25th Summer Institute in Statistical Genetics (SISG)

Module 12: Mixed Models in Quantitative Genetics

Wed, July 22 to Fri, July 24

Module dates/times: Wednesday, July 22; Thursday, July 23, and Friday, July 24. Live sessions will start no earlier than 8 a.m. Pacific and end no later than 2:30 p.m. Pacific, except for Wednesdays. For modules that end on Wednesday, live sessions will end by 11 a.m. Pacific. For modules that start on Wednesday, live sessions will begin no earlier than 11:30 a.m.

This module assumes the material in Modules 1 and 5 and provides a foundation for Module 14.``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 maybe 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, 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, genotype by environment interaction models. Suggested pairing: Modules 9 and 15.

Access 2019 course materials.

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

  1. Understand the key idea from matrix theory for linear models (multiplication, inverse, rank, eigenstructure, quadratic forms).
  2. Understand the construction general linear models.
  3. Understand the construction of mixed models.
  4. Apply mixed models for estimating breeding values.
  5. Apply mixed models for GWAS.
  6. Apply mixed models for genomic selection and genomic prediction