Whole-genome QTL analysis for MAGIC

Abstract

Key message

An efficient whole genome method of QTL analysis is presented for Multi-parent advanced generation integrated crosses.

Abstract

Multi-parent advanced generation inter-cross (MAGIC) populations have been developed for mice and several plant species and are useful for the genetic dissection of complex traits. The analysis of quantitative trait loci (QTL) in these populations presents some additional challenges compared with traditional mapping approaches. In particular, pedigree and marker information need to be integrated and founder genetic data needs to be incorporated into the analysis. Here, we present a method for QTL analysis that utilizes the probability of inheriting founder alleles across the whole genome simultaneously, either for intervals or markers. The probabilities can be found using three-point or Hidden Markov Model (HMM) methods. This whole-genome approach is evaluated in a simulation study and it is shown to be a powerful method of analysis. The HMM probabilities lead to low rates of false positives and low bias of estimated QTL effect sizes. An implementation of the approach is available as an R package. In addition, we illustrate the approach using a bread wheat MAGIC population.

Appendix

The size of $\mathbf{P}_A$ and hence the number of effects in $\mathbf{a}$, $(r-c)n_\mathrm{f}$ for interval-based analyses and $rn_\mathrm{f}$ for marker-based analyses, can be very large. This usually results in the number of effects required to be estimated being bigger than the sample size $n$. Verbyla et al. (2012) propose an approach that reduces the dimension for model fitting and the same approach can be used for MPWGAIM. This reduces the dimension for model fitting to the number of lines $n_g$, in the same manner as for the bi-parental situation.

If $\mathbf{a}^* \sim N(\mathbf 0 , \sigma _a^2 \mathbf{I}_{n_g})$, the model

$$\begin{aligned} \mathbf{u}_g = (\mathbf{P}_A \mathbf{P}_{A}^{\rm T})^{1/2} \mathbf{a}^* + \mathbf{u}_p \end{aligned}$$

results in the same variance model as (7), but the number of effects in $\mathbf{a}^*$ equals the number of lines $n_g$. Then as in Verbyla et al. (2012), the BLUPs of $\mathbf{a}^*$ and $\mathbf{a}$, denoted by $\tilde{\mathbf{a}}^*$ and $\tilde{\mathbf{a}}$ respectively, are related by

$$\begin{aligned} \tilde{\mathbf{a}} = \mathbf{P}_{A}^{\rm T} (\mathbf{P}_A \mathbf{P}_{A}^{\rm T})^{-1/2} \tilde{\mathbf{a}}^* \end{aligned}$$

with variance matrix

$$\begin{aligned} \mathrm{var}\left( \tilde{\mathbf{a}}\right) = \mathbf{P}_{A}^{\rm T} (\mathbf{P}_A \mathbf{P}_{A}^{\rm T})^{-1/2} \mathrm{var}\left( \tilde{\mathbf{a}}^*\right) (\mathbf{P}_A \mathbf{P}_{A}^{\rm T})^{-1/2}\mathbf{P}_A \end{aligned}$$

and only the diagonal elements of this matrix are required in the calculation of the outlier statistics (12). Thus, an efficient computational approach exists for high-dimensional situations.