C. R. Henderson, the statistician; and his contributions to variance components estimation.

C. R. Henderson's 1953 Biometrics paper "Estimation of Variance and Covariance Components" is an outstanding landmark in the discipline of statistics. It sets out the very first ideas of how to estimate variance components from unbalanced (unequal subclass numbers) data in situations more complicated than the one-way classification (completely randomized design). As such it had three important, long-lasting impacts. First, it provided methods for actually using unbalanced data, even in large quantity, for estimating variance components. And this has played a tremendous role in population genetics and in animal breeding where the use of estimated variance components is vital to the application of selection theory and selection index techniques. Second, that 1953 paper stimulated numerous statisticians to become interested in random effects, mixed models, and variance components estimation, with such statistical greats as H. O. Hartley and C. R. Rao making contributions in the late 1960s and early 1970s. By then, improved methods of estimating variance components from unbalanced data had been developed, namely maximum likelihood (ML) and restricted maximum likelihood (REML). Once computing power had expanded to the point where these methods became feasible, Henderson made notable contributions to these methods, allied to his two great interests: animal breeding and feasible computing procedures. For both of these, his mixed model equations were a salient feature. Third, these methods reached a wide audience of geneticists and statisticians.     

Maximum Likelihood Estimation of Variance Components in Dairy Cattle Breeding Research

A common problem in animal breeding research is estimation of variance and covariance components. Usual methods of estimation have been described by Henderson in 1953. In 1973 Henderson reported a computing algorithm for maximum likelihood estimation of variance components which may have been overlooked. This note reviews the Henderson computing technique and illustrates application of maximum likelihood estimation to two specific types of models for large, unbalanced data sets.     

A 100-Year Review: Methods and impact of genetic selection in dairy cattle—From daughter–dam comparisons to deep learning algorithms

In the early 1900s, breed society herdbooks had been established and milk-recording programs were in their infancy. Farmers wanted to improve the productivity of their cattle, but the foundations of population genetics, quantitative genetics, and animal breeding had not been laid. Early animal breeders struggled to identify genetically superior families using performance records that were influenced by local environmental conditions and herd-specific management practices. Daughter–dam comparisons were used for more than 30 yr and, although genetic progress was minimal, the attention given to performance recording, genetic theory, and statistical methods paid off in future years. Contemporary (herdmate) comparison methods allowed more accurate accounting for environmental factors and genetic progress began to accelerate when these methods were coupled with artificial insemination and progeny testing. Advances in computing facilitated the implementation of mixed linear models that used pedigree and performance data optimally and enabled accurate selection decisions. Sequencing of the bovine genome led to a revolution in dairy cattle breeding, and the pace of scientific discovery and genetic progress accelerated rapidly. Pedigree-based models have given way to whole-genome prediction, and Bayesian regression models and machine learning algorithms have joined mixed linear models in the toolbox of modern animal breeders. Future developments will likely include elucidation of the mechanisms of genetic inheritance and epigenetic modification in key biological pathways, and genomic data will be used with data from on-farm sensors to facilitate precision management on modern dairy farms.     

C. R. Henderson: farm boy, athlete, and scientist.

Charles R. Henderson was proud to be a product of a farm in Page County, Iowa. He was a one man track team in Coin, Iowa, and a brilliant student. He became a world class competitor in track at Iowa State College and, at the same time, compiled a top academic record. His early experiences set the stage for the exceptional contributions of his animal breeding career, which did not begin until he was nearly 40 yr of age, but which spanned 40 yr when he was the acknowledged leader in development of statistical methodology applied to animal breeding. His career goals were to find the best possible ways to analyze data and to provide the best genetic evaluations to the livestock industry. If the best could not be done because of computational limitations, then he would pragmatically work to find the best way that was possible. Only his interest in Cornell hockey overshadowed his enjoyment in listening to classical music. He was an avid sports fan, especially for the St. Louis Cardinals or any midwestern team against the New York Yankees. Midwestern trips during the weeks when the Drake Relays were held were as often as possible. Henderson's acknowledged scientific hero was Jay L. Lush, with whom he studied during his Ph.D. program at Iowa State College and with whom he shared similar talents and the intuition that made both of them leaders in the field of animal breeding.     

C. R. Henderson: contributions to the dairy industry.

Through C. R. Henderson's position and the application of his knowledge, he had a major influence on genetic improvement in dairy cattle beginning in the 1950s. He developed herdmate comparisons in the United States. The first extensive program using pedigree selection and progeny testing of sires for use in AI was because of his suggestion. This program established the direction of dairy cattle improvement that still continues. He developed BLUP and discovered how to write the inverse of an additive genetic relationship matrix, A-1, without inverting the matrix. These accomplishments had a major impact on evaluation methods of dairy cattle and other livestock species. Use of BLUP and A-1 are standards for evaluation of breeding values all over the world. His pioneering work in estimation of components of variance and analyses of unbalanced data were also of primary importance for animal evaluation and many other applications. Henderson made a major contribution to mankind.     

Short communication: Alteration of priors for random effects in Gaussian linear mixed models

Linear mixed models, for which the prior multivariate normal distributions of random effects are assumed to have a mean equal to 0, are commonly used in animal breeding. However, some statistical analyses (e.g., the consideration of a population under selection into a genomic scheme breeding, multiple-trait predictions of lactation yields, and Bayesian approaches integrating external information into genetic evaluations) need to alter both the mean and (co)variance of the prior distributions and, to our knowledge, most software packages available in the animal breeding community do not permit such alterations. Therefore, the aim of this study was to propose a method to alter both the mean and (co)variance of the prior multivariate normal distributions of random effects of linear mixed models while using currently available software packages. The proposed method was tested on simulated examples with 3 different software packages available in animal breeding. The examples showed the possibility of the proposed method to alter both the mean and (co)variance of the prior distributions with currently available software packages through the use of an extended data file and a user-supplied (co)variance matrix.     

Solving large mixed linear models using preconditioned conjugate gradient iteration

Continuous evaluation of dairy cattle with a random regression test-day model requires a fast solving method and algorithm. A new computing technique feasible in Jacobi and conjugate gradient based iterative methods using iteration on data is presented. In the new computing technique, the calculations in multiplication of a vector by a matrix were recorded to three steps instead of the commonly used two steps. The three-step method was implemented in a general mixed linear model program that used preconditioned conjugate gradient iteration. Performance of this program in comparison to other general solving programs was assessed via estimation of breeding values using univariate, multivariate, and random regression test-day models. Central processing unit time per iteration with the new three-step technique was, at best, one-third that needed with the old technique. Performance was best with the test-day model, which was the largest and most complex model used. The new program did well in comparison to other general software. Programs keeping the mixed model equations in random access memory required at least 20 and 435% more time to solve the univariate and multivariate animal models, respectively. Computations of the second best iteration on data took approximately three and five times longer for the animal and test-day models, respectively, than did the new program. Good performance was due to fast computing time per iteration and quick convergence to the final solutions. Use of preconditioned conjugate gradient based methods in solving large breeding value problems is supported by our findings.     

Integration of Interbull's multiple across-country evaluation approach breeding values into the multiple-trait single-step random regression test-day genetic evaluation for yield traits of Australian Red breeds

Interbull's multiple across-country evaluaftion provides national breeding organizations with breeding values for internationally used bulls, which integrate performance data obtained in different breeding populations, environments, and production systems. However, breeding value-based selection decisions on domestic individuals born to foreign sires can only benefit from Interbull breeding values if they are integrated such that their information can contribute to the breeding values of all related domestic animals. For that purpose, several methods have been proposed which either model Interbull breeding values as prior information in a Bayesian approach, as additional pseudo data points, or as correlated traits, where these methods also differ in their software and parameterization requirements. Further, the complexity of integration also depends on the traits and genetic evaluation models. Especially random regression models require attention because of the dimensionality discrepancy between the number of Interbull breeding values and the number of modeled genetic effects. This paper presents the results from integrating 16,063 Interbull breeding values into the domestic single-step random regression test-day model for milk, fat, and protein yield for Australian Red dairy cattle breeds. Interbull breeding values were modeled as pseudo data points with data point-specific residual variances derived within animal across traits, ignoring relationships between integrated animals. Results suggest that the integration was successful with regard to alignment of Interbull breeding values with their domestic equivalent as well as with regard to the individual and population-wide increase in reliabilities. Depending on the relationship structure between integration candidates, further work is required to account for those relationships in a computationally feasible manner. Other traits with separate parity effects nationally could use a similar approach, even if not modeled with a test-day model.     

Effect of Selected Pretreatments on Convective Drying Process of Blueberries (var. O’neil)

The effects of different pretreatments on the convective drying kinetics of blueberries (var. O??Neil) at 70?°C were investigated. The sodium hydroxide, enzymatic, microwaves, and high hydrostatic pressure pretreatments were applied and compared with control samples (non-pretreated). In order to simulate experimental drying data, the following mathematical models were selected: logarithmic, two terms, modified Henderson?CPabis, Midilli?CKucuk, and Weibull. Fick??s second law of diffusion was applied to determine the water diffusion coefficient for all the treatments. All pretreatments decreased significantly the drying time of the control samples. High hydrostatic pressures together with microwave pretreatments presented lower drying times than non-pretreated samples. Moreover, based on statistical test results, Weibull and modified Henderson?CPabis models presented the best fit for the experimental drying curves. Thus, both models can be satisfactorily applied to estimate the drying time of blueberries as well as to evaluate the effects of different pretreatments on fruit drying rates.     

Short communication: genetic evaluation of the interval from first to last insemination with survival analysis and linear models

Sire breeding values for the interval between the first and last insemination were predicted using 4 proportional hazards models (survival analyses) and 2 linear mixed models to determine which would result in a more accurate genetic evaluation. A stochastic simulation describing the reproductive cycle of first-parity cows was conducted, in which true breeding values for conception rate were created. The model included the effects of sire and herd. The highest correlations between true breeding values for conception rate and breeding values for the interval between first and last insemination predicted by the survival analysis model and the linear model were 0.803 and 0.744, respectively. The results showed that when pregnancy status was known, survival models were more accurate than linear models to predict breeding values for conception rate when using observations on the interval between first and last insemination.     

The future role of molecular genetics in the control of meat production and meat quality

Current applications of quantitative genetics for genetic improvement of farm animals rely on sophisticated statistical procedures applied to failly simple genetic models and have been effective in producing large cumulative genetic changes in many traits. Recent advances in molecular genetics provide a potential for renewed methods in animal breeding. The two main possible fields of application of recombinant DNA methologies, i.e. marker-assisted breeding and gene transfer, are reviewed. Use of genetic markers as an aid to present breeding practice appears to be rather promising, but research effort remains to be done before implementation of marker-assisted breeding schemes on a significant scale. It is not, at this stage, obvious that transgenesis will be an important way of improving meat-producing animals, at least in the near future.     

Short communication: Genomic prediction using different single-step methods in the Finnish red dairy cattle population

Single-step genomic prediction models utilizing both genotyped and nongenotyped animals are likely to become the prevailing tool in genetic evaluations of livestock. Various single-step prediction models have been proposed, based either on estimation of individual marker effects or on direct prediction via a genomic relationship matrix. In this study, a classical pedigree-based animal model, a regular single-step genomic BLUP (ssGBLUP) model, algorithm for proven and young (APY) with 2 strategies for choosing core animals, and a single-step Bayesian regression (ssBR) model were compared for 305-d production traits (milk, fat, protein) in the Finnish red dairy cattle population. A residual polygenic effect with 10% of total genetic variance was included in the single-step models to reduce inflation of genomic predictions. Validation reliability was calculated as the squared Pearson correlation coefficient between genomically enhanced breeding value (GEBV) and yield deviation for masked records for 2,056 validation cows from the last year in the data set investigated. The results showed that gains of 0.02 to 0.04 on validation reliability were achieved by using single-step methods compared with the classical animal model. The regular ssGBLUP model and ssBR model with an extra polygenic effect yielded the same results. The APY methods yielded similar reliabilities as the regular ssGBLUP and ssBR. Exact prediction error variance of GEBV could be obtained by ssBR to avoid any approximation methods used for ssGBLUP when inversion left-hand side of mixed model equations is computationally infeasible for large data sets.     

食品致敏性评价的动物和细胞模型研究进展

食品过敏原致敏性的评价方法多种多样,而动物模型和细胞模型的致敏性评价是常用的方法之一。小鼠模型拥有繁殖周期短和遗传基因可操作性等优点,但却有着遗传背景差异性、伦理上等局限性;而体外培养细胞模型正好弥补了动物模型上的不足从而反映出机体中过敏反应从大体到细节上的变化。虽然目前有许多评价食品致敏性的方法,如常用的胃肠道消化实验法和热稳定性试验法,然而这些方法都存在着一定的局限性。本综述概括了动物和细胞模型在目前研究中的优缺点以及与其他实验方法的相互关系,客观分析其在评估食品过敏原的致敏性中的作用。     

The Contributions of A. E. Freeman

Albert Eugene (Gene) Freeman completed his B.S. and M.S. degrees at University of West Virginia in 1952 and 1954, and his Ph.D. at Cornell University in 1957. In 1957, he started his professional career at Iowa State University and since 1978 has served as Charles F. Curtiss Distinguished Professor of Agriculture in the Animal Science Department. His major contributions have been the graduate students he trained; the research he has guided, conducted, and reported; the counsel on genetic improvement he has offered; and leadership of industry and academia he has provided. Freeman guided more than 55 students through Ph.D. and/or M.S. programs. These students came from many different parts of the world and a number are now in positions of leadership. They are primarily employed on university faculties and in the genetic improvement industry. Freeman's research has covered a vast range of topics and has involved a number of experimental approaches. His research has formed the basis of major improvements in dairy cattle breeding practices. He has provided leadership to the animal breeding group at Ames, the long-term regional breeding projects conducted across the Unitred States, the American Dairy Science Association, and the World Congress on Genetics Applied to Livestock Production. In recognition of his many accomplishments, he has received numerous major awards from a variety of organizations. Freeman has made a significant impact on the genetic improvement of food-producing animals worldwide through his research and counsel and through the students he has trained.     

Correlated responses in reproduction accompanying selection for milk yield in Jerseys.

Reproductive traits of heifers and primiparous cows from a long-term selection project were analyzed to determine correlated response to single-trait selection for milk yield. Data were from 1056 daughters (765 selection, 291 control) of 37 bulls (17 selection, 20 control). Traits in heifers were ages at first observed estrus and at first breeding, services to conception, interval from first service to conception, and length of first gestation. Traits in primiparous cows were ages at first calving and at first breeding, after calving; services to conception; length of second gestation; and intervals from calving to first observed estrus, to first breeding, and to conception, from first service to conception, and from first to second calving. Analyses for services to conception in heifers and primiparous cows were categorical using models containing genetic group and generation. Analyses of other traits were by linear mixed models using fixed effects of genetic group, generation within group, and year-season of birth. Sires were assumed random and nested within genetic group. The mean square for sires within group was used to test for group differences. No significant differences were found between genetic groups in traits measured in heifers; however, the interval from first service to conception approached significance (control superior). In primiparous cows, differences between genetic groups were significant for the intervals of calving to first breeding and calving to conception and for length of second gestation (control superior). For other traits, reproductive performance of the control was better but not significantly different from that of the selected group. Reproductive performance should be monitored during selection for high milk yield.     

Survival analysis applied to genetic evaluation for female fertility in dairy cattle

The objective of this research was to study whether survival analysis results in a more accurate genetic evaluation for female fertility traits compared with the usual methodology based on linear models. The fertility trait studied was interval between calving and last insemination. A stochastic simulation describing the reproductive cycle of first-parity cows was done, in which true breeding values for conception rate were created. A model containing effects of sire and herd was used both with survival analysis and with mixed linear model analysis to predict sire breeding values. Correlations between true breeding values for conception rate and breeding values for calving to last insemination predicted by the best survival analysis model or the best linear model were 0.77 and 0.68, respectively. The results showed that when pregnancy status is known, survival analysis is a better method than linear models for genetic evaluation of conception rate when using observations on the interval between calving and last insemination.     

MOISTURE SORPTION CHARACTERISTICS of STARCH GELS. PART 1: MATHEMATICAL DESCRIPTION of EXPERIMENTAL DATA

The moisture sorption isotherms of potato starch, starch‐sugar and starch‐salt gels were determined using a gravimetric static method at 30, 45 and 60C, and over a range of relative humidities from 0.10 to 0.84. the starch gels exhibited Type II behavior, with incorporation of sugar or salt into the samples resulting in Type III form. the sorption capacity decreased with increasing temperature. the experimental data were analyzed using seven models; two‐parameter relationships (Halsey, Henderson, Smith), three‐parameter equations (Ferro‐Fontan, Guggenheim‐Anderson‐de Boer, modified‐Oswin) and four‐parameter equation (Peleg). the empirical Peleg equation and kinetic GAB model (parameters have physical significance) were found to be the most suitable for describing the sorption characteristics within the temperature range 30–60C and water activity range 0.05–0.95.     

Genetics—A tool to improve productivity and profitability

Until recently most international breeding programmes in dairy cattle have focused solely on milk production and have made large contributions to the rate of improvement in milk production but to the determinant of reproduction. Improved statistical techniques and computing resources as well as better phenotypic measurement tools have increased the ability to identify genetically superior animals. 'Omic' technologies have huge potential to offer in the near future to further improve genetic gains in productivity and profitability. However, maximum exploitation of these technologies can only be achieved if the basics of the most pertinent breeding goal and breeding programme are correct.     

Different methods to calculate genomic predictions--comparisons of BLUP at the single nucleotide polymorphism level (SNP-BLUP), BLUP at the individual level (G-BLUP), and the one-step approach (H-BLUP)

Several strategies to use genomic data in predictions have been proposed. The aim of this study was to compare different genomic prediction methods. The response variables used in the genomic predictions were deregressed proofs, which were derived from 2 estimated breeding value (EBV) data sets. The full EBV data set from March 2010 included the EBV for production and mastitis traits for all Nordic red bulls. The reduced data set included the same animals as the full data set, but the EBV were predicted from a data set that excluded the last 5 yr of observations. Genomic predictions were obtained using different BLUP models: BLUP at the single nucleotide polymorphism level (SNP-BLUP), BLUP at the individual level (G-BLUP), and the one-step approach (H-BLUP). For the selection candidate bulls, the SNP-BLUP and G-BLUP models gave the same direct genomic breeding values (e.g., correlation of direct genomic breeding values between SNP-BLUP and G-BLUP for protein was 0.99), but slightly different from genomic EBV obtained from H-BLUP (correlations of SNP-BLUP or G-BLUP with H-BLUP were about 0.96). For all traits, SNP-BLUP and G-BLUP gave the same validation reliability, whereas H-BLUP led to slightly higher reliability. Therefore, the results support a slight advantage of using H-BLUP for genomic evaluation.