Production and pedigree data of Iranian Holsteins were collected from 1991 to the end of 2001 on 45 herds in Isfahan province. Data on culled cows (birth and culling dates) were used to estimate the effect of age at first calving on total lifetime and productive life; and the effect of age at first calving on first-lactation yields was estimated from corrected (2× 305 d) firstlactation records of 12,082 dairy heifers that calved between 1995 and 2001. The estimate of heritability of age at first calving obtained in this study was 0.086. This low heritability indicates the importance of using available information on relatives for selection on this trait. Age at first calving significantly affected all the traits investigated, including: milk yield, fat yield, fat percentage, lifetime, and productive life. Results indicated a positive effect of reducing age at first calving on milk yield and productive life, although reducing age at first calving to 21 mo of age had a negative effect on yields of milk and milk fat. Lifetime did not show a similar trend with age at first calving. However, a slight positive phenotypic correlation (0.052) was detected between age at first calving and lifetime. We conclude that due to negative effects of age at first calving on productive life and because of optimum age at first calving for milk yield was 24 mo in this study, the reduction of age at first calving to 24 mo of age could be an effective management practice.

The inverses of the pedigree and genomic relationship matrices (A, G) are required for single-step GBLUP (ssGBLUP). While, inverting A is possible for millions of animals at a linear cost, inverting G has a cubic cost and feasible for at most 150,000 animals, using the current conventional algorithms. The algorithm for proven and young (APY) provides approximations of the regular ssGBLUP by splitting genotyped animals into core and noncore groups, with computational costs being cubic for core and linear for noncore animals. The data consisted of 9,406,096 animals in the pedigree, 6,243,753 weaning weight phenotypes, and 46,949 genotyped animals from 5 breeds, composites, and animals with missing breed information from New Zealand. Aiming to find a core sample for a multibreed sheep population that can provide evaluations similar to those from the regular ssGBLUP, different core types, and core sizes were studied. Core types random, composite, oldest, youngest, the most inbred animals in G (GINB), and in A (AINB) were studied in 5K, 10K, and 20K core sizes (K = 1,000). Romney core was studied in 5K and 10K, and Coopworth-Perendale core was studied in 5K. Correlation and regression coefficient (slope) between GEBV from the non-APY and the APY analyses, as indicators for consistency with non-APY and bias from non-APY, showed a large impact of APY on noncore and a small impact on nongenotyped animals. Breed-based 5K cores resulted in large bias from non-APY even for nongenotyped animals. Random and GINB at 20K core size resulted in the highest consistency with non-APY and the lowest bias from non-APY. However, GINB did not perform as well as Random at lower core sizes. The number of animals from a breed in the core sample was very important for the evaluation of that breed. We observed that cores without Texel or Highlander animals resulted in poor evaluations for those breeds. Solving the mixed model equations, within core type, the smallest core size, and within core size, Random core converged in the least number of iterations. However, APY per se did not necessarily reduce the solving time. Random cores performed the best, as they could give a good coverage on the generations and breeds, representative for the genotyped population. Core size 20K performed better than 5K and 10K, and the optimum core size was found to be 18.8K, according to the eigenvalue decomposition of G.

The need to implement a method that can handle multiple traits per country in international genetic evaluations is evident. Today, many countries have implemented multiple-trait national genetic evaluations and they may expect to have their traits simultaneously analyzed in international genetic evaluations. Traits from the same country are residually correlated and the method currently in use, single-trait multiple across-country evaluation (ST-MACE), cannot handle nonzero residual correlations. Therefore, multiple-trait, multiple across-country evaluation (MT-MACE) was proposed to handle several traits from the same country simultaneously. To test the robustness of MT-MACE on real data, female fertility was chosen as a complex trait with low heritability. Data from 7 Holstein populations, 3 with 2 traits and 4 with 1 trait, were used. The differences in the estimated genetic correlations by MT-MACE and the single ST-MACE analysis (average absolute deviation of 0.064) were due to the bias of considering several traits from the same country in the ST-MACE analysis. However, the differences between the estimated genetic correlations by MT-MACE and multiple ST-MACE analyses avoiding more than one trait per country in each analysis (average absolute deviation of 0.066) were due to the lack of analysis of the correlated traits from the same country together and using the reported within-country genetic correlations. Applying MT-MACE resulted in reliability gain in international genetic evaluations, which was different from trait to trait and from bull to bull. The average reliability gain by MT-MACE over ST-MACE was 3.0 points for domestic bulls and 6.3 points for foreign bulls. Even countries with 1 trait benefited from the joint analysis of traits from the 2-trait countries. Another superiority of MT-MACE over ST-MACE is that the bulls that do not have national genetic evaluation for some traits from multiple trait countries will receive international genetic evaluations for those traits. Rank correlations were high between ST-MACE and MT-MACE when considering all bulls. However, the situation was different for the top 100 bulls. Simultaneous analysis of traits from the same country affected bull ranks, especially for top 100 bulls. Multi-trait MACE is a recommendable and robust method for international genetic evaluations and is appropriate for handling multiple traits per country, which can increase the reliability of international genetic evaluations.

For the past few decades, the international exchange of genetic materials has accelerated. This acceleration has been more substantial for dairy cattle compared with other species. The industry faced the need to put international genetic evaluation (IGE) systems in place. The Interbull Centre has been conducting IGE for various dairy cattle breeds and traits. This study reviews the past and the current status of IGE for dairy cattle, emphasizing the most prominent and wellestablished method of IGE, namely multiple acrosscountry evaluation (MACE), and the challenges that should be addressed in the future of IGE. The first IGE methods were simple conversion equations. Only a limited number of common bulls between pairs of countries were considered. These bulls were a biased sample of highly selected animals, with their daughters under preferential treatment in the importing countries. Genetic relationships among animals were not considered either. The MACE method was the first IGE method based on mixed-model theory that could handle genotype by environment interaction (G × E) between countries. The G × E between countries is handled by treating the same trait in different countries as different traits, with genetic correlations less than unity between the traits. The G × E between countries is not solely due to different genetic expressions in different environments (countries), but is also attributable to different units or ways of measuring the trait, data editing, and statistical approaches and models used in different countries. The MACE method also considers different genetic means, genetic groups for unknown parents, heterogeneous genetic and residual variances among countries, and heterogeneous residual variances (precision weights for observations) within countries. Other IGE methods that came after MACE are rooted in MACE. The genomic revolution of the industry created new needs and opportunities. However, an unwanted aspect of it was genomic preselection bias. Genomic preselection causes directional information loss from pre-culled animals (bias) in statistical models for genetic and genomic evaluations, and preselected progeny of a mating are no longer a random sample of possible progeny from that mating. National genetic evaluations without genotypes are input to MACE, and biases in national evaluations are propagated internationally through MACE. Genomic preselection for the Holstein breed is a source of concern for introducing bias to MACE, especially when genomic preselection is practiced intensively in the population. However, MACE continues to be useful for other breeds, among other species, or for non-IGE purposes. Future methods will need to make optimum use of genomic information and be free of genomic preselection bias.

Background R is a multi-platform statistical software and an object oriented programming language. The package archive network for R provides CRAN repository that features over 15,000 free open source packages, at the time of writing this article (https://cran.r-project.org/web/packages, accessed in October 2019). The package is introduced in this article. The purpose of this package is providing functions for checking and processing the pedigree, calculation of the additive genetic relationship matrix and its inverse, which are used to study the population structure and predicting the genetic merit of animals. Calculation of the dominance relationship matrix and its inverse are also covered. A concept in animal breeding is genetic groups, which is about the inequality of the average genetic merits for groups of unknown parents. The package provides functions for the calculation of the matrix of genetic group contributions (Q). Calculating Q is computationally demanding, and depending on the size of the pedigree and the number of genetic groups, it might not be feasible using personal computers. Therefore, a computationally optimised function and its parallel processing alternative are provided in the package. Results Using sample data, outputs from different functions of the package were presented to illustrate a real experience of working with the package. Conclusions The presented R package is a free and open source tool mainly for quantitative geneticists and ecologists, who deal with pedigree data. It provides numerous functions for handling pedigree data, and calculating various pedigree-based matrices. Some of the functions are computationally optimised for large-scale data.