The main objectives of this study were: (1) to compare quadratic and likelihood estimators of dispersion parameters in a sire plus maternal grandsire model (S-M) with respect to estimated bias (EB) and estimated mean squared error (EMSE) when the data are affected by selection, (2) to estimate direct and maternal (co)variance components (CVC) using an animal model (MAM) and genetic grouping for weaning weight in beef cattle, (3) to extend the theory of genetic grouping in models with maternal effects allowing for differential criteria to be used when assigning groups for direct and maternal effects, and (4) to present a Bayesian approach to estimation of CVC in MAM. To achieve objective (1) some designs based on S-M were compared with respect to the variance of estimates of heritability. Also, simulated data under S-M and either: (1) random, (2) translation invariant, or (3) location-variant selection were employed. Although perhaps the model and design did not permit to reveal large differences in EB and EMSE among estimators, likelihood based methods tended to outperform quadratic ones with respect to EMSE and, to a lesser extent, with respect to EB. This was specially so under non-random selection. Records from 935 Angus calves were used to estimate CVC in MAM by restricted maximum likelihood to attain objective (2). Estimates of CVC and of functions thereof did not differ very much in models which included or excluded genetic groups. Estimates of heritability for direct and maternal effects were smaller than those reported previously. The estimate of the additive correlation between direct and maternal effects was $-$0.31. Genetic and environmental trends for direct effects were positive whereas corresponding trends for maternal effects were close to zero. The Bayesian approach for making inferences about CVC in MAM used inverted-Wishart and inverted chi-square prior distributions. The joint posterior density of CVC was obtained in closed form and three methods to achieve further marginalization were discussed.

Mixed-effects models have found broad applications in various fields. As a result, the interest in learning and using these models is rapidly growing. On the other hand, some of these models, such as the linear mixed models and generalized linear mixed models, are highly parametric, involving distributional assumptions that may not be satisfied in real-life problems. Therefore, it is important, from a practical standpoint, that the methods of inference about these models are robust to violation of model assumptions. Fortunately, there is a full scale of methods currently available that are robust in certain aspects. Learning about these methods is essential for the practice of mixed-effects models.This research monograph provides a comprehensive account of methods of mixed model analysis that are robust in various aspects, such as to violation of model assumptions, or to outliers. It is suitable as a reference book for a practitioner who uses the mixed-effects models, and a researcher who studies these models. It can also be treated as a graduate text for a course on mixed-effects models and their applications.

Quantitative traits-be they morphological or physiological characters, aspects of behavior, or genome-level features such as the amount of RNA or protein expression for a specific gene-usually show considerable variation within and among populations. Quantitative genetics, also referred to as the genetics of complex traits, is the study of such characters and is based on mathematical models of evolution in which many genes influence the trait and in which non-genetic factors may also be important. Evolution and Selection of Quantitative Traits presents a holistic treatment of the subject, showing the interplay between theory and data with extensive discussions on statistical issues relating to the estimation of the biologically relevant parameters for these models. Quantitative genetics is viewed as the bridge between complex mathematical models of trait evolution and real-world data, and the authors have clearly framed their treatment as such. This is the second volume in a planned trilogy that summarizes the modern field of quantitative genetics, informed by empirical observations from wide-ranging fields (agriculture, evolution, ecology, and human biology) as well as population genetics, statistical theory, mathematical modeling, genetics, and genomics. Whilst volume 1 (1998) dealt with the genetics of such traits, the main focus of volume 2 is on their evolution, with a special emphasis on detecting selection (ranging from the use of genomic and historical data through to ecological field data) and examining its consequences.

The prediction of producing desirable traits in offspring such as increased growth rate or superior meat, milk and wool production is a vital economic tool to the animal scientist. Summarizing the latest developments in genomics relating to animal breeding values and design of breeding programs, this new edition includes models of survival analysis, social interaction and sire and dam models, as well as advancements in the use of SNPs in the computation of genomic breeding values.

Praise for the First Edition “This book will serve to greatly complement the growing number of texts dealing with mixed models, and I highly recommend including it in one’s personal library.” —Journal of the American Statistical Association Mixed modeling is a crucial area of statistics, enabling the analysis of clustered and longitudinal data. Mixed Models: Theory and Applications with R, Second Edition fills a gap in existing literature between mathematical and applied statistical books by presenting a powerful examination of mixed model theory and application with special attention given to the implementation in R. The new edition provides in-depth mathematical coverage of mixed models’ statistical properties and numerical algorithms, as well as nontraditional applications, such as regrowth curves, shapes, and images. The book features the latest topics in statistics including modeling of complex clustered or longitudinal data, modeling data with multiple sources of variation, modeling biological variety and heterogeneity, Healthy Akaike Information Criterion (HAIC), parameter multidimensionality, and statistics of image processing. Mixed Models: Theory and Applications with R, Second Edition features unique applications of mixed model methodology, as well as: Comprehensive theoretical discussions illustrated by examples and figures Over 300 exercises, end-of-section problems, updated data sets, and R subroutines Problems and extended projects requiring simulations in R intended to reinforce material Summaries of major results and general points of discussion at the end of each chapter Open problems in mixed modeling methodology, which can be used as the basis for research or PhD dissertations Ideal for graduate-level courses in mixed statistical modeling, the book is also an excellent reference for professionals in a range of fields, including cancer research, computer science, and engineering.

The Handbook for Statistical Genetics is widely regarded as the reference work in the field. However, the field has developed considerably over the past three years. In particular the modeling of genetic networks has advanced considerably via the evolution of microarray analysis. As a consequence the 3rd edition of the handbook contains a much expanded section on Network Modeling, including 5 new chapters covering metabolic networks, graphical modeling and inference and simulation of pedigrees and genealogies. Other chapters new to the 3rd edition include Human Population Genetics, Genome-wide Association Studies, Family-based Association Studies, Pharmacogenetics, Epigenetics, Ethic and Insurance. As with the second Edition, the Handbook includes a glossary of terms, acronyms and abbreviations, and features extensive cross-referencing between the chapters, tying the different areas together. With heavy use of up-to-date examples, real-life case studies and references to web-based resources, this continues to be must-have reference in a vital area of research. Edited by the leading international authorities in the field. David Balding - Department of Epidemiology & Public Health, Imperial College An advisor for our Probability & Statistics series, Professor Balding is also a previous Wiley author, having written Weight-of-Evidence for Forensic DNA Profiles, as well as having edited the two previous editions of HSG. With over 20 years teaching experience, he’s also had dozens of articles published in numerous international journals. Martin Bishop – Head of the Bioinformatics Division at the HGMP Resource Centre As well as the first two editions of HSG, Dr Bishop has edited a number of introductory books on the application of informatics to molecular biology and genetics. He is the Associate Editor of the journal Bioinformatics and Managing Editor of Briefings in Bioinformatics. Chris Cannings – Division of Genomic Medicine, University of Sheffield With over 40 years teaching in the area, Professor Cannings has published over 100 papers and is on the editorial board of many related journals. Co-editor of the two previous editions of HSG, he also authored a book on this topic.

Fundamental to any livestock improvement programme by animal scientists, is the prediction of genetic merit in the offspring generation for desirable production traits such as increased growth rate, or superior meat, milk and wool production. Covering the foundational principles on the application of linear models for the prediction of genetic merit in livestock, this new edition is fully updated to incorporate recent advances in genomic prediction approaches, genomic models for multi-breed and crossbred performance, dominance and epistasis. It provides models for the analysis of main production traits as well as functional traits and includes numerous worked examples. For the first time, R codes for key examples in the textbook are provided online. Suitable for graduate and postgraduate students, researchers and lecturers of animal breeding, genetics and genomics, this established textbook provides a thorough grounding in both the basics and in new developments of linear models and animal genetics.