Field Of Animal Breeding Research Articles

Inclusion of genetically identical animals to a numerator relationship matrix and modification of its inverse

In the field of animal breeding, estimation of genetic parameters and prediction of breeding values are routinely conducted by analyzing quantitative traits. Using an animal model and including the direct inverse of a numerator relationship matrix (NRM) into a mixed model has made these analyses possible. However, a method including a genetically identical animal (GIA) in NRM if genetic relationships between pairs of GIAs are not perfect, is still lacking. Here, we describe a method to incorporate GIAs into NRM using a K matrix in which diagonal elements are set to 1.0, off-diagonal elements between pairs of GIAs to (1-x) and the other elements to 0, where x is a constant less than 0.05. The inverse of the K matrix is then calculated directly by a simple formula. Thus, the inverse of the NRM is calculated by the products of the lower triangular matrix that identifies the parents of each individual, its transpose matrix, the inverse of the K matrix and the inverse of diagonal matrix D, in which the diagonal elements comprise a number of known parents and their inbreeding coefficients. The computing method is adaptable to the analysis of a data set including pairs of GIAs with imperfect relationships.

Scope of Process Patents in Farm Animal Breeding

The number of process patent applications concerning farm animal breeding is growing rapidly. Patent law is general in form and is seldom adapted to specific areas of innovation. It was initially created for the purpose of granting exclusive rights to technical inventions, and it was taken for granted that higher animals, food production and pharmaceuticals were too important for mankind to be included under exclusive private rights. Today, with patent law increasingly used in the animal sector, the question arises: how will the law apply to this particular field of innovation? The degree of legal uncertainty is particularly high because it is not clear how the courts of various countries will apply the general law to this particular field. Patent law has the potential to alter the existing legal conditions for competition and investments in the field of animal breeding, and thus merits greater attention among policy‐makers, animal breeders and farmers.

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.

EDITORIAL

Dear Readers, As you may have noted from the cover, from this issue onward the stewardship of the Journal of Animal Breeding and Genetics has passed from Georg Erhardt (Gießen, Germany) to Asko Mäki-Tanila (Jokioinen, Finland), thus marking a significant milestone in the Journal's history. Georg Erhardt steps down from his post as Executive Editor following 7 years of dedicated work on the journal. During his tenure, he accompanied editorially the growth of genomics, genetic diversity, computer-intensive methods, Bayesian applications and other modern technology used in animal breeding and genetics. Through his work, he has brought vision to the journal, publishing papers of high scientific import that have definitively furthered the research field of animal breeding. Moreover, he has mentored numerous authors through the sometimes tricky course of preparing their work for publication, and he deserves credit for the journal's significant increase in Impact Factor. On a different note, he inspired the change in cover design, reminiscent of cave paintings with an undercurrent of DNA. On behalf of Blackwell Verlag and the Editorial Board we give Georg Erhardt our heartfelt thanks and wish him great success in his future endeavours. Asko Mäki-Tanila will likely be a familiar figure to most of you due to his prominent position in research and his widely read articles, and indeed many of you will know him personally. We are extremely pleased to have won him for this demanding position and are confident that he will uphold the rigorous editorial standards of his predecessor. We eagerly anticipate the new benchmarks that Professor Mäki-Tanila will wish to set and the new topics he will address in the Journal. One innovation he will introduce in the next few months is an online submission and review system, essential to any scientific journal in this day and age. Please join us in welcoming him on board.

Characteristics of Convergence Curve of the PE Estimate of Variance Ratio in the Balanced Case

The pseudoexpectation (PE) methods are an iterative procedure for estimating variance components in the general mixed linear model. The computational loads in the PE methods are relatively small and the estimates converge faster, although the methods are an approximation to the restricted maximum likelihood (REML) procedure. In the field of animal breeding, it has been considered that the PE methods can be used in estimating from large data sets including no or weak influence of selection, or in obtaining initial values to use in the REML estimation. This paper reports some basic characteristics of the convergence curve of the PE variance ratio estimate in the case of balanced data. In the specific balanced case, the PE and REML estimates are identical, but their convergence curves are different. The ratios of the difference between the consecutive estimates in the ith and the i-1th rounds to that in the i+1th and the ith rounds vary, for instance, in the REML estimation using the expectation-maximization algorithm, while those with the PE methods take a constant value regardless of initial values and rounds of iteration. Hence, the PE curve of convergence can be exactly represented using the result for a geometric series. Consequently, the PE curve is equivalent to the curve assumed underlyingly in the extrapolation techniques, or the techniques of directly predicting the final value such as the Aitken extrapolation and the common intercept approach. In the unbalanced case, the property of this kind of the PE curve is no longer retained, and the degrees of discrepancies among the PE and the extrapolation estimates would be dependent on the structure of the data to be analyzed. When one wishes to accelerate convergence in the REML analysis of unbalanced data, it is important to notice that the PE and the extrapolation techniques each have the advantages and disadvantages for the purpose.

The EM-REML Iteration Equations for Estimation of Variance Components in a Sire and Dam Model.

Assuming a specific type of data in the field of animal breeding, the iteration equations based on the expectation-maximization algorithm are derived for the restricted maximum likelihood estimation of variance components in a Sire and Dam Model. The application of the iteration equations to the data leads to the same estimates of additive genetic and environmental variances as those under the lndividual Animal Model. With the procedure using the iteration equations, compared to the case for the lndividual Animal Model, the size of the coefficient matrix to be inverted of the mixed model equations relatively becomes small, and the speed of convergence of the estimates becomes rather fast. Consequently, the total computational burden to obtain the proper estimates of additive genetic and environmental variances is expected to be considerably reduced in the proposed procedure. A numerical illustration, comparing the proposed procedure with the lndividual Animal Model procedure, is given using simulated carcass data on beef cattle.

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.

家畜育種における多変量解析の応用

家畜育種における多変量解析の応用