Comparison of homogeneity and heterogeneity of residual variance using random regression test-day models for first lactation Japanese Holstein cows

Using a large‐scale data set that included first lactation test day records from 1975 to 2000 for Japanese Holsteins, genetic parameters for milk yield were estimated by using random regression (RR) test‐day models (TDM) with heterogeneous and homogeneous residual variances. It is necessary for the RR‐TDM to include a function that explains the shape of the lactation curve. The RR‐TDM with the LW curve, which combined Wilmink's curve and a Legendre polynomial, was used for fitting the model for milk yield. In recent years, increases in residual variance have been noted for Japanese dairy cattle. Thus, three kinds of heterogeneous residual variance over the calving year were considered: H1, H2 and HG. Linear and quadratic exponential functions for the calving year were used in H1 and H2, respectively. Residual variance of HG was divided into five groups according to calving year. Homogeneous residual variance was HO. All heterogeneous residual variances increased with calving year in an almost linear fashion. Residual variance increased over the study period. However, there is no need to consider heterogeneous residual variances in genetic evaluations, because the heterogeneity of residual variance over the years did not affect the ranking of top sires and cows.     

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.     

Effect of somatic cell count on milk and protein yields and female fertility in Tunisian Holstein dairy cows

The effects of test-day somatic cell scores (SCS) variations on milk and protein yields, and calving to first service and calving to conception intervals were studied in Tunisian Holsteins. There were 34,129, 25,700, and 18,077 test-day production records collected on first, second, and third parity cows, respectively. Records were of cows calving between 1996 and 2004 in 160 herds. Somatic cell scores and milk and protein yields were analysed using a linear model that included herd-test-day date and herd–year interactions, calving season, calving age, and calving to conception interval. Reproductive trait model included herd–year interaction, calving season, calving age, and month of insemination. Effects of SCS on milk and protein yields were studied by regressing current test-day yields on corresponding and preceding test-day SCS, while effects of SCS on fertility traits were investigated by separately regressing calving to first service and calving to conception intervals corrected for environmental and management factors on SCS corrected for actual milk yield. A cow produced around 19.0 kg (SD = 8.0 kg) and 0.6 kg (SD = 0.3 kg) milk and protein yields on a daily basis and had an average of 3.8 (SD = 2.1) SCS in the first three lactations. SCS varied consistently (p < 0.05) with herd-test-day date and herd–year interactions in all lactations. Days in milk, calving age, and calving to conception interval were all together important sources of variation (p < 0.05) for SCS mainly in the first and second parities. Test-day milk and protein yields were unfavourably affected by high SCS recorded in the same test-day and with a lesser degree by SCS observed in the nearest preceding test-day. Reduction in milk and protein productions from increased SCS varied from 0.23 to 1.76 kg and from 6 to 75 g, respectively. Likewise, increased test-day SCS lengthened both calving to first service (mean interval = 94.9 days; SD = 49.1 days) and calving to conception (mean interval = 161 days; SD = 69.6 days) intervals by 1.3 to 2.0 days for each unit increase in SCS. Using SCS in addition to milk traits as a criterion to select semen and improving veterinary care should result in increased milk and protein yields and in satisfactory fertility measures.     

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.     

Effect of lactation stage, season and parity on milk cortisol concentration in Holstein cows

This experiment was designed (1) to study the effects of lactation stage, season, and parity on milk cortisol concentrations in Holstein cows, and (2) to elucidate the relationships between milk yield, quality, and milk cortisol concentration. Subjects of this study were 24 dairy cows kept in a free stall barn. Milk samples were taken on test day in May, August, November, and February. Data of milk yield, quality, and cortisol concentration were collected. Random effects of animals and fixed effects of lactation stage, test day, and parity on milk yield, quality, and cortisol concentration were analyzed using mixed models. We estimated the best linear unbiased prediction of each trait (BLUP) which was an animal-specific value. Correlation among milk yield, quality, and cortisol concentration was calculated using raw data and BLUP. The effect of the lactation stage on milk cortisol concentration was significant: the value observed in early lactation was higher than in other stages. However, the correlation between milk yield and cortisol concentration was low. The beginning of lactation might be a strong stressor for every cow. Calculated with raw data, milk cortisol concentration had respectively significant negative correlation with milk protein contents and solid not-fat contents. Calculated with BLUP, milk cortisol concentration showed a significant and negative correlation with milk protein contents. The lactation stage and milk protein contents should be considered for measurement of milk cortisol concentrations.     

中国荷斯坦牛头胎产奶量和乳成分遗传参数估计

本研究旨在应用随机回归测定日模型对奶牛生产性状进行遗传评估。收集河南省内17个牧场2008年1月2017年5月共16 335头奶牛头胎174 634条生产性能记录,建立筛选标准对数据进行质控。遗传评估采用随机回归模型,场-测定日为固定效应,以固定回归拟合产犊月龄效应,随机效应包括加性遗传和永久环境效应。固定和随机回归均采用4阶Legendre多项式。结果表明:中国荷斯坦牛头胎测定日产奶量、乳脂率、乳蛋白率、体细胞评分总遗传力分别为0.144 1、0.289 1、0.373 2和0.089 8。本研究为区域性中国荷斯坦牛的遗传评估平台建设和育种规划制定奠定基础。     

Genetic evaluation of Australian dairy cattle for somatic cell scores using multi-trait random regression test-day model

Summary A multi-trait (MT) random regression (RR) test day (TD) model has been developed for genetic evaluation of somatic cell scores for Australian dairy cattle, where first, second and third lactations were considered as three different but correlated traits. The model includes herd-test-day, year-season, age at calving, heterosis and lactation curves modelled with Legendre polynomials as fixed effects, and random genetic and permanent environmental effects modelled with Legendre polynomials. Residual variance varied across the lactation trajectory. The genetic parameters were estimated using asreml . The heritability estimates ranged from 0.05 to 0.16. The genetic correlations between lactations and between test days within lactations were consistent with most of the published results. Preconditioned conjugate gradient algorithm with iteration on data was implemented for solving the system of equations. For reliability approximation, the method of Tier and Meyer was used. The genetic evaluation system was validated with Interbull validation method III by comparing proofs from a complete evaluation with those from an evaluation based on a data set excluding the most recent 4 years. The genetic trend estimate was in the allowed range and correlations between the two sets of proofs were very high. Additionally, the RR model was compared to the previous test day model. The correlations of proofs between both models were high (0.97) for bulls with high reliabilities. The correlations of bulls decreased with increasing incompleteness of daughter performance information. The correlations between the breeding values from two consecutive runs were high ranging from 0.97 to 0.99. The MT RR TD model was able to make effective use of available information on young bulls and cows, and could offer an opportunity to breeders to utilize estimated breeding values for first and later lactations.     

Genetic evaluation of weekly body weight in Japanese quail using random regression models

1. A total of 11 826 records from 2489 quails, hatched between 2012 and 2013, were used to estimate genetic parameters for BW (body weight) of Japanese quail using random regression models. Weekly BW was measured from hatch until 49 d of age. WOMBAT software (University of New England, Australia) was used for estimating genetic and phenotypic parameters.

2. Nineteen models were evaluated to identify the best orders of Legendre polynomials. A model with Legendre polynomial of order 3 for additive genetic effect, order 3 for permanent environmental effects and order 1 for maternal permanent environmental effects was chosen as the best model.

3. According to the best model, phenotypic and genetic variances were higher at the end of the rearing period. Although direct heritability for BW reduced from 0.18 at hatch to 0.12 at 7 d of age, it gradually increased to 0.42 at 49 d of age. It indicates that BW at older ages is more controlled by genetic components in Japanese quail.

4. Phenotypic and genetic correlations between adjacent periods except hatching weight were more closely correlated than remote periods. The present results suggested that BW at earlier ages, especially at hatch, are different traits compared to BW at older ages. Therefore, BW at earlier ages could not be used as a selection criterion for improving BW at slaughter age.     

Once-daily milking of Holstein cows for one-week decreases milk yield by twenty-five percent without any carry-over effect

Short-term (i.e. several days) once-daily milking (ODM) of dairy cows could help to improve work organization or quality of life for dairy farmers. ODM implemented during three periods of one week in the descending phase of lactation led to an average 23.4% decrease in the milk yield of 9 Holstein cows compared to 9 other cows on twice-daily milking (TDM). Short-term ODM significantly increased fat content (by 4.5 g/kg on average) and somatic cell count (by 73,000 cells/mL) and decreased lactose content by 1.9 g/kg. Protein content increased (by 2.1 g/kg) only in the third period. When twice-daily milking was resumed, there were no longer between-group differences in daily yields of milk, fat, protein, and somatic cells.     

Genetic analyses of partial egg production in Japanese quail using multi-trait random regression models

1. The aim of the present study was to estimate genetic parameters for average egg weight (EW) and egg number (EN) at different ages in Japanese quail using multi-trait random regression (MTRR) models.

2. A total of 8534 records from 900 quail, hatched between 2014 and 2015, were used in the study. Average weekly egg weights and egg numbers were measured from second until sixth week of egg production.

3. Nine random regression models were compared to identify the best order of the Legendre polynomials (LP). The most optimal model was identified by the Bayesian Information Criterion. A model with second order of LP for fixed effects, second order of LP for additive genetic effects and third order of LP for permanent environmental effects (MTRR23) was found to be the best.

4. According to the MTRR23 model, direct heritability for EW increased from 0.26 in the second week to 0.53 in the sixth week of egg production, whereas the ratio of permanent environment to phenotypic variance decreased from 0.48 to 0.1. Direct heritability for EN was low, whereas the ratio of permanent environment to phenotypic variance decreased from 0.57 to 0.15 during the production period.

5. For each trait, estimated genetic correlations among weeks of egg production were high (from 0.85 to 0.98). Genetic correlations between EW and EN were low and negative for the first two weeks, but they were low and positive for the rest of the egg production period.

6. In conclusion, random regression models can be used effectively for analysing egg production traits in Japanese quail. Response to selection for increased egg weight would be higher at older ages because of its higher heritability and such a breeding program would have no negative genetic impact on egg production.     

"万力补"饲喂荷斯坦牛效果分析

将 2 0头泌乳后期的荷斯坦牛分成 4组 ,每组 5头。一组作为对照组 ,另外 3组作为试验组分 3个水平进行“万力补”饲料饲喂试验。结果表明 ,饲喂“万力补”对牛奶的 p H值、体细胞无明显影响 ,对乳脂率和乳蛋白有较明显的效果。在试验组的 3个水平中 ,以万力补添加量为2 0 0 g/头·d效果最好 ,产奶量提高 2 .30 kg/d。     

Genetic evaluation of growth of Kenya Boran cattle using random regression models

Data consisting of 18 884 weight records collected from 1273 Boran cattle from birth to 24 months of age were used to estimate covariance functions and genetic parameters for growth of Boran cattle using random regression (RR) models under a situation of small herd size and inconsistent recording. The RR model fitted quadratic Legendre polynomials of age at recording for additive genetic and permanent environmental effects. Genetic variance increased from birth, reaching an asymptotic value at 455 days and was maximum at 525 days of age after which it gradually dropped. Permanent environmental variance increased throughout the trajectory. Estimates of temporary environmental variance were heterogeneous across ages. Direct heritability and permanent environmental variance as a proportion of phenotypic variance fluctuated greatly during the early ages but later stabilized at intermediate to later ages; the estimates ranged from 0.11 to 0.33 and from 0.18 to 0.83, respectively. Genetic correlation estimates were positive, ranging from 0.10 to unity. The estimates declined with increasing in lag between the age points. Phenotypic correlation pattern was erratic between early ages, negatively low (-0.02) between the extreme data points and moderate to highly positive (>0.50) between intermediate and later points, with prominent spikes along the diagonal. It is concluded that RR models have potential for modelling growth of Boran cattle, notwithstanding conditions of small herd sizes and inconsistent recording.     

荷斯坦牛泌乳曲线的拟合分析

通过对安徽荷斯坦牛泌乳曲线进行拟合分析，结果 Wood模型对泌乳曲线的拟合精度为（R^2)=0.2336-0.5661；若剔除第1个泌乳月，对2-10个泌乳月利用Wood模型再次拟合，拟合精度则显著提高，达到0.9左右，使用f(t)=∑i=1^5αit^i-1模型拟合泌乳曲线，拟合精度达到0.9442-0.9955。     

利用Wood模型拟合中国荷斯坦牛乳脂率变化的效果分析

为了解中国荷斯坦牛乳脂率变化规律,本文利用Wood模型对我国南方5个大中型奶牛场2008~2010年1~3胎中国荷斯坦牛33 194条测定日乳脂率进行曲线拟合。结果表明:中国荷斯坦牛乳脂率变化曲线为典型的倒抛物线形,第一胎拟合度最高(0.9820),第三胎最低(0.9789)。二胎牛乳脂率最先达到最低点(第16周),而三胎乳脂率最后达到(第19周)。就最低乳脂率而言,二胎牛最大(3.54%),而三胎牛最小(3.45%)。综合各方面情况得出,Wood模型适用于中国荷斯坦牛乳脂率变化的曲线拟合。     

高产荷斯坦奶牛泌乳曲线的特征及相关分析

选取285胎次第三、四胎305d产奶量超过8000kg的安徽荷斯坦牛的泌乳资料，利用Wood模型（Yt=ate^b-ct）进行高产荷斯坦奶牛泌乳曲线特征及相关的分析。结果表明：按照达到泌乳高峰周时间的不同对选取奶牛进行分级，11组Wood模型拟合泌乳曲线的平均拟合精度（R^2）为0.939（幅度为0.899-0.962）。随着达到泌乳高峰周时间的推迟，规模因子a具有逐渐降低的趋势；而产奶量上升率b、产奶量下降因子c、泌乳持久力表现与a相反的变化趋势。在相关分析中，MY（实际产奶量）与EMY（估计产奶量）、PY（高峰月产奶量）为强正相关，r(相关系数）分别为0.999和0.776，与持久力为中等正相关（r=0.379），与a、b、c的r分别是0.905、－0.875、0.731，与PY的相关程度较弱（r=-0.140）。     

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.     

The influence of breed and parity on milk yield, and milk yield acceleration curves

This study had two aims. Firstly, we wanted to quantify the effects of breed and parity on lactation curves. A parametric model for describing milk yield for cows [Friggens, N., Emmans, G., Veerkamp, R., 1999. On the use of simple ratios between lactation curve coefficients to describe parity effects on milk production. Livest. Prod. Sci. 62, 1–13] was used. The data contained 155,051 daily records of milk yield from 318 cows of three different breeds; Danish Red, Danish Holstein and Jersey. There were 276, 230, and 98 lactation curves for parities 1, 2 and 3 respectively. For every cow lactation, the parameters of the model were estimated using a least squares procedure for non-linear models. The resulting parameters were analysed in a mixed linear model. Significant effects of parity were observed on the same two parameters as in Friggens et al. [Friggens, N., Emmans, G., Veerkamp, R., 1999. On the use of simple ratios between lactation curve coefficients to describe parity effects on milk production. Livest. Prod. Sci. 62, 1–13]. Breed was also found to have a significant effect on some of the parameters. However, there was no significant interaction between breed and parity. The second aim of the study was to evaluate the properties of acceleration in milk yield in the context of providing an indicator for physiological stress and subsequent health problems. Milk yield acceleration was highest around calving and also reflected trends for higher stress/risk for higher yielding cows.     

Comparison of milk production of dairy cows kept in cold and warm loose-housing systems

A retrospective cohort study was conducted to test whether the lactation curves of cows kept in cold loose-housing systems (CLHs) were the same as for cows in warm loose-housing systems (WLHs) in the Nordic countries. Approximately 40 000 test-day records from 5366 Ayrshire or Black and White cows kept on 38 CLHs and 166 WLHs in Finland during 1996 and 1997 were used. Analysis used a random-coefficient model (correcting for parity, breed and calving-year-season and the correlation-structure between test-days of the same cow and cows of the same herd). Cows in a CLH produced up to 1 l less milk per test-day, but this difference was not statistically significant. Surprisingly, the difference in milk yield was not affected by calving-year-season, parity or breed.     

The effect of strain of Holstein-Friesian, feeding system and parity on lactation curves characteristics of spring-calving dairy cows

The purpose of the present study was to investigate the influence of strain of Holstein-Friesian (HF) cow and feeding system (FS) on the lactation curve characteristics of spring-calving cows. The Wilmink model was used to analyse the lactation curves. The three strains of HF cows compared were high production North American (HP), high durability North American (HD) and high Breeding Worth New Zealand (NZ). The three FS compared were a high milk output from pasture feed system (MP), a high concentrate feed system (HC) and a high stocking rate feed system (HS). A repeated measures model with a factorial arrangement of treatments was used to determine the influence of strain of HF, FS, parity and their interactions on the shape of the lactation curve. The curve was described based on yield at calving, the degree of ascendancy between calving and peak yield, and the persistency after peak yield. Analysis of the residuals indicated a good fit of the Wilmink curve to the data set. Strain of HF, FS, parity and the interaction of strain of HF with FS had significant effects on lactation curve characteristics. In all three FS, the HP strain achieved the highest milk production post-claving and peak yield, with the lowest persistency of lactation. In the HC system, milk production post-claving and at peak yield were higher for all three strains. Offering higher levels of concentrate supplementation to the HP strain on a pasture-based system improved their persistency of lactation. The highest persistency of lactation was achieved with NZ strain. The highest milk production post-claving and at peak and lowest persistency was achieved with third parity cows. The existence of strain by feed system interactions for lactation curve parameters clearly exhibits that the optimum system of production varies with strain of HF.     

Risk factors for udder edema and its association with lactation performance on primiparous Holstein cows in a large Florida herd, U.S.A

The objective of this study was to determine risk factors for udder edema (case–control study) and to evaluate the association of udder edema in primiparous Holstein cows with their lactation performance (cohort study). Values for the first 10 test day for milk yield, fat, protein, and somatic cell counts (SCC) linear score as well as mature equivalent (ME) 305 days milk yield, fat, protein, SCC linear score, and incidences of periparturient diseases from a computerized farm recording system were compared between primiparous cows with and without udder edema. Data consisted of 118 dairy heifers with udder edema, induced for parturition, and treated with diuretics and 889 control heifers that received no treatment. Primiparous cows giving birth to male calves, were 1.72 (1.01, 3.24; 95% CI) times more likely to develop udder edema than cows giving birth to female calves. Primiparous cows calving in winter season were 3.68 (1.09, 12.5; 95% CI) times more likely to develop udder edema than cows calving in summer. For each extra 10 cm in height the odds of udder edemas was 1.23 (1.03, 1.47; 95% CI). The first test day DHIA milk yield was lower in cows that developed udder edema (3.6 kg/day) than in normal cows. However, the subsequent test days and ME measurements were not statistically different between groups. Cows with udder edema were 1.62 (1.18, 2.14; 95% CI) times more likely to develop udder edema in the second lactation than control animals. It is concluded that the gender of the offspring, calving season and height at parturition were significant risk factors for udder edema. Only milk yield on the first DHIA test day was lower in cows with udder edema than in cows without udder edema.