Estimation of heterogeneous variances using empirical Bayes methods: theoretical considerations.

Procedures are described to estimate variances when heterogeneity of genetic and residual dispersion parameters exists for some criterion. Genetic and residual variances are considered to follow distributions with either known or unknown parameters. The estimates of variances obtained are weighted averages of the corresponding parameter and of a data-based statistic. Although the techniques presented are largely inspired by Bayesian ideas, the procedures can be given a frequentist interpretation, and the parameters of the prior distributions can be estimated from the data at hand. Techniques are described and illustrated for situations in which animals are related or unrelated across herds. We conjecture that the proposed estimators have smaller mean squared error than those obtained by grouping observations in some way and then applying REML within each group.     

Estimation of test-day model (co)variance components across breeds using New Zealand dairy cattle data

In New Zealand, a large proportion of cows are currently crossbreds, mostly Holstein-Friesians (HF) × Jersey (JE). The genetic evaluation system for milk yields is considering the same additive genetic effects for all breeds. The objective was to model different additive effects according to parental breeds to obtain first estimates of correlations among breed-specific effects and to study the usefulness of this type of random regression test-day model. Estimates of (co)variance components for purebred HF and JE cattle in purebred herds were computed by using a single-breed model. This analysis showed differences between the 2 breeds, with a greater variability in the HF breed. (Co)variance components for purebred HF and JE and crossbred HF × JE cattle were then estimated by using a complete multibreed model in which computations of complete across-breed (co)variances were simplified by correlating only eigenvectors for HF and JE random regressions of the same order as obtained from the single-breed analysis. Parameter estimates differed more strongly than expected between the single-breed and multibreed analyses, especially for JE. This could be due to differences between animals and management in purebred and nonpurebred herds. In addition, the model used only partially accounted for heterosis. The multibreed analysis showed additive genetic differences between the HF and JE breeds, expressed as genetic correlations of additive effects in both breeds, especially in linear and quadratic Legendre polynomials (respectively, 0.807 and 0.604). The differences were small for overall milk production (0.926). Results showed that permanent environmental lactation curves were highly correlated across breeds; however, intraherd lactation curves were also affected by the breed-environment interaction. This result may indicate the existence of breed-specific competition effects that vary through the different lactation stages. In conclusion, a multibreed model similar to the one presented could optimally use the environmental and genetic parameters and provide breed-dependent additive breeding values. This model could also be a useful tool to evaluate crossbred dairy cattle populations like those in New Zealand. However, a routine evaluation would still require the development of an improved methodology. It would also be computationally very challenging because of the simultaneous presence of a large number of breeds.     

Method and effect of adjustment for heterogeneous variance.

Lactation records were standardized for differing genetic and error variances across herds and over time based on phenotypic variance for each herd-year-parity group. Each herd-year-parity phenotypic variance estimate was combined with those of adjacent years and regressed toward a region-year-parity variance. Heritability was assumed to be .25 at mean variance within year and to range from .2 for herds with smallest phenotypic SD to .3 for herds with largest phenotypic SD. Lactation deviations from management group mean were adjusted by ratio of base genetic SD to genetic SD estimated from heritability and phenotypic SD. The base was defined as 1987 calvings for first parity and 1988 calvings for later parities. Records were weighted according to heritability by multiplying lactation length weight by herd error weight defined as ratio of base error variance to error variance in the adjusted record. Estimated genetic trend for milk increased by nearly 5 kg/yr for Holsteins with this adjustment, which caused predicted breeding values of oldest animals to be lower by about 100 kg. Most correlations of parent and progeny information were slightly higher with adjusted data. Cows in high variance herds were most likely to have large reductions in their evaluations. Adjustment for heterogeneous variance was implemented in July 1991 for national evaluations for yield traits.     

Estimation of mutton carcass components using two predictors

Carcass weight and the GR measurement (a measure of fatness) were used as predictors in models for estimating mutton carcass components. These parameters explained a moderate to large amount of the variation in component weights (r² = 0·47−0·93) except for trunk meat (of a 50% visual lean specification) with an r² = 0·15.

The 557 carcasses used ranged in weight from 9·2 to 43·8 kg and in fat depth at the GR site from 0 to 41·0 mm.

Analysis of the trunk meat components designated 50%, 80% and 90% visual lean showed that despite rigorous slicing the observed chemical lean percentage of the two former categories was less than expected.

The application of the models for price setting of carcasses based on derived rather than nominal values is discussed.     

Estimation of variance components and genetic trends for twinning rate in Holstein dairy cattle of Iran

Calving records from the Animal Breeding Center of Iran, collected from January 1991 to December 2007 and comprising 1,163,594 Holstein calving events from 2,552 herds, were analyzed using a linear animal model, linear sire model, threshold animal model, and threshold sire model to estimate variance components, heritabilities, genetic correlations, and genetic trends for twinning rate in the first, second, and third parities. The overall twinning rate was 3.01%. Mean incidence of twins increased from first to fourth and later parities: 1.10, 3.20, 4.22, and 4.50%, respectively. For first-parity cows, a maximum frequency of twinning was observed from January through April (1.36%), and second- and third-parity cows showed peaks from July to September (at 3.35 and 4.55%, respectively). The phenotypic rate of twinning decreased from 1991 to 2007 for the first, second, and third parities. Sire predicted transmitting abilities were estimated using linear sire model and threshold sire model analyses. Sire transmitting abilities for twinning rate in the first, second, and third parities ranged from −0.30 to 0.42, −0.32 to 0.31, and −0.27 to 0.30, respectively. Heritability estimates of twinning rate for parities 1, 2, and 3 ranged from 1.66 to 10.6%, 1.35 to 9.0%, and 1.10 to 7.3%, respectively, using different models for analysis. Heritability estimates for twinning rate, obtained from the analysis of threshold models, were greater than the estimates of linear models. Solutions for age at calving for the first, second, and third parities demonstrated that cows older at calving were more likely to have twins. Genetic correlations for twinning rate between parities 2 and 3 were greater than correlations between parities 1 and 2 and between parities 1 and 3. There was a slightly increasing trend for twinning rate in parities 1, 2, and 3 over time with the analysis of linear animal and linear sire models, but the trend for twinning rate in parities 1, 2, and 3 with threshold animal model analysis was decreased over the years. There was a significant decreasing trend for twinning rate in parities 1 and 2 over time with the threshold sire model analysis, but the genetic trend for twinning rate in parity 3 with this model of analysis was significant and positive. In general, there were increasing genetic trends for twinning rate from parities 1 through 3 using different models of analysis.     

Discoloration and mineralization of Orange II using different heterogeneous catalysts containing Fe: a comparative study

Four heterogeneous catalysts containing Fe including a bentonite-clay-based Fe nanocomposite (Fe-B), hematite (alpha-Fe2O3), amorphous FeOOH, and calcined FeOOH (denoted as FeOOH-M) were employed for the photo-Fenton discoloration and mineralization of 0.2 mM Orange II in the presence of 10 mM H2O2 and 8 W UVC at two different initial solution pH values (3.0 and 6.6). It was found that, at an initial solution pH of 3.0, their photocatalytic activities follow the order Fe-B > FeOOH, FeOOH-M > alpha-Fe2O3. When the Fe-B nanocomposite, FeOOH, and FeOOH-M were used as heterogeneous catalysts, both heterogeneous and homogeneous photo-Fenton reactions were responsible for the discoloration and mineralization of 0.2 mM Orange II because homogeneous photo-Fenton reaction occurred due to the presence of Fe ions leached from the catalysts. At an initial solution pH of 6.6, their photocatalytic activities still follow the order Fe-B > FeOOH, FeOOH-M > alpha-Fe2O3. However, only heterogeneous photo-Fenton reaction accounted for the discoloration and mineralization of 0.2 mM Orange II because Fe leaching from the catalysts was significantly depressed. In the case of alpha-Fe2O3 as a catalyst, whether at an initial solution pH of 3.0 or 6.6, only heterogeneous photo-Fenton reaction happened for the discoloration and mineralization of 0.2 mM Orange II because Fe leaching from the catalyst is negligible. The apparent discoloration kinetics of Orange II with the four catalysts at two different initial solution pH values was also investigated.     

Estimating variance components and breeding values for number of oocytes and number of embryos in dairy cattle using a single-step genomic evaluation

Reproductive technologies such as multiple ovulation and embryo transfer (MOET) and ovum pick-up (OPU) accelerate genetic improvement in dairy breeding schemes. To enhance the efficiency of embryo production, breeding values for traits such as number of oocytes (NoO) and number of MOET embryos (NoM) can help in selection of donors with high MOET or OPU efficiency. The aim of this study was therefore to estimate variance components and (genomic) breeding values for NoO and NoM based on Dutch Holstein data. Furthermore, a 10-fold cross-validation was carried out to assess the accuracy of pedigree and genomic breeding values for NoO and NoM. For NoO, 40,734 OPU sessions between 1993 and 2015 were analyzed. These OPU sessions originated from 2,543 donors, from which 1,144 were genotyped. For NoM, 35,695 sessions between 1994 and 2015 were analyzed. These MOET sessions originated from 13,868 donors, from which 3,716 were genotyped. Analyses were done using only pedigree information and using a single-step genomic BLUP (ssGBLUP) approach combining genomic information and pedigree information. Heritabilities were very similar based on pedigree information or based on ssGBLUP [i.e., 0.32 (standard error = 0.03) for NoO and 0.21 (standard error = 0.01) for NoM with pedigree, 0.31 (standard error = 0.03) for NoO, and 0.22 (standard error = 0.01) for NoM with ssGBLUP]. For animals without their own information as mimicked in the cross-validation, the accuracy of pedigree-based breeding values was 0.46 for NoO and NoM. The accuracies of genomic breeding values from ssGBLUP were 0.54 for NoO and 0.52 for NoM. These results show that including genomic information increases the accuracies. These moderate accuracies in combination with a large genetic variance show good opportunities for selection of potential bull dams.     

Clinical mastitis in Norwegian cattle: frequency, variance components, and genetic correlation with protein yield.

Records of clinical mastitis in first lactation Norwegian Cattle from 1978 onward were analyzed. Variance components for clinical mastitis were estimated with a linear sire model using records of more than 1.2 million cows from 2043 sires, resulting in heritability estimates of 0.035. Different strategies for extracting data gave very similar results, and estimated heritability for mastitis was the same with univariate and bivariate (with protein yield) analyses, which indicates that selection bias caused by correlated responses from other traits in the breeding goal is not a problem with this data set. The estimated genetic correlation between clinical mastitis and protein yield is 0.25.     

Short communication: Correlation between within-herd antibody-prevalence and bulk tank milk antibody levels to Mycobacterium avium ssp. paratuberculosis using 2 commercial immunoassays

The objective of this study was to determine the correlation between the results obtained with the ELISA technique for antibodies to Mycobacterium avium ssp. paratuberculosis in serum and bulk tank milk at the herd level. For this purpose, 203 samples of bulk tank milk were analyzed with 2 commercial ELISA from dairy herds with a prevalence of seropositive animals that was also determined. In regard to the reference test (results in blood serum), the sensitivity of the bulk tank milk test to detect high-positive herds (≥10% seroprevalence) ranged from 85.7 to 71.4%. The specificity to detect herds with no seropositive animals ranged from 70.5 to 53%. In a quantitative approach, Pearson correlation coefficients, reported as a measure of the linear association between herd seroprevalences and transformed optical density values recorded in bulk tank milk, were 0.39 and 0.54 for the studied ELISA. Although the test results were relatively fairly correlated with the within-herd prevalence, the practical utility of bulk tank milk testing for Mycobacterium avium ssp. paratuberculosis seems limited, especially regarding specificity.     

A study of assessors'' performance using graphical methods

The performance of a sensory panel is studied through analysis of variance and in particular the assessors × products interaction. A graphic can illustrate the partitioning of the interaction by a sum of distances between the assessors. The decomposition of the sum of the product effect plus the interaction allows a vector representation of the assessors. These vectors are classified with an original method in order to point out homogeneous sub-panels. The new classification allows aggregation of groups only when all the correlations between assessors are greater than a threshold.     

Estimation of metabolisable energy for ruminants by near infrared reflectance photometry using multivariate methods

Partial least squares calibration is used to relate in-vivo metabolisable energy for ruminants to N I R spectral data. The accuracy of predictions is compared with metabolisable energy estimated by rumen digestible organic matter in vitro. The measurement accuracy is in favour of the biological method. This is probably due to the lack of specificity of the N I R technique, ie chemical compounds that are different to rumen bacteria appear to the NIR spectrometer to be similar. This means that although a high precision is obtained the prediction accuracy is lessened as a result of low spectral selectivity. If sampling error and speed of analysis also are considered, the advantage of N I R spectroscopy becomes apparent.     

Grapevine productivity and yield components: A case study using field vines of Zante currant

Yield components of the parthenocarpic cultivar Zante were analysed for five vineyards of diverse age and management. The data was obtained as part of an experiment to improve fruit set and yield by applying combinations of gibberellin and 2-chloroethyltrimethyl ammonium chloride or 4-chlorophenoxyacetic acid. Four of the vineyards were located in the Brockman valley north of Perth, Western Australia, two of these were irrigated, one was rain fed and one received supplementary flood irrigation. The fifth lay in an adjacent area of coastal sand plain, at the foot of the Darling scarp, and was irrigated. The vines were aged from 6 to 50 years.
Principal component analysis showed that vine age was negatively correlated with vigour (pruning weight) and with berry number per bunch. Vine age however was not strongly related to either yield or yield components (bunch number and berry volume). Sugar concentration was negatively correlated with all yield components but imprecisely modelled based on any combination of the measured variables. Berry number per vine appeared to be the underlying factor determining 'sink' strength though this was inextricably confounded with bunch number per vine. Interpretation of the data leads to the conclusion that increased berry volume is an inefficient means of increasing dried yield. This conclusion argues for caution in the application of plant growth regulators that act primarily to increase berry volume.
Yield of sugar per vine was accurately modelled based on second order relationships with bunch number per vine, berry number per bunch, berry volume and pruning weight. Vine age also showed a second order relationship to yield although the range was relatively small. The observations are considered in terms of developing strategies for maximising dried yield and devising mathematical models to account for photoassimilate (dry matter) partitioning in Vitis .     

Radio frequency reheating behavior in a heterogeneous food: A case study of pizza

Radio frequency (RF) energy could rapidly raise the material bulk temperature with deep power penetration and high energy efficiency. Although many studies on RF treatments have been carried out on different agricultural commodities or food, application of RF energy for studying heating behavior of heterogeneous food matrix is limited. Pizza is typically a heterogeneous food model with a base, cheese matrix and added toppings, and has been rarely evaluated for RF reheating. This study was aimed at using computer simulation for evaluating the RF reheating uniformity of a typical model pizza after baking based on measured thermal and dielectric properties (DPs) of its components (pizza base, cheese, salami and onion). The validation experiments were carried out up to a maximum reheating temperature of 85 °C in a 6 kW, 27.12 MHz RF system. The results showed that both dielectric constant and loss factor of pizza components increased with temperature, and at elevated temperatures, DP values for salami were the highest cheese, onion and pizza base. Both computer simulation and experiment provided similar temperature-time histories (with the maximum RMSE of 0.034 °C) in pizza base, cheese, salami and onion after RF reheating for 7.33 min. The fast RF reheating rate was observed in cooked salami both from the temperature-time history and predicted temperature distribution due to closed dielectric loss to constant value. The high sample temperature resulted in low moisture content. The RF heating uniformity could be improved by moving or rotating pizza and specially locating components in the further studies.     

不同方法定量检测花椒油中花椒麻味物质的效果比较研究

本文应用气相色谱法、高效液相色谱法、分光光度计法对花椒麻味物质的含量进行了定量检测分析,并比较了三种检测方法的技术指标以及在实际检测中的效果。结果发现三种检测方法在实际应用中各有其自身的优缺点,从技术指标来看,气相色谱法、高效液相色谱法要优于分光光度计法,在实际的样品检测中,前两种方法也要比分光光度计法更加准确,但相比较而言分光光度计法的使用成本要低于前两种检测方法。通过对三种方法的差异显著性分析发现,在检测不同样品时,三种方法的差异显著性也存在不同。在实际运用中应该从对结果的准确性与实际经济性的比较中进行考虑选择合理的检测方法。      

Optimization of hot water extraction of roselle juice using response surface methodology: a comparative study with other extraction methods

Roselle has regained the attention of many fruit juice manufacturers in Malaysia as a product that contains high ascorbic acid and anthocyanins. However, ascorbic acid and anthocyanin pigments can be easily destroyed during processing of fruit juice. Therefore, in the present study, the effects of different processing methods, namely hot water extraction (HWE), hot water blending, cold water blending and screw press, on the changes in anthocyanins and ascorbic acid contents of roselle juice were evaluated. The anthocyanins and ascorbic acid contents of roselle were determined using the pH differential method and high‐performance liquid chromatography respectively. The physico‐chemical characteristics and sensory properties of roselle juice were also evaluated. The results of the study indicate that the HWE method is the most effective extraction method, resulting in high anthocyanins and ascorbic acid contents of 43 g l^?1 (as delphinidin‐3‐glucoside) and 2.34 g kg^?1 respectively. The optimum juice extraction conditions were 3.5 h at 60 °C. Copyright © 2003 Society of Chemical Industry     

The diagnosis of subclinical mastitis by redefinition of the interquarter ratio and definition of the interquarter variation using analysis of variance methods

A definition is proposed for the interquarter ratio of markers of inflammation in the bovine mammary gland which in contrast to present measurement procedures has well-defined distributional properties and thus facilitates statistical analysis. Our proposal of an interquarter ratio is equally applicable to evaluation of both single and multi-sample experiments. Finally, we define a new index for diagnosis of subclinical mastitis at the cow level, the interquarter variation, which assesses the degree of dispersion of the four quarter levels for values of any continuous inflammatory marker.     

Stillbirth (co)variance components for a sire-maternal grandsire threshold model and development of a calving ability index for sire selection

(Co)variance components for stillbirth in US Holsteins were estimated under a sire-maternal grandsire threshold model using subsets of data from the national calving ease database, which includes over 6 million calving records with associated stillbirth scores. Stillbirth was coded as a binomial trait indicating whether the calf was alive 48 h postpartum. Records were selected for calves whose sire and maternal grandsire (MGS) were among the 2,600 most frequently appearing bulls (2,578 sires and 2,586 MGS). Herd-years were required to contain at least 20 records and only single births were used. After editing, the data set included 2,083,979 calving records from 5,765 herds and 33,304 herd-years. Six sample datasets of approximately 250,000 records each were created by randomly selecting herd codes. Quasi-REML and Bayesian approaches were used to estimate (co)variance components from each sample. The model included fixed year-season, parity-sex, birth year group of sire, and birth year group of MGS effects and random herd-year, sire, MGS, and residual effects. Quasi-REML and Bayesian analyses produced similar results, although the Bayesian estimates were slightly larger. Marginal posterior means (and standard deviations) from the Bayesian analysis averaged 0.0085 (0.0015), 0.0181 (0.0020), 0.0872 (0.0538), and 0.00410 (0.0001) for sire, MGS, and herd-year variances and the sire-MGS covariance, respectively. Mean direct and maternal heritabilities were 0.030 (0.003) and 0.058 (0.005), respectively, and the mean genetic correlation between the 2 effects was −0.02 (0.16). A calving ability index combining stillbirth (SB) and calving ease (CE) was developed for inclusion in the Lifetime Net Merit index. The index was calculated as −4(sire CE)−3(daughter CE)−4(sire SB) −8(daughter SB).     

A comparison of three different isotopic methods for measuring body components of sheep.

A comparison has been made of the three isotopes, deuterium, tritium and ⁴²K for the measurement of body composition of wether sheep by the dilution technique. Eighteen sheep of a small breed were divided into three groups of six and given either a high, maintenance or low plane of nutrition. After an interval of 6-9 weeks the sheep were injected with the three isotopes, slaughtered within 24 h and composition determined directly by chemical analyses. The live weight at the time of slaughter ranged from 21.6 to 34.8 kg and the fat content from 9.9 to 19.7% of live weight. Tritiated water under-estimated total body water by 4.6 ± 3.1 g per 100 g. The overall mean for deuterium oxide agreed closely with that for total body water but the actual results were a little more variable than those for tritiated water. Mean exchangeability of potassium for all wethers was 89.4% and a very close relationship was found between exchangeable potassium and total body potassium. For the prediction of empty body nitrogen, the inclusion of either tritiated water space, deuterium oxide space or exchangeable potasium along with live weight in a multiple regression improved the precision over the use of live weight alone. Similarly multiple regressions including either deuterium or tritium space with live weight predicted body fat content with significantly greater precision than live weight alone and tritiated water was significantly better than deuterium oxide for this purpose. Either tritiated water space or exchangeable potassium with live weight significantly improved the prediction of fat-free empty body weight over the use of live weight alone, and tritiated water was significantly better than ⁴²K for this predictive purpose.