Analysis of water intake, dry matter intake and daily milk yield using different error covariance structures

The aim of the present study was to investigate the daily measured traits milk yield, water intake and dry matter intake with fixed and random regression models added with different error covariance structures. It was analysed whether these models deliver better model fitting in contrast to conventional fixed and random regression models. Furthermore, possible autocorrelation between repeated measures was investigated. The effect of model choice on statistical inference was also tested. Data recording was performed on the Futterkamp dairy research farm of the Chamber of Agriculture of Schleswig-Holstein. A dataset of about 21 000 observations from 178 Holstein cows was used. Average milk yield, water intake and dry matter intake were 34.9, 82.4 and 19.8 kg, respectively. Statistical analysis was performed using different linear mixed models. Lactation number, test day and the parameters to model the function of lactation day were included as fixed effects. Different structures were tested for the residuals; they were compared for their ability to fit the model using the likelihood ratio test, and Akaike's and Bayesian's information criteria. Different autocorrelation patterns were found. Adjacent repeated measures of daily milk yield were highest correlated (p1 = 0.32) in contrast to measures further apart, while for water intake and dry matter intake, the measurements with a lag of two units had the highest correlations with p2 = 0.11 and 0.12. The covariance structure of TOEPLITZ was most suitable to indicate the dependencies of the repeated measures for all traits. Generally, the most complex model, random regression with the additional covariance structure TOEPLITZ(4), provided the lowest information criteria. Furthermore, the model choice influenced the significance values of one fixed effect and therefore the general inference of the data analysis. Thus, the random regression + TOEPLITZ(4) model is recommended for use for the analysis of equally spaced datasets of milk yield, water intake and dry matter intake.     

Genetic trend for milk yield in Guzerat herds participating in progeny testing and MOET nucleus schemes

Genetic trends for 305-day milk yield (P305) in Brazilian Guzerat herds under selection were compared. Data from 4898 lactations of 3179 purebred and crossbred cows from various regions of Brazil were used. Milk yield was adjusted for mature age and the contemporary groups were defined as herd and calving year. Genetic parameters were estimated using the MTDFREML program. The model included the random effects of animals and permanent environment, and herd-calving year, calving season and genetic composition as fixed effects. Genetic trends were estimated by linear regression of weighted average estimated breeding values as a function of calving year. The average P305 was 2065 +/- 922 kg and the heritability was 0.23 +/- 0.03. The annual genetic trend in estimated breeding values of cows for P305 was 7.09 +/- 0.71 kg between 1987 and 2004, and 6.47 +/- 2.35 kg between 1997 and 2004. For cows born and raised in the multiple ovulation and embryo transfer (MOET) nucleus, this trend was 36.46 +/- 24.54 kg/year between 1997 and 2004, 183.14 +/- 47.94 kg/year between 1997 and 2000, and 9.13 +/- 19.19 kg/year between 2001 and 2004. An average inbreeding coefficient of 0.04 was found for inbred MOET cows in 2004. Increasing the size of the family and introducing new progenies changed reliabilities and predicted transmitting ability estimates of MOET sires. In conclusion, there was a positive genetic trend for milk yield in the MOET nucleus at low inbreeding coefficients due to the increased accuracy and estimated genetic merit, but no changes in the average milk yield were observed.     

Random regression analyses using B-spline functions to model growth of Nellore cattle

The objective of this study was to estimate (co)variance components using random regression on B-spline functions to weight records obtained from birth to adulthood. A total of 82 064 weight records of 8145 females obtained from the data bank of the Nellore Breeding Program (PMGRN/Nellore Brazil) which started in 1987, were used. The models included direct additive and maternal genetic effects and animal and maternal permanent environmental effects as random. Contemporary group and dam age at calving (linear and quadratic effect) were included as fixed effects, and orthogonal Legendre polynomials of age (cubic regression) were considered as random covariate. The random effects were modeled using B-spline functions considering linear, quadratic and cubic polynomials for each individual segment. Residual variances were grouped in five age classes. Direct additive genetic and animal permanent environmental effects were modeled using up to seven knots (six segments). A single segment with two knots at the end points of the curve was used for the estimation of maternal genetic and maternal permanent environmental effects. A total of 15 models were studied, with the number of parameters ranging from 17 to 81. The models that used B-splines were compared with multi-trait analyses with nine weight traits and to a random regression model that used orthogonal Legendre polynomials. A model fitting quadratic B-splines, with four knots or three segments for direct additive genetic effect and animal permanent environmental effect and two knots for maternal additive genetic effect and maternal permanent environmental effect, was the most appropriate and parsimonious model to describe the covariance structure of the data. Selection for higher weight, such as at young ages, should be performed taking into account an increase in mature cow weight. Particularly, this is important in most of Nellore beef cattle production systems, where the cow herd is maintained on range conditions. There is limited modification of the growth curve of Nellore cattle with respect to the aim of selecting them for rapid growth at young ages while maintaining constant adult weight.     

Relationship between the magnitude of the inbreeding coefficient and milk traits in Holstein and Jersey dairy bull semen used in Brazil

Artificial insemination has been used to improve production in Brazilian dairy cattle; however, this can lead to problems due to increased inbreeding. To evaluate the effect of the magnitude of inbreeding coefficients on predicted transmitting abilities (PTAs) for milk traits of Holstein and Jersey breeds, data on 392 Holstein and 92 Jersey sires used in Brazil were tabulated. The second-degree polynomial equations and points of maximum or minimal response were estimated to establish the regression equation of the variables as a function of the inbreeding coefficients. The mean inbreeding coefficient of the Holstein bulls was 5.10%; this did not significantly affect the PTA for percent milk fat, protein percentage and protein (P = 0.479, 0.058 and 0.087, respectively). However, the PTAs for milk yield and fat decreased significantly after reaching inbreeding coefficients of 6.43 (P = 0.034) and 5.75 (P = 0.007), respectively. The mean inbreeding coefficient of Jersey bulls was 6.45%; the PTAs for milk yield, fat and protein, in pounds, decreased significantly after reaching inbreeding coefficients of 15.04, 9.83 and 12.82% (P < 0.001, P = 0.002, and P = 0.001, respectively). The linear regression was only significant for fat and protein percentages in the Jersey breed (P = 0.002 and P = 0.005, respectively). The PTAs of Holstein sires were more affected by smaller magnitudes of inbreeding coefficients than those of Jersey sires. It is necessary to monitor the inbreeding coefficients of sires used for artificial insemination in breeding schemes in Brazil, since the low genetic variability of the available sires may lead to reduced production.     

Post-insemination milk progesterone concentration and embryo survival in dairy cows

Logistic regression analysis was used to evaluate the relationship between post-insemination milk progesterone concentration and embryo survival, and between milk yield and milk progesterone concentration. Milk samples were collected on Days 1, 4, 5, 6, and 7 (insemination=Day 0) following 871 inseminations in spring-calving dairy cows. Milk progesterone concentrations were measured by enzyme-immunoassay and pregnancy diagnosis was conducted with transrectal ultrasonography at approximately Day 30. There was a negative linear relationship (P<0.01) between milk progesterone concentration on Day 4 and embryo survival while, in contrast, there was a positive linear and quadratic relationship between milk progesterone concentration on Days 5, 6 and 7 (P<0.05) and also between the rate of change in progesterone concentrations between Days 4 and 7 inclusive and embryo survival (P<0.05). There was a weak negative linear relationship between average daily milk yield at the time of insemination and milk progesterone concentrations (P<0.001). There was no association between many production parameters, including liveweight and body condition score measured at various stages between calving and insemination, and milk progesterone concentration between Days 4 and 7 inclusive (P>0.05). In conclusion, low progesterone during Days 5-7 (after insemination) was associated with low fertility in dairy cows and there were indications of a range of progesterone concentrations within which embryo survival was maximal.     

Linear and non-linear regression analysis of genotype X environment interactions in pearl millet

Summary Regression analysis was computed on the grain yield of 15 single cross F₁ hybrids of pearl millet (Pennisetum typhoides (Burm.) S. & H.) evaluated in 20 environments at 19 sites in India to assess the nature of genotype X environment interactions. Linear, quadratic, cubic, twoand three-intersecting straight line models were examined for fit. The interactions of six hybrids viz. MH 110, MH 113, MH 114, MH 115, MH 120 and MBH 110 were explained by the linear regression model. The response of the remaining nine hybrids was largely non-linear. The two and three-intersecting straight line models fit better than the quadratic and cubic models and explained non-linearity of response. The two-intersecting straight line models fit for 6 hybrids MH 106, MH 107, MH 112, MH 116, MH 117 and BJ 104. The response of MH 109 was best explained by a three-intersecting straight line model, but there still existed a significant remainder variation. The truncation of environmental range by assuming moving division points was more efficient than the fixed division points for the segmental regression models. The stability of hybrid varieties on the best fitting model has been discussed.     

Genetic and phenotypic parameters for test day milk yield of Sahiwal cattle in the semi-arid tropics

A total of 19 376 test day (TD) milk yield records from the first three lactations of 1618 cows daughters of 162 sires were used to estimate genetic and phenotypic parameters and determine the relationship between daily milk yield and lactation milk yield in the Sahiwal cattle in Kenya. Variance components were estimated using animal models based on a derivative free restricted maximum likelihood procedure. Variance components were estimated using various univariate and multi-trait fixed regression test day models (TDM) that defined contemporary groups either based on the year-season of calving (YSCV) or on the year-season of TD milk sampling (YSTD). Variance components were influenced by CG which resulted in differences in heritability and repeatability estimates between TDM. Models considering YSTD resulted in higher additive genetic variances and lower residual variances compared with models in which YSCV was considered. Heritability estimates for daily yield ranged from 0.28 to 0.46, 0.38 to 0.52 and 0.33 to 0.52 in the first, second and third lactation, respectively. In the first and second lactation, the heritability estimates were highest between TD 2 and TD 4. Genetic correlations among daily milk yields ranged from 0.41 to 0.93, 0.50 to 0.83 and 0.43 to 86 in the first, second and third lactation, respectively. The phenotypic correlations were correspondingly lower. Genetic correlations were different from unit when fitting multi-trait TDM. Therefore, a multiple trait model would be more ideal in determining the genetic merit of dairy sires and bulls based on daily yield records. Genetic and phenotypic correlations between daily yield and lactation yields were high and positive. Genetic correlations ranged from 0.84 to 0.99, 0.94 to 1.00 and 0.94 to 0.97 in the first, second and third lactations, respectively. The corresponding phenotypic correlation estimates ranged from 0.50 to 0.85, 0.50 to 0.83 and 0.53 to 0.87. The high genetic correlation between daily yield and lactation yield imply that both traits are influenced by similar genes. Therefore daily yields records could be used in genetic evaluation in the Sahiwal cattle breeding programme.     

Relation of Milk Production Loss to Milk Somatic Cell Count

Milk production loss was studied in relation to increased somatic cell count (SCC). Available data were weekly test-day milk yields and SCC (in 1,000 cells/ml), and mastitis incidences. In total, 18,131 records from 274 cows were used. Production loss was determined for test-day kg milk, kg protein, and kg energy-corrected milk. Least-squares analysis of variance was used to estimate the direct effect of Log10(SCC) on production. The recorded measures of production were first corrected for fixed effects, with adjustment factors estimated from a healthy data-set. The average daily milk yield was 19.7 kg/day in first lactation and 22.0 in later lactations. The geometric mean of SCC was 63.1 in first lactation and 107.2 in later lactations. The incidence of clinical mastitis treated by a veterinarian was 19.8% of the lactations-at-risk. Linear relationships were found between the production parameters and Log10(SCC). Quadratic and cubic effects were evaluated, but were found to contribute little to the overall fit of the models. The individual milk yield loss was 1.29 kg/day for each unit increase in Log10(SCC) for cows in first lactation. Milk yield decreased by 2.04 kg/day per unit Log10(SCC) for older cows. Corresponding values for protein yield were 0.042 and 0.067 kg/day for first and later lactations, respectively.     

Linking pasture, livestock productivity and vertebrate pest management

The study of pastures, pests (rabbits and caterpillars) and sheep productivity by Barlow (1987; New Zeal J Ecol 10: 43–55) is reviewed, updated and extended. Pasture growth was modelled as a dynamic process, though sheep and rabbit abundance were not dynamic. The model predicted that there was a parabolic relationship between sheep productivity and sheep stocking rate with the effects of rabbits being to shift the relationship lower and to the left. The relationship is analogous to a model of sustained harvest of a wild population, and the shape parameter of each has similar numerical values (2 to 3). The Barlow model also predicted a negative relationship between sheep productivity and rabbit abundance, with the relationship being curved with fixed stocking rates. Analysis of data from an independent experimental study shows more support for a negative quadratic (concave down, R2 = 0.509) than a negative linear (R2 = 0.416, ΔAICc = 2.770) relationship. The Barlow (1987) study assumed a positive linear relationship between the area of denuded pasture and pest abundance. A model selection analysis of a priori models of disturbance by feral pigs provides support for a positive curved relationship (R2 = 0.854) and a positive linear relationship (R2 = 0.357; ΔAICc = 0.03) between the area of denuded pasture (as disturbed ground) and pig abundance. The general results and their implications are discussed.     

Modeling to Predict Cases of Hantavirus Pulmonary Syndrome in Chile

Background

Hantavirus pulmonary syndrome (HPS) is a life threatening disease transmitted by the rodent Oligoryzomys longicaudatus in Chile. Hantavirus outbreaks are typically small and geographically confined. Several studies have estimated risk based on spatial and temporal distribution of cases in relation to climate and environmental variables, but few have considered climatological modeling of HPS incidence for monitoring and forecasting purposes.

Methodology

Monthly counts of confirmed HPS cases were obtained from the Chilean Ministry of Health for 2001–2012. There were an estimated 667 confirmed HPS cases. The data suggested a seasonal trend, which appeared to correlate with changes in climatological variables such as temperature, precipitation, and humidity. We considered several Auto Regressive Integrated Moving Average (ARIMA) time-series models and regression models with ARIMA errors with one or a combination of these climate variables as covariates. We adopted an information-theoretic approach to model ranking and selection. Data from 2001–2009 were used in fitting and data from January 2010 to December 2012 were used for one-step-ahead predictions.

Results

We focused on six models. In a baseline model, future HPS cases were forecasted from previous incidence; the other models included climate variables as covariates. The baseline model had a Corrected Akaike Information Criterion (AICc) of 444.98, and the top ranked model, which included precipitation, had an AICc of 437.62. Although the AICc of the top ranked model only provided a 1.65% improvement to the baseline AICc, the empirical support was 39 times stronger relative to the baseline model.

Conclusions

Instead of choosing a single model, we present a set of candidate models that can be used in modeling and forecasting confirmed HPS cases in Chile. The models can be improved by using data at the regional level and easily extended to other countries with seasonal incidence of HPS.     

人工红松树干内部节子体积预测模型

基于黑龙江省林口林业局林场和东京城林业局林场29块标准地中49株人工红松1207个节子数据,使用图片处理软件Digimizer对节子纵剖面图片数据进行提取,将节子形状用一个二维散点图表示。根据节子二维形状散点图,把人工红松节子分为3种类型: 活节(整个节子为健全节)、未包藏死节(节子由健全节和疏松节组成)和包藏死节(节子的健全节和疏松节部分被树干包藏)。3个类型节子的健全节体积通过对健全节形状参数方程求积得到;疏松节体积利用圆柱体的体积计算得到;节子总体积等于健全节体积与疏松节体积之和。最后,基于节子变量(节子直径、节子相对高、节子总长度)和树木变量(胸径),采用样地和树木水平的线性混合模型建立了红松人工林健全节体积、疏松节体积和节子总体积的预测模型。与基础模型相比,考虑样地和树木水平的混合效应所建立的健全节体积、疏松节体积和节子总体积预测模型,其参数估计更精准,残差分布更均匀,拟合精度明显提高。检验结果表明,基础模型预估精度均在90%以上,引入样地和树木效应的混合模型的预估精度均在93%以上,说明所建模型可以很好地预测红松人工林节子体积大小。     

Effects of stage of pregnancy on variance components,daily milk yields and 305-day milk yield in Holstein cows,as estimated by using a test-day model

Pregnancy and calving are elements indispensable for dairy production, but the daily milk yield of cows decline as pregnancy progresses, especially during the late stages. Therefore, the effect of stage of pregnancy on daily milk yield must be clarified to accurately estimate the breeding values and lifetime productivity of cows. To improve the genetic evaluation model for daily milk yield and determine the effect of the timing of pregnancy on productivity, we used a test-day model to assess the effects of stage of pregnancy on variance component estimates, daily milk yields and 305-day milk yield during the first three lactations of Holstein cows. Data were 10 646 333 test-day records for the first lactation; 8 222 661 records for the second; and 5 513 039 records for the third. The data were analyzed within each lactation by using three single-trait random regression animal models: one model that did not account for the stage of pregnancy effect and two models that did. The effect of stage of pregnancy on test-day milk yield was included in the model by applying a regression on days pregnant or fitting a separate lactation curve for each days open (days from calving to pregnancy) class (eight levels). Stage of pregnancy did not affect the heritability estimates of daily milk yield, although the additive genetic and permanent environmental variances in late lactation were decreased by accounting for the stage of pregnancy effect. The effects of days pregnant on daily milk yield during late lactation were larger in the second and third lactations than in the first lactation. The rates of reduction of the 305-day milk yield of cows that conceived fewer than 90 days after the second or third calving were significantly (P<0.05) greater than that after the first calving. Therefore, we conclude that differences between the negative effects of early pregnancy in the first, compared with later, lactations should be included when determining the optimal number of days open to maximize lifetime productivity in dairy cows.     

Statistical analysis of test-day milk yields using random regression models for the comparison of feeding groups during the lactation period

Random regression models are widely used in the field of animal breeding for the genetic evaluation of daily milk yields from different test days. These models are capable of handling different environmental effects on the respective test day, and they describe the characteristics of the course of the lactation period by using suitable covariates with fixed and random regression coefficients. As the numerically expensive estimation of parameters is already part of advanced computer software, modifications of random regression models will considerably grow in importance for statistical evaluations of nutrition and behaviour experiments with animals. Random regression models belong to the large class of linear mixed models. Thus, when choosing a model, or more precisely, when selecting a suitable covariance structure of the random effects, the information criteria of Akaike and Schwarz can be used. In this study, the fitting of random regression models for a statistical analysis of a feeding experiment with dairy cows is illustrated under application of the program package SAS. For each of the feeding groups, lactation curves modelled by covariates with fixed regression coefficients are estimated simultaneously. With the help of the fixed regression coefficients, differences between the groups are estimated and then tested for significance. The covariance structure of the random and subject-specific effects and the serial correlation matrix are selected by using information criteria and by estimating correlations between repeated measurements. For the verification of the selected model and the alternative models, mean values and standard deviations estimated with ordinary least square residuals are used.     

河北省年均降水量插值方法比较

以河北省及临近区域120个气象观测站点1971～2000年均降水量数据为基础,选择其中的40个作为检验站点,其余站点分别取80、40、20个作为插值站点,采用局部插值、整体插值、多元线性回归、综合模拟等多种插值模型讨论了降水空间插值问题,主要结论如下:插值站点数、模型类型、模型参数都会影响插值精度.局部插值模型相对误差最小值出现在Spline、IDW模型中,其次为Kridging模型,而整体模型Trend、多元线性回归模型误差均较大,但综合了局部插值模型和统计模型的综合模型一定程度上能改善插值精度及误差分布.河北省80和40个站点的最优插值模型为综合模型,20个站点的最优插值模型为IDW2.     

Integration of the effects of animal and dietary factors on total dry matter intake of dairy cows fed silage-based diets

An empirical regression model for the prediction of total dry matter intake (DMI) of dairy cows was developed and compared with four published intake models. The model was constructed to include both animal and dietary factors, which are known to affect DMI. For model development, a data set based on individual cow data from 10 change-over and four continuous milk production studies was collected (n = 1554). Relevant animal (live weight (LW), days in milk (DIM), parity and breed) and dietary (total and concentrate DMI, concentrate composition, forage digestibility and fermentation quality) data were collected. The model factors were limited to those that are available before the diets are fed to animals, that is, standardized energy corrected milk (sECM) yield, LW, DIM and diet quality (total diet DMI index (TDMI index)). As observed ECM yield is a function of both the production potential of the cow and diet quality, ECM yield standardized for DIM, TDMI index and metabolizable protein concentration was used in modelling. In the individual data set, correlation coefficients between sECM and TDMI index or DIM were much weaker (0.16 and 0.03) than corresponding coefficients with observed ECM (0.65 and 0.46), respectively. The model was constructed with a mixed model regression analysis using cow within trial as a random factor. The following mixed model was estimated for DMI prediction: DMI (kg DM/day) = -2.9 (±0.56)+0.258 (±0.011) × sECM (kg/day) + 0.0148 (±0.0009) × LW (kg) -0.0175 (±0.001) × DIM -5.85 (±0.41) × exp (-0.03 × DIM) + 0.09 (±0.002) × TDMI index. The mixed DMI model was evaluated with a treatment mean data set (207 studies, 992 diets), and the following relationship was found: Observed DMI (kg DM/day) = -0.10 (±0.33) + 1.004 (±0.019) × Predicted DMI (kg DM/day) with an adjusted residual mean square error of 0.362 kg/day. Evaluation of the residuals did not result in a significant mean bias or linear slope bias, and random error accounted for proportionally >0.99 of the error. In conclusion, the DMI model developed is considered robust because of low mean prediction error, accurate and precise validation, and numerically small differences in the parameter values of model variables when estimated with mixed or simple regression models. The Cornell Net Carbohydrate and Protein System was the most accurate of the four other published DMI models evaluated using individual or treatment mean data, but in most cases mean and linear slope biases were relatively high, and, interestingly, there were large differences in both mean and linear slope biases between the two data sets.     

Curvilinear inbreeding effects on some performance traits in laying hens

Quadratic partial regression coefficients were estimated for the inbreeding level on five performance traits (body weight, average egg weight, age at first egg, percentage of fertilized eggs, and hatchability of set eggs) of two strains of laying hens. Data on 5631 of H77 layers and 3563 of N88 layers from nine consecutive generations were analysed. Only dams were accounted for. Partial regression coefficients were estimated by REML with a single-trait animal model, which included fixed effects (generation and hatching period) and random effects (additive genetic and error effects). The mean inbreeding level was 0.87% in strain H77 and 1.08% in strain N88. The inbreeding effects were analysed based on the quadratic partial regression equations. A slight inbreeding depression was found for all the traits analysed in N88. In strain H77, negative effects of inbreeding were only noted for body weight and average egg weight. The small inbreeding effects shown here resulted from a relatively low level of homozygosity in the populations studied. The strains were found to differ in the effects of inbreeding. It is worth pointing out that differences were noted both between the inbreeding depression estimated from the partial linear regression equation and the quadratic partial regression equation, as well as different inbreeding levels.     

Statistical analysis of test-day milk yields using random regression models for the comparison of feeding groups during the lactation period

Abstract

Random regression models are widely used in the field of animal breeding for the genetic evaluation of daily milk yields from different test days. These models are capable of handling different environmental effects on the respective test day, and they describe the characteristics of the course of the lactation period by using suitable covariates with fixed and random regression coefficients. As the numerically expensive estimation of parameters is already part of advanced computer software, modifications of random regression models will considerably grow in importance for statistical evaluations of nutrition and behaviour experiments with animals. Random regression models belong to the large class of linear mixed models. Thus, when choosing a model, or more precisely, when selecting a suitable covariance structure of the random effects, the information criteria of Akaike and Schwarz can be used. In this study, the fitting of random regression models for a statistical analysis of a feeding experiment with dairy cows is illustrated under application of the program package SAS. For each of the feeding groups, lactation curves modelled by covariates with fixed regression coefficients are estimated simultaneously. With the help of the fixed regression coefficients, differences between the groups are estimated and then tested for significance. The covariance structure of the random and subject-specific effects and the serial correlation matrix are selected by using information criteria and by estimating correlations between repeated measurements. For the verification of the selected model and the alternative models, mean values and standard deviations estimated with ordinary least square residuals are used.     

Changes in mammary blood flow during the lactation period in goats measured by the ultrasound Doppler principle

1. Mammary blood flow was measured during the lactation period in two low- and two high-yielding dairy goats (peak milk yields approx. 1.5 and 3.6 kg/day respectively), using the ultrasound Doppler principle for determination of blood velocity in both milk veins (subcutaneous abdominal veins) of the animals, and ultrasound scanning for measurement of cross-sectional area of the veins. 2. Milk vein cross-sectional area ranged from 0.11 to 0.38 cm2 in the four goats, with a close to significant (P = 0.06) difference between the veins in the two sides of the animals. Cross-sectional area remained constant during the lactation period. Changes in mammary blood flow was therefore caused by changes in blood velocity. 3. Milk vein blood velocities ranged from 4.4 to 34.7 cm/sec independently of the time of the day, and were of the same magnitude in the two sides of the animals. Except in one goat (P = 0.1), blood velocity decreased significantly (P less than 0.01) with progressing lactation, during which period also milk yield was declining. 4. In the two low-yielding goats, a positive linear relationship (R2 = 0.20) was found between milk yield and milk vein blood velocity, whereas a diminishing exponential relationship (R2 = 0.97) was found in the two high-yielding goats. At a given milk vein blood velocity, high-yielding goats obtained a higher milk yield and also responded to changes in blood velocity (up to approx. 15 cm/sec) with greater increases in milk yield than low-yielding goats.(ABSTRACT TRUNCATED AT 250 WORDS)     

Milk trait heritability and correlation with heterozygosity in yak

382 yak cows were examined for milk yield, fat, protein and lactose contents. Six polymorphic loci, alphas1-CN, kappa-CN, beta-CN, beta-Lg, alpha-La and MUC-1, were scored by PAGE electrophoresis for each individual. The values of milk yield, fat, protein and lactose content were 247.13 kg, 5.81%, 5.18% and 4.93%, respectively. Based on the 6 polymorphism loci, the average heterozygosity of the yak population was 0.1794. Calculated by the marker-based method, heritability estimates for milk yield, fat, protein and lactose contents were 0.353 +/- 0.093, 0.316 +/- 0.101, 0.415 +/- 0.098 and 0.481 +/- 0.035, respectively. The relatively high or medium heritability of these traits indicate that it is feasible to rely directly on them in breeding for the improvement in a relatively short period. The significant linear regression between heterozygosity and fat percentage with a positive slope (R = 0.0420) indicated that inbreeding affected milk fat content in this population.     

Random regression models using different functions to model test-day milk yield of Brazilian Holstein cows

We analyzed 152,145 test-day records from 7317 first lactations of Holstein cows recorded from 1995 to 2003. Our objective was to model variations in test-day milk yield during the first lactation of Holstein cows by random regression model (RRM), using various functions in order to obtain adequate and parsimonious models for the estimation of genetic parameters. Test-day milk yields were grouped into weekly classes of days in milk, ranging from 1 to 44 weeks. The contemporary groups were defined as herd-test-day. The analyses were performed using a single-trait RRM, including the direct additive, permanent environmental and residual random effects. In addition, contemporary group and linear and quadratic effects of the age of cow at calving were included as fixed effects. The mean trend of milk yield was modeled with a fourth-order orthogonal Legendre polynomial. The additive genetic and permanent environmental covariance functions were estimated by random regression on two parametric functions, Ali and Schaeffer and Wilmink, and on B-spline functions of days in milk. The covariance components and the genetic parameters were estimated by the restricted maximum likelihood method. Results from RRM parametric and B-spline functions were compared to RRM on Legendre polynomials and with a multi-trait analysis, using the same data set. Heritability estimates presented similar trends during mid-lactation (13 to 31 weeks) and between week 37 and the end of lactation, for all RRM. Heritabilities obtained by multi-trait analysis were of a lower magnitude than those estimated by RRM. The RRMs with a higher number of parameters were more useful to describe the genetic variation of test-day milk yield throughout the lactation. RRM using B-spline and Legendre polynomials as base functions appears to be the most adequate to describe the covariance structure of the data.