23rd Summer Institute in Statistical Genetics (SISG)

Module 11: Mixed Models in Quantitative Genetics

Session 4: Wed Jul 18 to Fri Jul 20

Module dates/times: Wednesday, July 18, 1:30-5 p.m.; Thursday, July 19, 8:30 a.m.-5 p.m., and Friday, July 20, 8:30 a.m.-5 p.m.

Assumes the material in Module 1: Probability and Statistical Inference and Module 4: Regression Methods: Concepts & Applications.

Provides a foundation for Module 14: Advanced Quantitative Genetics and Module 18: Statistical & Quantitative Genetics of Disease.

”Mixed models” refers to the analysis of linear models with arbitrary (co)variance structures among and within random effects and may be due to such factors as relationships or shared environments, cytoplasm, maternal effects and history. Mixed models are utilized in complex data analysis where the usual assumption(s) of independence and/or homogeneous variances fail.

Mixed models allow effects of nature to be separated from those of nurture and are emerging as the default method of analysis for human data. These issues are pervasive in human studies due to the lack of ability to randomize subjects to households, choice, and prior history.

In plant breeding, growth and yield data are correlated due to shared locations, but diminish by distance resulting in spatial correlations. In animal breeding, performance data are correlated because individuals may be related and may share common material environment as well as common pens or cages. Further, when individuals share a common space, they may experience indirect genetics effects (IGEs), which is an inherited effect in one individual experienced as an environmental effect in an associated individual. The evolution of cooperation and competition is based on IGEs, the estimation of which require mixed model analysis. Detection of cytoplasmic and epigenetic effects rely heavily on mixed model methods because of shared material or parental histories.

Topics to be discussed include a basic matrix algebra review, the general linear model, derivation of the mixed model, BLUP and REML estimation, estimation and design issues, and Bayesian formulations.

Applications to be discussed include estimation of breeding values and genetic variances in general pedigrees, association mapping, genomic selection, spatial correlations and corrections, maternal genetic effects, detecting selection from genomic data, admixture detection and correction, direct and indirect genetic effects, models of general group and kin selection, and genotype by environment interaction models.

Guilherme Rosa is Professor of Animal Science at the University of Wisconsin, Madison. He teaches courses and develops research on quantitative genetics and statistical genomics, including design of experiments and data analysis tools. Some specific areas of interest include mixed effects models, graphical models, Bayesian analysis and Monte Carlo methods, and prediction of complex traits using genomic information. He recently published “One hundred years of statistical developments in animal breeding.” Annual Review of Animal Biosciences 3:19-56, 2015

Bruce Walsh is Professor, Ecology and Evolutionary Biology, University of Arizona. His interests are broadly in using mathematical models to explore the interface of genetics and evolution, with particular focus on two areas: the evolution of genome structure and the analysis of complex genetic characters (aka quantitative genetics). He is well-known as co-author of “Genetics and Analysis of Quantitative Characters.” 980 pp. Sinauer Associations.

Access 2017 Course Materials (2018 materials will be uploaded to this page prior to the start of the module)