in the analyses. Only test-day records belonging to 5 to 305 days of lactation were used. The data belonged to cows were born between 1988 and 2015 with age at first calving ranged between 21 to 48 m. In addition, the existence of at least one monthly record in the first 90 days after calving was essential for the cow, otherwise it would be eliminated. These data were collected by National breeding center, Karaj, Iran. Genetic parameters were estimated by a random regression model and Bayesian approach using GIBSS3F90 software. The estimated breeding values at all days of lactation were calculated and standardized using the standard score (z). Then, Correlation matrices among breeding values at different days of lactation and genetic principal components of breeding values were estimated by PROC CORR and PROC PRINCOMP of SAS software, respectively. Finally, we could calculate principal component score as a selection criterion (selection index) for the selection of dairy cattle. For this purpose, the standardized score coefficient was obtained by dividing the daily eigenvector of each principal component by square root of its eigenvalue. The principal component score were calculated of the sum of the multiply between standardized score coefficient and daily standardized breeding values for each cow. However, the principal components could be used as an index to multiple traits evaluation of animals. The genetic correlations matrix between the estimated breeding values at different days of lactation demonstrated that the breeding values at the middle stage of lactation were highly correlated with the breeding values at the reaming stages of lactation. The genetic principal component analysis revealed that the first two principal components accounted for a high percent of total genetic variance of all studied traits. For milk yield, the first principal component explained 99.48% of genetic variance, while two first components explained almost 98.19% and 100% of genetic variance for fat percent and protein percent traits, respectively. The absolute value of correlations between the first principal component of milk yield and all breeding values (except for day 56 and day 231) were more than 0.056. The absolute values of correlations between the first principal component of fat percent and the daily breeding values were greater than 0.06 for days between 83 and 222; and for protein percent were greater than 0.07 for days 99 to 168 and days 289 to 305.
Considering the high correlation between breeding values seem to, were estimated breeding values for all days is not required. The first principal component milk yield trait with nearly all estimated breeding values, high correlation and first two principal component fat percent trait of estimated breeding values in the early and middle of lactation period had a high relationship. But first two principal component protein percent trait of estimated breeding values in the middle and later of lactation period had a high correlation. Considering the high cost of recording system in dairy cattle industry and the high correlation between the breeding values, it seems that there is no need to predict the breeding value for all days of lactation. In other words, reducing the number of records per each cow may be beneficial at both economic and genetics stand points. Furthermore, due to the high, direct correlation between the principal components and daily breeding values, the implementation of principal components in the genetic merit evaluation of selection candidates for production-related traits is suggested.

Introduction Mastitis is recognized as one of the most costly diseases of the dairy industry. Somatic cell count (SCC) is a widely used indicator trait for mastitis, which in many countries is used as an indirect selection criterion for improving mastitis resistance. This is based on the positive genetic correlation between clinical mastitis (CM) and SCC. Recent estimates of the genetic correlation between mastitis and SCC range between 0.53 and 0.77 and the heritability is estimated between 0.05 and 0.31. Individual test day SCC are influenced by systematic environmental effects, such as stage of lactation, lactation number, season of calving, and season of recording. The aim of this study was to investigate factors affecting milk somatic cell score (SCC) and estimation of its heritability and correlation with the other productive traits.
Materials and Methods A total of 185688 test day records of production and pedigree from 54 herds in Khorasan Razavi State were used. To normalize SCC, log transformation of natural records were considered from cows, which had at least one calving up to 10th. Environmental effects such as herdyear of record (247 levels), stage of lactation (15 levels), lactation number (10 levels), month of recording (12 levels), year of calving (9 levels) and season of calving (4 levels), and the 1st and 2nd regression coefficient of milk production were included in the model. Heritability of SCS was estimated by animal model test-day random regression and correlations between traits were analyzed by bivariate animal model of Wombat. Fixed effects in model included herdyear of record, Holstein gene percentage, and stage of lactation as covariate, as well as additive genetic effect and common permanent environmental effects as random effects with 5-degree of Legendre.
Results and Discussion Analysis of variance revealed that all factors in models were significant (P

With development of mixed models, lactation model (LM) was replaced with random regression model (RRM). However, the minimum number of required test day (TD) records per animal to replace LM with RRM is a challenge in genetic evaluations. In this study, 381,236 test day records of 44,117 first parity dairy cattle which collected by Animal Breeding Center of Iran were used from 2006 to 2016. Based on number of TD records per animal, cows were divided into five groups by restricting cows that presented at least 2, 4, 6, 8 or 10 test day records in the lactation. The rank correlation between predicted breeding values (EBV) for LM and RRM irrespective of number of TD records was relatively moderate (0.44) and the rank correlation between two models using at least 2 TD records was 0.71. When 10 top percent of cows were used for comparison of LM with RRM, the rank correlation decreased to 0.08. The correlation of EBV of cows with ≥2 TD records with cows with ≥10 records in RRM was 0.85. The mean of breeding values accuracy in RRM was 4% higher than LM. Overall, use of RRM has advantages over LM and it is suggested to use RRM with at least 2 TD records instead of LM for genetic evaluation of milk yield trait.

In this research data of Iranian native buffaloes which were collected by the animal breeding center of Iran in 20 years from 1993 to 2013 were used. Data for first, second and third parities included 4339, 4439 and 4445 test-day records, respectively, which were distributed in 298 herds. The GLM procedure of SAS was used for determining the environmental effects affecting on milk protein percentage. The fixed effects of herd-test day, year-season and days in milk and age at calving as covariate were fitted in the model of analysis. Genetic parameters were estimated for milk protein percentage on different days in milk using single trait random regression model of the Wombat software. Heritability estimates for this trait in the first, second and third parities ranged from 0.005 to 0.14, 0.03 to 0.7 and 0.005 to 0.24, respectively. The highest heritability for milk protein percentage in the first, second and third parities were estimated in 300th, 300th and 5th days in milk as 0.14, 0.7 and 0.24, respectively. The means of genetic correlation in the first, second and third parities were estimated to be 0.09, 0.98 and 0.95, respectively. The heritability estimates of milk protein percentage were relatively high in this study. Therefore, optimal milk protein percentage can be obtained by selection in Iranian buffaloes.

In order to estimate genetic parameters of body weight trait using random regression model 19388 test day records from 6013 Moghani sheep which were collected at Moghan Research Station located in Ardebil province, Iran, during 1995 to 2009 were used. In the model, year-season, birth year-season, sex of lamb, birth type and dam parity were classified as fixed effects and age of dam at parturition and age of animal were as covariates. Random effects of model were direct additive genetic effect, maternal additive genetic effect, direct permanent environmental effect and residual effect. Model 9 with 2nd order of fit for genetic effects and 4th order of fit for permanent environmental effect and 21 parameters was considered as the most appropriate model. Direct heritability estimated for weight at birth, 90, 180, 270 and 360 days were 0.069, 0.002, 0.005, 0.013 and 0.021, respectively. Results showed that direct heritability reduced after birth and reached to the lowest amount at 90 days of age, but after that increased as the age increased. Maternal heritability had considerable reduction after birth and then increased to 360 days. Weights at 270 and 360 days had the highest correlation. Commonly genetic and phenotypic correlations reduced as the age increased.

The present study was conducted on Kurdi ewes of Hossein Abad Sheep Breeding Station of Shirvan. In order to estimate genetic parameters, 1065 test day records of milk protein percentage from 245 ewes were collected. Data collection was started from April 2012 up to the end of lactation period. For genetic analysis of data, test day models with random regression coefficient were utilized. In random regression model, parity, litter size, month of recording as fixed effects and age at recording and days in milk as covariates were included. Random regression test day model was carried out using WOMBAT software. Genetic and environmental (co)variance components of milk protein percentage were estimated using restricted maximum likelihood. Orthogonal Legendre polynomials with different orders were applied for taking into account of genetic and permanent environmental effects. Legendre polynomial with the order of 2 was the best fitting model.In this research, the average milk protein percentage in Kurdi ewes was 6.69±0.70. The lowest and highest additive genetic variances were at the beginning) 0.058) and the end (0.114) of lactation, respectively. Phenotypic and permanent environmental variances were high at the beginning and at the end of lactation. Estimates of heritability increased over the lactation. Minimum and maximum heritabilities were estimated at the beginning (0.096) and end (0.178) of lactation, respectively. The higher the distance between days of lactation, the less were the genetic and permanent environmental correlations. Generally, results indicated that Shirvan Kordi ewes had high milk protein production potential. Moreover, higher heritability for this trait at the end of lactation probably indicated higher contribution of additive genetic variation to the total variation and selection of ewes in this part of lactation would be preferred.

This research used the test day data of the milk production of Holstein cows from Golestan, Mazandaran and Guilan provinces collected by Animal Breeding Center of Iran between the years of 1988-2011. Permanent effects of model, including cattle blend, breeding year and season, also percent of Holstein gene and age during recording, were used as a secondary variable. All data obtained in this research was 92943 test day records of milk production from 12855 Holstein heifers. DFREML was applied to estimate variance components and genetic parameters in test day models (with random regression restricted maximum likelihood method). A third-order Legendre polynomial has been used in order to considering genetic and permanent environmental variations of milk production for cows lactation period. Analyzing the environmental factors made by SAS software program. Maximum estimation of genetic, phenotypic and permanent environmental correlations of milk yield was 0.99, 0.61 and 0.98, respectively The results of this research shows that the heritability of milk production are different from each other in the different months of lactation period and was achieved in the range of 0.08- 0.19, respectively.

(Co) variance components of milk, fat and protein yield of 11368 first lactation Iranian Holstein dairy cow were estimated by single trait random regression test-day models and restricted maximum likelihood (REML) method. In this study the homogeneous residual variance was assumed throughout lactation. Estimated heritability for 305-day production traits ranged from 0.25 to 0.31 and the highest genetic correlation between different days in milk was observed for protein yield. Persistency is one of the key factors determines the amount of total milk yield during a lactation period. Persistency is heritable economic trait and an important parameter of lactation curve in dairy cattle. In this research five different persistency measures were included: 1) different between estimated breeding values (EBVs) from d 290 and d 90; 2) different between EBVS from d 1 to 100 from d 101 to 200; 3) different average of EBVs from d 255 to d 305 from d 50 to d 70; 4) summation of different EBVS for d 61 to 280 from d 60; 5) summation of the EBVS from d 60 to 279 as a deviation from d 280, were used. Heritability’s as a function of time were calculated. Heritabilities estimated for persistency of protein yield (6-31 percentage) were slightly higher than this values for persistency of milk (7-28 percentage) and fat (3-25 percentage) yield, as well as genetic correlations between persistency and 305-day production were estimated slightly higher for protein and milk yield than thus for fat yield.

In this research in order to estimate genetic parameters for milk yield at different milking times for Holstein cows of Razavi Khorasan، a total of 180،462 monthly test day records belonging to first lactation cows calved from 2000 to 2009 were utilized. The records were analysed by a random regression test day model. In the model، the fixed effects of contemporary group of geographical location – herd – year of recording – production season – sperm type، linear covariables of Holstein gene percentage، age at recording، as well as additive genetic and permanent random effects were included. For morning (M1) and night (M3) milking times، maximum additive genetic variances were found in month eight (0. 808 and 0. 659، respectively) while the minimum value (0. 399 and 0. 319، respectively) was found for both milking times in month two of the lactation curve. Maximum and minimum additive genetic variances for noon (M2) milking times were observed in months ten (0. 732) and two (0. 278)، respectively. Permanent and residual variance components were the greatest values at the end of the lactation course. Maximum heritability estimates of M1، M2 and M3 were found to be 0. 143 (month eight)، 0. 137 (month nine) and 0. 139 (months eight and nine)، respectively. For all milking times، minimum additive genetic correlations were found between month one and month eight and ranged from 0. 216 to 0. 285، while the maximum values were observed between month six and month seven and ranged from 0. 993 to 0. 996. For all milking times، permanent environment correlations were maximum between months five and six (ranged from 0. 992 to 0. 993) and minimum between months one and ten (ranged from 0. 411 to 0. 445).

In this research a random regression test day model was used to estimate heritability values and calculation genetic correlations between test day milk records. a total of 140357 monthly test day milk records belonging to 28292 first lactation Holstein cattle (trice time a day milking) distributed in 165 herd and calved from 2001 to 2010 belonging to the herds of Tehran province were used. The fixed effects of herd-year-month of calving as contemporary group and age at calving and Holstein gene percentage as covariate were fitted. Orthogonal legendre polynomial with a 4th-order was implemented to take account of genetic and environmental aspects of milk production over the course of lactation. RRM using Legendre polynomials as base functions appears to be the most adequate to describe the covariance structure of the data. The results showed that the average of heritability for the second half of lactation period was higher than that of the first half. The heritability value for the first month was lowest (0. 117) and for the eighth month of the lactation was highest (0. 230) compared to the other months of lactation. Because of genetic variation was increased gradually، and residual variance was high in the first months of lactation، heritabilities were different over the course of lactation. The RRMs with a higher number of parameters were more useful to describe the genetic variation of test-day milk yield throughout the lactation. In this research estimation of genetic parameters، and calculation genetic correlations were implemented by random regression test day model، therefore using this method is the exact way to take account of parameters rather than the other ways.

The objective of this study was to investigate the effect of principal components (PC) of the regression coefficients (co)variance matrix on the lactation curve, and on the formation of selection index to modify the curve, based on these PC’s, and as well to estimate additive genetic and phenotypic variances and heritability of the constructed selection index. Lactation period of 301 d (5-305) was partitioned into 10 equal stages, such that the values of weighted coefficients (unrestricted selection index) were considered the same value as of the lactation stage. In contrast, the value of weighted coefficients (restricted selection index) which were calculated based on the genetic gain in each stage of lactation. The results showed that the first PC had an impact on milk production and the second PC was associated with persistency. The third PC increased (decreased) milk production in early and late (middle) lactation and the fourth PC decreased (increased) milk production in early (late) as well as middle of second (first) part of lactation curve. Because of more emphasis on persistency and decreasing genetic gain in early lactation in compared with, the value of weighted coefficients first (third) and second (fourth) PC were decreased (increased). Because of decreasing the variance of additive genetic in due to negative genetic covariance between the stages of lactation, the heritability of (0.08) decreased in comparison with (0.33) which lead to decline genetic gain.

In this research a random regression test day model was used to estimate genetic parameters and genetic trend for 305-day milk yield in Iranian Holsteins. A total of 171360 monthly test day milk records obtained from 34257 first lactation Iranian Holstein cattle (three times a day milking) distributed in 96 herds and calved from 1999 to 2008, were used. The fixed effects of province-herd- year-season of test day as contemporary group and age at calving and Holstein gene percentage as covariates were fitted in the model of analysis. Orthogonal Legendre polynomial up to order 3 was implemented to take account of genetic and environmental aspects of milk production over the course of lactation. The results showed that average of heritability estimates for the second half of lactation period was higher than that of the first half. The heritability estimate for the first month was lowest and for the eighth and ninth months of the lactation were the highest compared to the other months of lactation. The genetic correlations between monthly test day records decreased by increasing the distances between months of lactation. Linear regression of estimated breeding values on calving year was used to estimate genetic trend. Estimated genetic trends for sires and dams for milk yield were 25.13 and 15.45 kg per year, respectively. In this research, genetic trends were estimated by a random regression test day model; therefore using this method is the exact way to take account of genetic trend rather than the other ways.