Bayesian Modeling of Haplotype Effects in Multiparent Populations

A general Bayesian model, Diploffect, is described for estimating the effects of founder haplotypes at quantitative trait loci (QTL) detected in multiparental genetic populations; such populations include the Collaborative Cross (CC), Heterogeneous Socks (HS), and many others for which local genetic variation is well described by an underlying, usually probabilistically inferred, haplotype mosaic. Our aim is to provide a framework for coherent estimation of haplotype and diplotype (haplotype pair) effects that takes into account the following: uncertainty in haplotype composition for each individual; uncertainty arising from small sample sizes and infrequently observed haplotype combinations; possible effects of dominance (for noninbred subjects); genetic background; and that provides a means to incorporate data that may be incomplete or has a hierarchical structure. Using the results of a probabilistic haplotype reconstruction as prior information, we obtain posterior distributions at the QTL for both haplotype effects and haplotype composition. Two alternative computational approaches are supplied: a Markov chain Monte Carlo sampler and a procedure based on importance sampling of integrated nested Laplace approximations. Using simulations of QTL in the incipient CC (pre-CC) and Northport HS populations, we compare the accuracy of Diploffect, approximations to it, and more commonly used approaches based on Haley–Knott regression, describing trade-offs between these methods. We also estimate effects for three QTL previously identified in those populations, obtaining posterior intervals that describe how the phenotype might be affected by diplotype substitutions at the modeled locus.