SISG MODULE 11

This module covers the use of “mixed models” for analysis in a wide range of genetic applications from human disease to animal and plant breeding. Mixed models are utilized in complex data analysis where the usual assumption(s) of independence and/or homogeneous variances fail. They allow effects of nature to be separated from those of nurture and are emerging as the default method of analysis for human data since it is not possible to randomize subjects to households, choices, or 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 maybe related and may share common material environment as well as common pens or cages. Further, individuals may share indirect genetics effects where an inherited effect in one individual is experienced as an environmental effect in an associated individual. Dissection of epigenetic effects can also require the use of mixed model analysis.

Learning Objectives: After attending this module, participants will be able to: 

1. Implement the key idea from matrix theory for linear models (multiplication, inverse, rank, eigenstructure, quadratic forms).

2. Understand the construction of general linear models and of linear mixed models.

3. Apply mixed models for estimating breeding values, while detecting and correcting for admixture. 

4. Apply mixed models for GWAS and for genomic selection and prediction.

5. Perform BLUP and REML estimation, understanding design issues in Bayesian formulations. 

6. Model genotype-by-environment interactions.

Bruce Walsh is Professor of Ecology and Evolutionary Biology at the University of Arizona, Tucson. He is broadly interested in using mathematical models to explore the interface of genetics and evolution, with particular focus on the evolution of genome structure and the analysis of complex genetic characters, and is co-author with Mike Lynch of “The Genetic Analysis of Quantitative Traits” and “Evolution and Selection of Quantitative Traits.”

Guilherme Rosa is Professor of Animal and Dairy Science at the Animal and Dairy Sciences at the University of Wisconsin, Madison.  His teaching and research engages 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.  Learn more about Guilherme’s work here.