Selecting the desirable method for predicting 305‐day lactation yields in Mongolia

In Mongolia, milk production must be improved both quantitatively and qualitatively, and we must find the most desirable method for predicting 305‐day milk yields for cows in Mongolia. Therefore, the predicted 305‐day milk yield from the test interval method (TIM), multiple‐trait prediction (MTP) and the random regression model (RRM) were compared. The daily milk production records during 305 days for cows calving from 1986 to 2007 from the National Livestock Breeding Center in Japan, and the test day records every month for cows calving from 1985 to 2005 from the Hokkaido Dairy Milk Recording and Testing Association were used. Wilmink's model for the average of lactation curve in MTP was adopted. A cubic Legendre polynomials and the parameters of Wilmink's function were used for RRM. The results suggested that RRM was the most desirable method for predicting 305‐day milk yields in Mongolia because estimates by RRM were the most accurate when using over four records. Further analyses will be required to examine the properties of RRM when predicting 305‐day milk yields using test day records in Mongolia.     

Genetic evaluation of heat tolerance in Holstein cows in Japan

We used test‐day records and daily records from provincial weather stations in Japan to evaluate heat tolerance (HT) in Holstein cows according to a random regression test‐day model. Data were a total of 1,641,952 test‐day records for heritability estimates and 17,245,694 test‐day records for genetic evaluation of HT by using milk yield and somatic cell score (SCS) in Holstein cows that had calved for the first time in 2000 through 2015. Temperature–humidity index (THI) values were estimated by using average daily temperature and average daily relative humidity records from 60 provincial Japanese weather stations. The model contained herd–test‐day, with lactation curves on days in milk within month–age group as a fixed effect. General additive genetic effect and HT of additive genetic effect were included as random effects. The threshold value of THI was set to 60. For milk yield, estimated mean heritabilities were lower during heat stress (THI = 78; 0.20 and 0.28) than when below the heat stress threshold (THI ≤ 60; 0.26 and 0.31). For SCS, heritability estimates (range 0.08–0.10) were similar under all heat stress conditions. Genetic trends of HT indicated that EBVs of HT are changing in an undesirable direction.     

Polynomial order selection in random regression models via penalizing adaptively the likelihood

Orthogonal Legendre polynomials ( LP ) are used to model the shape of additive genetic and permanent environmental effects in random regression models ( RRM ). Frequently, the Akaike ( AIC ) and the Bayesian ( BIC ) information criteria are employed to select LP order. However, it has been theoretically shown that neither AIC nor BIC is simultaneously optimal in terms of consistency and efficiency. Thus, the goal was to introduce a method, ‘penalizing adaptively the likelihood’ ( PAL ), as a criterion to select LP order in RRM. Four simulated data sets and real data (60 513 records, 6675 Colombian Holstein cows) were employed. Nested models were fitted to the data, and AIC, BIC and PAL were calculated for all of them. Results showed that PAL and BIC identified with probability of one the true LP order for the additive genetic and permanent environmental effects, but AIC tended to favour over parameterized models. Conversely, when the true model was unknown, PAL selected the best model with higher probability than AIC. In the latter case, BIC never favoured the best model. To summarize, PAL selected a correct model order regardless of whether the ‘true’ model was within the set of candidates.     

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.     

Selection of locations of knots for linear splines in random regression test‐day models

Using spline functions (segmented polynomials) in regression models requires the knowledge of the location of the knots. Knots are the points at which independent linear segments are connected. Optimal positions of knots for linear splines of different orders were determined in this study for different scenarios, using existing estimates of covariance functions and an optimization algorithm. The traits considered were test‐day milk, fat and protein yields, and somatic cell score (SCS) in the first three lactations of Canadian Holsteins. Two ranges of days in milk (from 5 to 305 and from 5 to 365) were taken into account. In addition, four different populations of Holstein cows, from Australia, Canada, Italy and New Zealand, were examined with respect to first lactation (305 days) milk only. The estimates of genetic and permanent environmental covariance functions were based on single‐ and multiple‐trait test‐day models, with Legendre polynomials of order 4 as random regressions. A differential evolution algorithm was applied to find the best location of knots for splines of orders 4 to 7 and the criterion for optimization was the goodness‐of‐fit of the spline covariance function. Results indicated that the optimal position of knots for linear splines differed between genetic and permanent environmental effects, as well as between traits and lactations. Different populations also exhibited different patterns of optimal knot locations. With linear splines, different positions of knots should therefore be used for different effects and traits in random regression test‐day models when analysing milk production traits.     

Computing options for multiple‐trait test‐day random regression models while accounting for heat tolerance

Data included 90 242 799 test day records from first, second and third parities of 5 402 484 Holstein cows and 9 326 754 animals in the pedigree. Additionally, daily temperature humidity indexes (THI) from 202 weather stations were available. The fixed effects included herd test day, age at calving, milking frequency and days in milk classes (DIM). Random effects were additive genetic, permanent environment and herd‐year and were fit as random regressions. Covariates included linear splines with four knots at 5, 50, 200 and 305 DIM and a function of THI. Mixed model equations were solved using an iteration on data program with a preconditioned conjugate gradient algorithm. Preconditioners used were diagonal (D), block diagonal due to traits (BT) and block diagonal due to traits and correlated effects (BTCORR). One run included BT with a ‘diagonalized’ model in which the random effects were reparameterized for diagonal (co)variance matrices among traits (BTDIAG). Memory requirements were 8.7 Gb for D, 10.4 Gb for BT and BTDIAG, and 24.3 Gb for BTCORR. Computing times (rounds) were 14 days (952) for D, 10.7 days (706) for BT, 7.7 days (494) for BTDIAG and 4.6 days (289) for BTCORR. The convergence pattern was strongly influenced by the choice of fixed effects. When sufficient memory is available, the option BTCORR is the fastest and simplest to implement; the next efficient method, BTDIAG, requires additional steps for diagonalization and back‐diagonalization.     

Direct and maternal genetic effects for preweaning growth in Retinta cattle estimated by a longitudinal approach throughout the calving trajectory of the cow

The direct and maternal genetic effects were estimated for the preweaning growth of Retinta calves with a multitrait model across parities, using a longitudinal approach with random regression models (RRM). The 120 (P120) and 180 days (P180) weights (5972 calves) were considered as different traits in each calving. The heritability of direct effect across parities was on average 0.37 for P120 and 0.58 for P180, slightly higher than the estimates by univariate (0.30 and 0.56) and bivariate models (0.30 and 0.51, respectively). The heritability for maternal effects was 0.16 for P120 and 0.26 for P180 and very similar by uni‐ (0.16 and 0.23) and multivariate model (0.16 and 0.22, respectively). The correlation between direct and maternal effects by RRM showed a pronounced antagonism ?0.64 for P120 and ?0.78 for P180), likewise uni‐ (?0.62 and ?0.72) and multivariate case (?0.64 and ?0.74, respectively). The preweaning weights should be considered as different traits across parities, because the genetic correlations were different from unity. The RRM also allowed us to estimate all the parameters throughout the calving trajectory of the cow. The use of multiple traits RRM across parities can provide very useful information for the breeding programmes.     

Genetics of milk yield and fertility traits in Holstein-Friesian cattle on large-scale Kenyan farms

Purebred Holstein-Friesian cows are the main exotic breed used for milk production on large, medium, and small farms in Kenya. A study was undertaken on seven large-scale farms to investigate the genetic trends for milk production and fertility traits between 1986 and 1997 and the genetic relationships between the traits. This involved 3,185 records from 1,614 cows, the daughters of 253 sires. There was a positive trend in breeding value for 305-d milk yield of 12.9 kg/ yr and a drop in calving interval of 0.9 d/yr over the 11-yr period. Bulls from the United States (U.S.) had an average total milk yield breeding value 230 kg higher than the mean of all bulls used; Canada (+121 kg), Holland (+15 kg), the United Kingdom (U.K., 0 kg), and Kenya (-71 kg) were the other major suppliers of bulls. Average breeding values of bulls for calving interval by country of origin were -1.31 (Canada), -1.27 (Holland), -0.83 (U.S.), -0.63 (Kenya), and 0.68 d (U.K.). The genetic parameters for 305-d milk yield were 0.29 (heritability), 0.05 (permanent environment effect as proportion of phenotypic variance) resulting in an estimated repeatability of 0.34. Using complete lactation data rather than 305-d milk yield resulted in similar estimates of the genetic parameters. However, when lactation length was used as a covariate heritability was reduced to 0.25 and the permanent environment effect proportion increased to 0.09. There was little genetic control of either lactation length (heritability, 0.09) or calving interval (heritability, 0.05); however, there were strong genetic correlations between first lactation milk yield, calving interval, and age at first calving.     

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.     

A practical longitudinal model for evaluating growth in Gelbvieh cattle

Genetic evaluation of growth in Gelbvieh beef cattle was examined by multiple-trait (MTM) and random regression (RRM) analysis. The data set comprised 541,108 animals with 1,120,086 records. Approximately 15% of the animals in the data set had at least one record measured outside of the accepted MTM age ranges for weaning weight (Wwt) and yearling weight (Ywt). Fourteen percent of Wwt records and 19% of Ywt records were measured outside the accepted ranges for MTM analysis, and thus were excluded from MTM evaluations. Two RRM evaluations were performed using cubic Legendre polynomials (RRML) and linear splines (RRMS) with three knots at 1, 205, and 365 d of age. Data Set 1 (d1) utilized all available records, whereas Data Set 2 (d2) included only records measured within MTM ranges (1 d, 160 to 250 d, and 320 to 410 d). The RRML models did not reach convergence until diagonalization was imposed. After diagonalization, it was found that all longitudinal models required fewer iterations to converge than the MTM. Correlations between the MTM, RRML-d2, and RRMS-d2 evaluations were >or=0.99 for all three traits, indicating that these models were equivalent when predicting breeding values from data within the MTM age ranges. Correlations between MTM, RRML-d1, and RRMS-d1 were >0.99 for Bwt and >0.95 for Wwt and Ywt. The lower correlations for Wwt and Ywt indicate that the added information does affect breeding value prediction. The RRM has the capability to incorporate records measured at all ages into genetic evaluations at a computing cost similar to the MTM.     

Estimation of genetic parameters for heat stress,including dominance gene effects,on milk yield in Thai Holstein dairy cattle

Heat stress in tropical regions is a major cause that strongly negatively affects to milk production in dairy cattle. Genetic selection for dairy heat tolerance is powerful technique to improve genetic performance. Therefore, the current study aimed to estimate genetic parameters and investigate the threshold point of heat stress for milk yield. Data included 52 701 test‐day milk yield records for the first parity from 6247 Thai Holstein dairy cattle, covering the period 1990 to 2007. The random regression test day model with EM‐REML was used to estimate variance components, genetic parameters and milk production loss. A decline in milk production was found when temperature and humidity index (THI) exceeded a threshold of 74, also it was associated with the high percentage of Holstein genetics. All variance component estimates increased with THI. The estimate of heritability of test‐day milk yield was 0.231. Dominance variance as a proportion to additive variance (0.035) indicated that non‐additive effects might not be of concern for milk genetics studies in Thai Holstein cattle. Correlations between genetic and permanent environmental effects, for regular conditions and due to heat stress, were ? 0.223 and ? 0.521, respectively. The heritability and genetic correlations from this study show that simultaneous selection for milk production and heat tolerance is possible.     

Genetic parameters for mastitis incidence and its indicators based on somatic cell score for Holsteins in Hokkaido,Japan

The objectives of this study were to estimate the heritability of mastitis incidence and genetic correlations between the mastitis and the somatic cell score (SCS) statistics, and to compare the practicability between different models. We used test‐day records with the mastitis incidence and SCS collected from Holstein cows calving from 1988 to 2015 in Hokkaido, Japan. As indicators of mastitis, the average SCS (avSCS), the standard deviation of SCS (sdSCS), and the maximum SCS (maxSCS) were calculated using test‐day records up to the first 305 days in milk within a lactation. We compared a four‐trait repeatability animal model (MTRP) with a four‐trait multiple‐lactation animal model (MTML). The heritability for mastitis was equal to or lower than 0.05 in all the models. Genetic correlations between lactations with MTML within the same trait were positive and close to 1. With MTRP, the estimated genetic correlations of the mastitis incidence with avSCS, sdSCS, and maxSCS were 0.66, 0.79, and 0.82, respectively. A joint evaluation with SCS statistics is expected to give an extra reliability for mastitis because of high and positive genetic correlations among the traits.     

Random regression model of growth during the first three months of age in Spanish Merino sheep

A total of 88,727 individual BW records of Spanish Merino lambs, obtained from 30,214 animals between 2 and 92 d of age, were analyzed using a random regression model (RRM). These animals were progeny of 546 rams and 15,586 ewes raised in 30 flocks, between 1992 and 2002, with a total of 45,941 animals in the pedigree. The contemporary groups (animals of the same flock, year, and season, with 452 levels), the lambing number (11 levels), the combination sex of lambs with type of litter (4 levels), and a fixed regression coefficient of age on BW were included as fixed effects. A total of 7 RRM were compared, and the best fit was obtained for a model of order 3 for the direct and maternal genetic effects and for the individual permanent environmental effect. For the maternal permanent environmental effect the best model had an order 2. The residual variance was assumed to be heterogeneous with 10 age classes; the covariance between both genetic effects was included. According to the results of the selected RRM, the heritability for both genetic effects (h(a)2 and h(m)2) increased with age, with estimates of 0.123 to 0.186 for h(a)2 and of 0.059 to 0.108 for h(m)2. The correlations between direct and genetic maternal effects were -0.619 to -0.387 during the first 45 d of age and decreased as age increased, until reaching values from -0.366 to -0.275 between 45 to 75 d of age. Important changes in ranking of the animals were found based on the breeding value estimation with the current method and with the random regression procedure. The use of RRM to analyze the genetic trajectory of growth in this population of Merino sheep is highly recommended.     

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.     

Estimation of genetic parameters for racing speed at different distances in young and adult Spanish Trotter horses using the random regression model

A total of 71 522 records (from 3154 horses) with the times per kilometre (TPK), recorded in Spanish Trotter horses (individual races) from racing performances held from 1991 to 2007, were available for this study. The TPK values for the different age groups (young and adult horses) and different distances (1600–2700 m) were considered as different traits, and a bi character random regression model (RRM) was applied to estimate the (co)variance components throughout the trajectory of age groups and distances. The following effects were considered as fixed: the combination of hippodrome‐date of race (404 levels); sex of the animals (3 levels); type of start (2 levels) and a fixed regression of Legendre polynomials (order 2). Those considered as random effects were the random regression Legendre polynomial (order 1) for animals (9201 animals in the pedigree); the individual environment permanent (3154 animals with data) and the driver (n = 957 levels). The residual variance was considered as heterogeneous with two classes (ages). The heritability estimated by distance ranged from 0.12 to 0.34, with a different trajectory for the two age groups. Within each age group, the genetic correlations between adjacent distances were high (>0.90), but decreased when the differences between them were over 400 metres for both age groups. The genetic correlations for the same distance across the age groups ranged from 0.47 to 0.78. Accordingly, the analysed trait (TPK) can be considered as positive genetic correlated but as different traits along the trajectory of distance and age. Therefore, some re‐ranking should be expected in the breeding value of the horses at different characteristics of the racing. The use of RRM is recommended because it allows us to estimate the breeding value along the whole trajectory of race competition.     

Estimation of genetic parameters for functional longevity in the South African Holstein cattle using a piecewise Weibull proportional hazards model

Non‐genetic factors influencing functional longevity and the heritability of the trait were estimated in South African Holsteins using a piecewise Weibull proportional hazards model. Data consisted of records of 161,222 of daughters of 2,051 sires calving between 1995 and 2013. The reference model included fixed time‐independent age at first calving and time‐dependent interactions involving lactation number, region, season and age of calving, within‐herd class of milk production, fat and protein content, class of annual variation in herd size and the random herd–year effect. Random sire and maternal grandsire effects were added to the model to estimate genetic parameters. The within‐lactation Weibull baseline hazards were assumed to change at 0, 270, 380 days and at drying date. Within‐herd milk production class had the largest contribution to the relative risk of culling. Relative culling risk increased with lower protein and fat per cent production classes and late age at first calving. Cows in large shrinking herds also had high relative risk of culling. The estimate of the sire genetic variance was 0.0472 ± 0.0017 giving a theoretical heritability estimate of 0.11 in the complete absence of censoring. Genetic trends indicated an overall decrease in functional longevity of 0.014 standard deviation from 1995 to 2007. There are opportunities for including the trait in the breeding objective for South African Holstein cattle.     

Surgical Repair of Mid‐body Proximal Sesamoid Bone Fractures in 25 Horses

Objective— To describe the characteristics of unilateral mid‐body proximal sesamoid bone (PSB) fractures, to determine factors associated with the outcome of horses after surgical repair, and to describe a technique for arthroscopically assisted screw fixation in lag fashion. Study Design— Retrospective case series. Animals— Horses (n=25) with unilateral mid‐body PSB fracture. Methods— Medical records (1996–2006), radiographs, and arthroscopic videos of horses with surgically repaired unilateral mid‐body PSB fractures were reviewed. Retrieved data included signalment, affected limb and PSB, fracture characteristics, and surgical technique. Outcome was established by radiographic assessment of healing and race records; categorical data were analyzed using Fisher's Exact test. Results— Medial forelimb PSBs were most commonly affected (80%). Surgical technique and degree of reduction were significantly associated with outcome; 44% of horses with screw repair and none of the horses with wire fixation raced (P=.047). Factors that may have influenced this outcome were differences in fracture reduction (improved reduction in 22% wire repairs and 88% screw repairs, P=.002) and use of external coaptation (22% wire repair and 88% lag screw repair, P=.002). None of the horses with unimproved reduction raced after surgery. Conclusions— Only 28% of horses with mid‐body PSB fractures raced after surgery. Compared with wire fixation, screw fixation in lag fashion resulted in good reduction and is seemingly a superior repair technique. Clinical Relevance— For mid‐body PSB fractures, arthroscopically assisted screw fixation in lag fashion and external coaptation for anesthesia recovery and initial support provides the best likelihood of return to athletic use.     

Test-day somatic cell score, fat-to-protein ratio and milk yield as indicator traits for sub-clinical mastitis in dairy cattle

Test-day (TD) records of milk, fat-to-protein ratio (F:P) and somatic cell score (SCS) of first-lactation Canadian Holstein cows were analysed by a three-trait finite mixture random regression model, with the purpose of revealing hidden structures in the data owing to putative, sub-clinical mastitis. Different distributions of the data were allowed in 30 intervals of days in milk (DIM), covering the lactation from 5 to 305 days. Bayesian analysis with Gibbs sampling was used for model inferences. Estimated proportion of TD records originated from cows infected with mastitis was 0.66 in DIM from 5 to 15 and averaged 0.2 in the remaining part of lactation. Data from healthy and mastitic cows exhibited markedly different distributions, with respect to both average value and the variance, across all parts of lactation. Heterogeneity of distributions for infected cows was also apparent in different DIM intervals. Cows with mastitis were characterized by smaller milk yield (down to -5 kg) and larger F:P (up to 0.13) and SCS (up to 1.3) compared with healthy contemporaries. Differences in averages between healthy and infected cows for F:P were the most profound at the beginning of lactation, when a dairy cow suffers the strongest energy deficit and is therefore more prone to mammary infection. Residual variances for data from infected cows were substantially larger than for the other mixture components. Fat-to-protein ratio had a significant genetic component, with estimates of heritability that were larger or comparable with milk yield, and was not strongly correlated with milk and SCS on both genetic and environmental scales. Daily milk, F:P and SCS are easily available from milk-recording data for most breeding schemes in dairy cattle. Fat-to-protein ratio can potentially be a valuable addition to SCS and milk yield as an indicator trait for selection against mastitis.     

An Approximate Bayesian Analysis of Somatic Cell Score Curves in Holsteins

Somatic cell score (SCS) decreases to a minimum at around 60 days postpartum and then increases until the end of lactation. This pattern was described with three non-linear mixed effects models. Parameters of the models were linear in fixed and random (cow) effects. Data were 1705 SCS test-day records (155 primiparous Holsteins) taken from 14 to 300 days in milk. Point estimates were the mode of the joint posterior distribution of fixed and random effects (given dispersion parameters) and approximate marginal maximum likelihood estimates of covariance components. Intramammary infection during lactation, season and period of calving affected SCS patterns. Estimates were similar with or without a relationship matrix. There was between-cow variation of trajectories, suggesting that SCS curve parameters can be modified by selection in some advantageous manner.