Genetic parameters for total lactation yields of milk,fat, protein,and somatic cell score in New Zealand dairy goats

The aim of this study was to estimate genetic parameters for lactation yields of milk (MY), fat (FY), protein (PY), and somatic cell score (SCS) of New Zealand dairy goats. The analysis used 64,604 lactation records from 23,583 does, kidding between 2004 and 2017, distributed in 21 flocks and representing 915 bucks. Estimates of genetic and residual (co) variances, heritabilities, and repeatabilities were obtained using a multiple‐trait repeatability animal model. The model included the fixed effects of contemporary group (does kidding in the same flock and year), age of the doe (in years), and as covariates, kidding day, proportion of Alpine, Nubian, Toggenburg, and “unknown” breeds (Saanen was used as the base breed), and heterosis. Random effects included additive animal genetic and doe permanent environmental effects. Estimates of heritabilities were 0.25 for MY, 0.24 for FY, 0.24 for PY, and 0.21 for SCS. The phenotypic correlations between MY, FY, and PY ranged from 0.90 to 0.96, and the genetic correlations ranged from 0.81 to 0.93. These results indicate lactation yield traits exhibit useful heritable variation and that multiple trait selection for these traits could improve milk revenue produced from successive generations of New Zealand dairy goats.     

Genetic analysis of liability to clinical mastitis, with somatic cell score and production traits using bivariate threshold–linear and linear–linear models

Inferences about genetic and residual correlation estimates and sire evaluations involving a categorical trait with linear model are ambiguous and mostly based on data simulations. In this study, estimates of variance components and prediction of breeding values in a model with a categorical and a continuous trait were compared between threshold–linear (TLM) and linear–linear models (LLM) in analysis of large clinical mastitis (CM) field data. Data on CM, somatic cell score (SCS), 305-day milk (MY), protein (PY) and fat yield (FY) from first-lactation Finnish Ayrshire cows were used. Four bivariate analyses were made using a TLM in Bayesian analysis. Each analysis fitted CM and one continuous trait at a time. Corresponding bivariate analyses were made using a Gaussian linear model. Estimates of heritabilities for CM were 0.06 and 0.02 from TLM and LLM, respectively whilst heritability estimates of the continuous traits were similar from both models. Genetic correlations between CM–SCS, CM–MY, CM–PY, and CM–FY from TLM and LLM were 0.63 and 0.63; 0.36 and 0.36; 0.32 and 0.32; 0.30 and 0.29, respectively. Estimates of residual correlations were 0.11 and 0.06; − 0.04 and − 0.02; − 0.03 and − 0.02; − 0.05 and − 0.03 between CM–SCS, CM–MY, CM–PY, and CM–FY, respectively. Comparison between the models indicates similar estimates of genetic correlations with no underestimation with the linear model analysis. In CM evaluation, the comparison of model's predictive ability showed greater improvements in accuracy with the bivariate than with the univariate models. There was, however no clear advantage of univariate threshold model over univariate linear model, except for less accuracy sires.     

A whole genome scan to map QTL for milk production traits and somatic cell score in Canadian Holstein bulls

The detection and mapping of genetic markers linked to quantitative trait loci (QTL) can be utilized to enhance genetic improvement of livestock populations. With the completion of the bovine genome sequence assembly, single nucleotide polymorphisms (SNP) assays spanning the whole bovine genome and research work on large scale identification, validation and analysis of genotypic variation in cattle has become possible. The objective of the present study was to perform a whole genome scan to identify and map QTL affecting milk production traits and somatic cell scores using linkage disequilibrium (LD) regression and 1536 SNP markers. Three and 18 SNP were found to be associated with only milk yield (MY) at a genome and chromosome wise significance (p < 0.05) level respectively. Among the 21 significant SNP, 16 were in a region reported to have QTL for MY in other dairy cattle populations and while the rest five were new QTL finding. Four SNP out of 21 are significant for the milk production traits (MY, fat yield, protein yield (PY), and milk contents) in the present study. Six and nine SNP were associated with PY at a genome and chromosome wise significant (p < 0.05) level respectively. Three and 17 SNP were found to be associated with FY at a genome and chromosome wise significant (p < 0.05) level. Five and seven SNP were mapped with somatic cell score at a genome and chromosome wise significant (p < 0.05) level respectively. The results of this study have revealed QTL for MY, PY, protein percentage, FY, fat percentage, somatic cell score and persistency of milk in the Canadian dairy cattle population. The chromosome regions identified in this study should be further investigated to potentially identify the causative mutations underlying the QTL.     

Growth, slaughter performance and feeding behaviour of young bulls belonging to three native cattle breeds raised in the Alps

Most studies on lactation curves only consider milk yield and describe a standard lactation curve of dairy cows, showing a peak or maximum daily yield occurring between 4 and 8 weeks after calving, followed by a daily decrease in milk yield until the cow is dried off. Wood's model is a widely used lactation curve function. Wood's model was fitted to test-day records of 95,405 lactations of parities lower than 5. Milk traits were milk yield (MY), fat percentage (F%), protein percentage (P%), fat yield (FY) and protein yield (PY), and the lactation curve was individually considered as a cluster of five linked curves. Milk trait and parity influence the goodness of fit of Wood's model. In 19.3% of the lactations, the shape of the MY, FY and PY curves follows the standard lactation curve while F% and P% have the reversed standard shape. The initial phase of lactation with the FY and PY curves contributes to the high variability of shapes.     

Genetic associations between milk fat‐to‐protein ratio,milk production and fertility in the first two lactations of Thai Holsteins dairy cattle

The aims of this study were to estimate, simultaneously, the genetic parameters of test‐day milk fat‐to‐protein ratio (FPR), test‐day milk yield (MY), and days‐open (DO) in the first two lactations of Thai Holsteins. A total of 76 194 test‐day production records collected from 8874 cows with 8674 DO records between 2001 and 2011 from different lactations were treated as separated traits. The estimates of heritability for test‐day FPR in the first lactation showed an increasing trend, whereas the estimates in the second lactation showed a U‐shape trend. Genetic correlations for FPR‐DO and MY‐DO showed a decreasing trend along days in milk (DIM) in both lactations, whereas genetic correlations for FPR‐MY increased along DIM in the first lactation but decreased in the second lactation. Genetic correlations of FPR between consecutive DIM were moderate to high, which showed the effectiveness of simultaneous analyses. Selection of FPR in the early stage has no adverse effect on MY and DO for the first lactation but has a negative effect on MY and positive effect on DO for the second lactation. This study showed that genetic improvement of the energy balance using FPR, MY and DO with multi‐trait test day model could be applied in a Thailand dairy cattle breeding program.     

Autoregressive and random regression test-day models for multiple lactations in genetic evaluation of Brazilian Holstein cattle

Autoregressive (AR) and random regression (RR) models were fitted to test-day records from the first three lactations of Brazilian Holstein cattle with the objective of comparing their efficiency for national genetic evaluations. The data comprised 4,142,740 records of milk yield (MY) and somatic cell score (SCS) from 274,335 cows belonging to 2,322 herds. Although heritabilities were similar between models and traits, additive genetic variance estimates using AR were 7.0 (MY) and 22.2% (SCS) higher than those obtained from RR model. On the other hand, residual variances were lower in both traits when estimated through AR model. The rank correlation between EBV obtained from AR and RR models was 0.96 and 0.94 (MY) and 0.97 and 0.95 (SCS), respectively, for bulls (with 10 or more daughters) and cows. Estimated annual genetic gains for bulls (cows) obtained using AR were 46.11 (49.50) kg for MY and −0.019 (−0.025) score for SCS; whereas using RR these values were 47.70 (55.56) kg and −0.022 (−0.028) score. Akaike information criterion was lower for AR in both traits. Although AR model is more parsimonious, RR model assumes genetic correlations different from the unity within and across lactations. Thus, when these correlations are relatively high, these models tend to yield to similar predictions; otherwise, they will differ more and RR model would be theoretically sounder.     

Genetic relationships of fertility traits with test‐day milk yield and fat‐to‐protein ratio in tropical smallholder dairy farms

The test‐day milk fat‐to‐protein ratio (TD‐FPR) could serve as a measure of energy balance status and might be used as a criterion to improve metabolic stability and fertility through genetic selection. Therefore, genetic parameters for fertility traits, test‐day milk yield (TD‐MY) and TD‐FPR, as well as, their relationships during different stages of lactation, were estimated on data collected from 25 968 primiparous Thai dairy crossbred cows. Gibbs sampling algorithms were implemented to obtain (co)variance components using both univariate linear and threshold animal models and bivariate linear‐linear and linear‐threshold animal models with random regression. Average TD‐MY and TD‐FPR were 12.60 and 1.15. Heritability estimates for TD‐MY, TD‐FPR and selected fertility traits ranged from 0.31 to 0.58, 0.17 to 0.19 and 0.02 to 0.05, respectively. Genetic correlations among TD‐FPR and TD‐MY, TD‐FPR and fertility traits, and TD‐MY and fertility traits ranged from 0.05 to ‐0.44, from ‐0.98 to 0.98 and ‐0.22 to 0.79, respectively. Selection for lower TD‐FPR would decrease numbers of inseminations per conception and increase conception at first service and pregnancy within 90 days. In addition, cow selection based only on high milk production has strong effects to prolong days to first service, days open and calving interval.     

Modeling lactation curves and estimation of genetic parameters in Holstein cows using multiple‐trait random regression models

We compared the goodness of fit of three mathematical functions (including: Legendre polynomials, Lidauer‐Mäntysaari function and Wilmink function) for describing the lactation curve of primiparous Iranian Holstein cows by using multiple‐trait random regression models (MT‐RRM). Lactational submodels provided the largest daily additive genetic (AG) and permanent environmental (PE) variance estimates at the end and at the onset of lactation, respectively, as well as low genetic correlations between peripheral test‐day records. For all models, heritability estimates were highest at the end of lactation (245 to 305 days) and ranged from 0.05 to 0.26, 0.03 to 0.12 and 0.04 to 0.24 for milk, fat and protein yields, respectively. Generally, the genetic correlations between traits depend on how far apart they are or whether they are on the same day in any two traits. On average, genetic correlations between milk and fat were the lowest and those between fat and protein were intermediate, while those between milk and protein were the highest. Results from all criteria (Akaike's and Schwarz's Bayesian information criterion, and ?2*logarithm of the likelihood function) suggested that a model with 2 and 5 coefficients of Legendre polynomials for AG and PE effects, respectively, was the most adequate for fitting the data.     

Effects of Acyl-CoA:diacylglycerol acyl transferase 1 (DGAT1) gene on milk production traits in crossbred Holstein dairy cattle

The objective of this study was to analyze and investigate the genotype frequency and the association between Acyl-CoA:diacylglycerol acyltransferase1 gene, DGAT1 gene, and milk yield (MY), milk composition, protein yield (PY), fat yield (FY), solid not fat yield (SNF), total solid (TS), the content of fat, protein, solid not fat, and total solid, (%Fat,%Prot,%SNF,%TS) in two herds of crossbred Holstein dairy cattle in Thailand. Two hundred and twenty-seven crossbred Holstein cows were used and their blood samples were taken for the study. PCR–RFLP was used to identify the allele and genotype of DGAT1 gene. A general linear model and the least square method were used to estimate the least square mean and additive, and the dominant effect of the gene on the traits and the least significant differences were used to compare the mean of each trait between genotypes. Two alleles (K, A) and three genotypes (AA, KA, KK) were detected, the highest allele and genotype frequencies were A and AA, respectively. The least mean squares of each genotype were compared and significant differences between genotype were detected. Genotype KK has the greatest effect on all milk composition content traits, while genotype AA has the greatest effect on yield traits. Highly significant additive gene effect was detected. From the results, it can be concluded that the DGAT1 gene can be used as a gene marker for assisted selection in milk composition traits.     

Genetic association between milk yield,stayability, and mastitis in Holstein cows under tropical conditions

The objective of this study was to estimate genetic parameters for milk yield, stayability, and the occurrence of clinical mastitis in Holstein cows, as well as studying the genetic relationship between them, in order to provide subsidies for the genetic evaluation of these traits. Records from 5,090 Holstein cows with calving varying from 1991 to 2010, were used in the analysis. Two standard multivariate analyses were carried out, one containing the trait of accumulated 305-day milk yields in the first lactation (MY1), stayability (STAY) until the third lactation, and clinical mastitis (CM), as well as the other traits, considering accumulated 305-day milk yields (Y305), STAY, and CM, including the first three lactations as repeated measures for Y305 and CM. The covariance components were obtained by a Bayesian approach. The heritability estimates obtained by multivariate analysis with MY1 were 0.19, 0.28, and 0.13 for MY1, STAY, and CM, respectively, whereas using the multivariate analysis with the Y305, the estimates were 0.19, 0.31, and 0.14, respectively. The genetic correlations between MY1 and STAY, MY1 and CM, and STAY and CM, respectively, were 0.38, 0.12, and ?0.49. The genetic correlations between Y305 and STAY, Y305 and CM, and STAY and CM, respectively, were 0.66, ?0.25, and ?0.52.     

Genetic trends in a Holstein × other breeds multibreed dairy population in Central Thailand

Genetic variability and genetic trends for 305-day milk yield (MY), 305-day fat yield (FY), and average 305-day fat percent (FP) were evaluated using monthly test-day records from first-lactation cows collected from 1991 to 2005 in 92 farms located in Central Thailand. Estimates of variance and covariance components and breeding values (EBV) were obtained using a multiple-trait animal model. Fixed effects were contemporary group (herd–year–season), calving age, additive genetic group as a function of Holstein fraction, and non-additive genetic group as function of heterosis effect. Random effects were animal and residual. Program ASREML was used to perform computations. Estimates of heritabilities were 0.38 ± 0.10 for MY, 0.25 ± 0.11 for FY, and 0.22 ± 0.11 for FP. Although the difference between the mean MY for cows in 1991 and 2005 was 324.1 kg, the regression of mean cow EBV for MY on year was 6.5 kg/year. Differences between mean cow EBV for FY and FP in 1991 and 2005 and their corresponding regressions of mean FY and FP on year were all near zero. Similarly, mean EBV for sires and dams of cows also showed near zero trends during these years. A factor contributing to the near complete absence of genetic trends was likely the variety of criteria used by producers to choose sires and to keep dams in addition to EBV (e.g., availability of semen, reproductive ability, adaptation to hot and humid conditions). It also appears that high percent Holstein cows failed to reach their production potential under the management, nutrition, and hot and humid climatic conditions in this tropical region. Changes in nutrition and management would be needed for high percent Holstein cows to show an upward trend in Central Thailand.     

An independent confirmation of a quantitative trait locus for milk yield and composition traits on bovine chromosome 26

Several reports have demonstrated that bovine chromosome 26 (BTA26) harbours significant or suggestive quantitative trait loci (QTL) for milk production and composition traits in dairy cattle. Our previous study showed that a C/T substitution in the bovine TCF7L2 gene on BTA26 was significantly linked to QTL for protein yield (PY) in a Canadian dairy cattle population. Actually, this polymorphism was one of the markers derived from a genome‐wide screening of QTL for milk PY using an amplified fragment length polymorphism technique combined with a DNA pooling strategy. In the present study, 990 Holstein bulls with complete genotype and phenotype data from 14 sire families were analysed to confirm, if the QTL effects exist in other populations. Statistical analysis revealed that this marker was significantly associated with PY, protein percentage, milk yield and fat yield (FY) (p < 0.001) in the US Holstein population. These results indicate that this QTL region has a pleiotrophic effect on different milk traits and is portable in different populations.     

Genetic analysis of the prevalence of abomasal displacement and its relationship to milk output characteristics in German Holstein cows

Genetic parameters for the prevalence of abomasal displacement and for milk yield traits were estimated using a data set of 3578 cows. The animals originated from 50 farms near Hanover being under the official milk recording scheme. At these farms all cases of abomasal displacement in German Holsteins were registered from July 2001 to January 2003. Using REML heritability estimates in linear animal models were h2 = 0.034 +/- 0.014, h2 = 0.017 +/- 0.013 and h2 = 0.029 +/- 0.011 for all cases of abomasal displacement, leftsided abomasal displacement and rightsided abomasal displacement, respectively. Additive genetic correlations between all cases of abomasal displacement and milk yield traits were small, ranging from rg = -0.20 (fat content) to rg = 0.08 (milk kg). However, there was a highly positive additive genetic correlation between leftsided abomasal displacement and milk yield of rg = 0.683 +/- 0.227. Leftsided abomasal displacement was correlated additive genetically to fat and protein yield, fat and protein content with rg = 0.595 +/- 0.297, r9 = 0.653 +/- 0.250, rg = -0.768 +/- 0.3280 und rg = -0.643 +/- 0.354, respectively. The additive genetic correlation to the ratio between fat and protein content was rg = -0.585 +/- 0.470. For rightsided abomasal displacement, additive genetic correlations were of similar size but with reversed signs. The estimates obtained for the residual correlations were negligibly small throughout.     

Genetic parameters of milk production traits and fatty acid contents in milk for Holstein cows in parity 1 – 3

The objective of this study was to estimate genetic parameters of milk, fat, and protein yields, fat and protein contents, somatic cell count, and 17 groups and individual milk fatty acid (FA) contents predicted by mid‐infrared spectrometry for first‐, second‐ and third‐parity Holstein cows. Edited data included records collected in the Walloon region of Belgium from 37 768 cows in parity 1, 22 566 cows in parity 2 and 8221 in parity 3. A total of 69 (23 traits for three parities) single‐trait random regression animal test‐day models were run. Approximate genetic correlations among traits were inferred from pairwise regressions among estimated breeding values of cow having observations. Heritability and genetic correlation estimates from this study reflected the origins of FA: de novo synthetized or originating from the diet and the body fat mobilization. Averaged daily heritabilities of FA contents in milk ranged between 0.18 and 0.47. Average daily genetic correlations (averaged across days in milk and parities) among groups and individual FA contents in milk ranged between 0.31 and 0.99. The genetic variability of FAs in combination with the moderate to high heritabilities indicated that FA contents in milk could be changed by genetic selection; however, desirable direction of change in these traits remains unclear and should be defined with respect to all issues of importance related to milk FA.     

Genetic relationships among direct and maternal components of milk yield and maternal weaning gain in a multibreed beef herd.

Data spanning 1980 to 1993 from a multibreed beef herd including primarily eight breeds (Angus, Charolais, Gelbvieh, Hereford, Maine-Anjou, Pinzgauer, Simmental, and Tarentaise) were used to obtain 2,207 records on 200-d weaning gain (WG) and 1,826 records on 200-d milk yield (MY), obtained by machine milking after oxytocin injection. Estimates of (co)variances for the two traits (WG and MY) were obtained with REML with breed of calf, breed of cow, and heterotic effects modeled for the two traits. Animal effects of calf (CalfWG, CalfMY) and cow (CowWG, CowMY) contributions to each trait were modeled including 2,926 animals. The permanent environmental effect of the cow was modeled for MY, with 693 levels. Estimates of breed differences were generally similar to literature estimates. Simmental, Charolais, and Maine-Anjou were highest for CalfWG, and Tarentaise, Simmental, Gelbvieh, and Maine-Anjou were highest for CowMY. Heterosis was estimated at 8.00, 2.58, 4.05, and 5.50% of the mean for CalfWG, CowWG, CalfMY, and CowMy, respectively. Variance attributable to repeated records on CowMy represented 9% of phenotypic variance. Heritabilities estimated were .22 and .24 for CalfWG and CowWG and .04 and .35 for CalfMY and CowMY. Genetic correlations estimated between CalfWG and CowWG and between CalfMY and CowMY were -.35 and -.64, respectively. A genetic correlation between CowWG and CowMY of .76 indicates that maternal weaning gain evaluations are a good predictor of a cow's potential for milk yield.     

Genetic parameters for milk fatty acids,milk yield and quality traits of a Holstein cattle population reared under tropical conditions

Information about genetic parameters is essential for selection decisions and genetic evaluation. These estimates are population specific; however, there are few studies with dairy cattle populations reared under tropical and sub‐tropical conditions. Thus, the aim was to obtain estimates of heritability and genetic correlations for milk yield and quality traits using pedigree and genomic information from a Holstein population maintained in a tropical environment. Phenotypic records (n = 36 457) of 4203 cows as well as the genotypes for 57 368 single nucleotide polymorphisms from 755 of these cows were used. Covariance components were estimated using the restricted maximum likelihood method under a mixed animal model, considering a pedigree‐based relationship matrix or a combined pedigree‐genomic matrix. High heritabilities (around 0.30) were estimated for lactose and protein content in milk whereas moderate values (between 0.19 and 0.26) were obtained for percentages of fat, saturated fatty acids and palmitic acid in milk. Genetic correlations ranging from −0.38 to −0.13 were determined between milk yield and composition traits. The smaller estimates compared to other similar studies can be due to poor environmental conditions, which may reduce genetic variability. These results highlight the importance in using genetic parameters estimated in the population under evaluation for selection decisions.     

Estimation of Variances and Covariances of Milk Traits by REML with an Individual Animal Model

Abstract

Records form Finnish Ayrshire cattle were used to estimate variances and covariances of milk traits by the restricted maximum likelihood (REML) method using the individual animal model (IAM). Two data sets were analyzed. The first data set consisted of 1423 sires and 16363 cows, of which 11911 had records on first lactation. The heritabilities estimated from this data set for milk yield, protein yield, protein content and fat content were 0.40, 0.31, 0.63 and 0.68, respectively. The second data set was a subset of first data set with herds with less than ten observations excluded and consisted of 1335 sires and 11262 cows with 8140 first, 5688 second and 3717 third lactation records. The heritability estimates from the second data set under a repeatability model for milk yield, protein yield, protein content and fat content were 0.30, 0.26, 0.59 and 0.66, respectively. The repeatability estimates for the same traits were 0.53, 0.51, 0.67 and 0.76, respectively. The second data set was also used to estimate genetic and phenotypic correlations among milk traits in first lactation. Both genetic and phenotypic correlations among protein yield and protein and fat content traits were small. The genetic correlation between milk yield and protein content was -0.61, between milk yield and fat content -0.50 and between protein content and fat content 0.67. Absolute values of phenotypic correlations for the same pairs of traits were somewhat smaller than respective genetic correlations.     

Estimation of genetic parameters for milk and fertility traits within and between low,medium and high dairy production systems in Kenya to account for genotype-by-environment interaction

Dairy records from the Dairy Recording Service of Kenya were classified into low, medium and high production systems based on mean 305-day milk yield using the K-means clustering method. Milk and fertility records were then analysed to develop genetic evaluation systems accounting for genotype-by-environment interaction between the production systems. Data comprised 26,638 lactation yield, 3,505 fat yield, 9,235 age at first calving and 17,870 calving interval records from 12,631 cows which were descendants of 2,554 sires and 8,433 dams. An animal model was used to estimate variance components, genetic correlations and breeding values for the production systems. Variance components increased with production means, apart from genetic group variances, which decreased from the low to the high production system. Moderate heritabilities were estimated for milk traits (0.21–0.27) and fat traits (0.11–0.38). Low heritabilities were estimated for lactation length (0.04–0.10) and calving interval (0.03–0.06). Moderate heritabilities (0.25–0.26) were estimated for age at first calving, except under the high production system (0.05). Within production systems, lactation milk yield, 305-day milk yield and lactation length had high positive genetic correlations (0.52–0.96), while lactation milk yield and lactation length with age at first calving had negative genetic correlations. Milk yield and calving interval were positively correlated except under the low production system. The genetic correlations for lactation milk yield and 305-day milk yield between low and medium (0.48 ± 0.20 and 0.46 ± 0.21) and low and high production systems’ (0.74 ± 0.15 and 0.62 ± 0.17) were significantly lower than one. Milk yield in the low production system is, therefore, a genetically different trait. The low genetic correlations between the three production systems for most milk production and fertility traits suggested that sires should be selected based on progeny performance in the targeted production system.     

Genetic and phenotypic parameters of milk yield, milk composition and age at first kidding in Saanen goats from Mexico

A total of 4007 lactation records from 1520 Saanen goats kidding from 1999 to 2006 and obtained from 10 herds in Guanajuato, Mexico, were analyzed to estimate the heritabilities, repeatabilities, as well as genetic, environmental and phenotypic correlations for milk yield (MILK), fat yield (FAT), protein yield (PROT), fat content (%FAT), protein content (%PROT) and age at fist kidding (AFK). A five-trait repeatability model was used to estimate (co)variances for milk traits, and a four-trait animal model for first lactation records was used to estimate (co)variances involving AFK. For MILK, FAT, PROT, %FAT, %PROT and AFK, heritability estimates were 0.17 ± 0.04, 0.19 ± 0.05, 0.17 ± 0.04, 0.32 ± 0.06, 0.38 ± 0.07 and 0.31 ± 0.09, respectively. Repeatabilities for MILK, FAT, PROT, %FAT and %PROT were 0.43 ± 0.02, 0.42 ± 0.02, 0.42 ±0.02, 0.64 ± 0.02, and 0.63 ± 0.02, respectively. The genetic correlations between MILK and FAT, and between MILK and PROT, were high and positive (0.72 ± 0.08 and 0.87 ± 0.04, respectively). Genetic correlations between MILK and %FAT, between MILK and %PROT and between MILK and AFK, were − 0.24 ± 0.16, − 0.30 ± 0.15 and − 0.18 ± 0.23, respectively. Genetic correlations between AFK and FAT and between AFK and PROT were − 0.09 ± 0.24 and − 0.17 ± 0.25, respectively; and genetic correlations between AFK and %FAT and between AFK and %PROT were 0.29 ± 0.35 and 0.14 ± 0.27, respectively. Selection for milk traits is possible using a repeatability animal model. Selection for milk production traits would probably not increase AFK, but more precise estimates of the genetic correlations are required. Selection to lower AFK is possible. These (co)variance estimates would make it possible to predict the selection responses from different economic indices in order to maximize the economic responses for the local markets.     

Random regression models to estimate genetic parameters for test‐day milk yield in Brazilian Murrah buffaloes

The objective of this work was to estimate covariance functions for additive genetic and permanent environmental effects and, subsequently, to obtain genetic parameters for buffalo’s test‐day milk production using random regression models on Legendre polynomials (LPs). A total of 17 935 test‐day milk yield (TDMY) from 1433 first lactations of Murrah buffaloes, calving from 1985 to 2005 and belonging to 12 herds located in São Paulo state, Brazil, were analysed. Contemporary groups (CGs) were defined by herd, year and month of milk test. Residual variances were modelled through variance functions, from second to fourth order and also by a step function with 1, 4, 6, 22 and 42 classes. The model of analyses included the fixed effect of CGs, number of milking, age of cow at calving as a covariable (linear and quadratic) and the mean trend of the population. As random effects were included the additive genetic and permanent environmental effects. The additive genetic and permanent environmental random effects were modelled by LP of days in milk from quadratic to seventh degree polynomial functions. The model with additive genetic and animal permanent environmental effects adjusted by quintic and sixth order LP, respectively, and residual variance modelled through a step function with six classes was the most adequate model to describe the covariance structure of the data. Heritability estimates decreased from 0.44 (first week) to 0.18 (fourth week). Unexpected negative genetic correlation estimates were obtained between TDMY records at first weeks with records from middle to the end of lactation, being the values varied from ?0.07 (second with eighth week) to ?0.34 (1st with 42nd week). TDMY heritability estimates were moderate in the course of the lactation, suggesting that this trait could be applied as selection criteria in milking buffaloes.