Inferring the Allelic Series in a Multiparental Population

Multiparental populations (MPPs) are experimental populations in which the genome of every individual is a mosaic of known founder haplotypes. These populations are useful for detecting quantitative trait loci (QTL) because tests of association can leverage inferred founder haplotype descent. It is difficult, however, to determine how haplotypes at a locus group into distinct functional alleles, termed the allelic series. The allelic series is important because it provides information about the number of causal variants at a QTL and their combined effects. In this study, we introduce a fully-Bayesian model selection framework for inferring the allelic series. This framework accounts for sources of uncertainty found in typical MPPs, including the number and composition of functional alleles. Our prior distribution for the allelic series is based on the Chinese restaurant process, a relative of the Dirichlet process, and we leverage its connection to the coalescent to introduce additional prior information about haplotype relatedness via a phylogenetic tree. We evaluate our approach via simulation and apply it to real QTL from two MPPs: the Collaborative Cross (CC) and the Drosophila Genetic Reference Population (DSPR). We find that, although posterior inference of the exact allelic series is often uncertain, we are able to distinguish biallelic QTL from more complex multiallelic cases. Additionally, our allele-based approach improves haplotype effect estimation when the true number of functional alleles is small. Our method, Tree-Based Inference of Multiallelism via Bayesian Regression (TIMBR), provides new insight into the genetic architecture of QTL in MPPs.