Trait and marker selection
Traits were selected on several differing criteria, including heritability, linkage found with other methods, and random selection. Heritabilities were computed by Yu et al.  for all expression-level phenotypes provided. Eight phenotypes were selected with heritabilities ranging from near 0 to 0.87. In addition, Yu et al.  found linkage with Merlin nonparametric LOD scores >3 for several phenotypes, and three of these phenotypes were selected to see if those results could be replicated with these methods. In addition, one phenotype was selected at random. Finally, we simulated data from a random normal distribution to provide a "null" for comparison.
The meiotic map assembled by Sung et al.  guided the selection of SNP markers to include in our linkage analysis. Only markers present in the Rutgers map were used because that map was more complete. Furthermore, because the implementation of the methods used here does not address the issue of two markers with the same map position, when two markers had the same meiotic map position, we used only the first. A total of 1386 SNPs were selected with an average distance of 2.7 cM (0.01 cM minimum, 16.8 cM maximum). Although less than ideal, this marker set was judged sufficient for testing. There were a few Mendelian inconsistencies in the selected markers, which were resolved via the auto-correction feature in Loki.
MCMC segregation and linkage analysis
To estimate the number, effects, and location of loci contributing to each phenotype, we applied the MCMC segregation and linkage analysis methods described by Heath . These methods also estimate covariate effects, and the trait model is given by , where μ is the "reference" trait value, X is the incidence matrix for covariate effects, β is the vector of covariate effects, Q
is the incidence matrix for the effects of QTL i, α
is the vector of effects for QTL i, e is the normally distributed residual effect, and k is the number of QTL currently estimated (k ≥ 0). The MCMC process samples μ, β, α
, i, and e as well as parameters such as unobserved marker genotypes. All of these parameters are sampled from the space of model values consistent with the data observed. Values are sampled proportional to their posterior probability. After a number of sampling iterations, the sampled values provide an estimate of the posterior probability distribution over the space of possible parameter configurations. Genome-wide analyses of each trait were run for 1,000,000 iterations with a LM sampler ratio of 0.2. In each analysis, all chromosomes were analyzed simultaneously. The raw (untransformed) traits were analyzed without covariates. Graphical analysis was used to assess MCMC mixing.
To evaluate evidence for linkage, we considered L-scores estimated over 1-cM wide bins along the chromosomes. An L-score is simply the posterior probability divided by the prior probability. In the absence of any data, the posterior probability should be equal to the prior probability. Thus, a L-score of 1 indicates that the data contains no information for or against linkage, while a L-score >1 indicates evidence for linkage, and an L-score <1 might be considered evidence against linkage.