Mixed Effects Models for Quantitative Trait Loci Mapping With Inbred Strains

Abstract

Fixed effects models have dominated the statistical analysis of genetic crosses between inbred strains. In spite of their popularity, the traditional models ignore polygenic background and must be tailored to each specific cross. We reexamine the role of random effect models in gene mapping with inbred strains. The biggest difficulty in implementing random effect models is the lack of a coherent way of calculating trait covariances between relatives. The standard model for outbred populations is based on premises of genetic equilibrium that simply do not apply to crosses between inbred strains since every animal in a strain is genetically identical and completely homozygous. We fill this theoretical gap by introducing novel combinatorial entities called strain coefficients. With an appropriate theory, it is possible to reformulate QTL mapping and QTL association analysis as an application of mixed models involving both fixed and random effects. After developing this theory, our first example compares the mixed effects model to a standard fixed effects model using simulated advanced intercross line (AIL) data. Our second example deals with hormone data. Here multivariate traits and parameter identifiability questions arise. Our final example involves random mating among eight strains and vividly demonstrates the versatility of our models.

Combined linkage disequilibrium and linkage mapping: Bayesian multilocus approach

“…The two articles [8,118] provide a full explanation of how Mendel captures polygenic background and imputes local strain origins (maternal strain j paternal strain). These are complicated stories motivated by the need for model realism and computational speed.…”

Quantitative Trait Loci Association Mapping by Imputation of Strain Origins in Multifounder Crosses

“…To pave the way for our imputation method, we generalize the notion of strain coefficients (Bauman et al 2008). Imagine a pedigree generated by a set of complicated crosses involving a certain number of inbred strains.…”

“…Third, the random effects part of a mixed-effects model readily captures polygenic background. Our recent model of polygenic inheritance in inbred strains (Bauman et al 2008) makes it possible to calculate trait variances and covariances across a pedigree, regardless of the number of founding strains and the internal complexity of the pedigree.…”

“…Recent articles touting random effects models in inbred strains include Xie et al (1998), Liu and Zeng (2000), and Bauman et al (2008). Bennett et al (2010) argue that association mapping with large SNP mouse panels has the potential for much higher mapping resolution.…”

“…The new polygenic models for inbred strain data derived by Bauman et al (2008) involve certain combinatorial (strain) coefficients that bear a strong resemblance to standard global (theoretical) kinship coefficients appropriate to outbred populations. Both kinds of coefficients can be quickly computed by simple recurrence relations.…”