Mapping quantitative trait loci onto a phylogenetic tree

Abstract

Despite advances in genetic mapping of quantitative traits and in phylogenetic comparative approaches, these two perspectives are rarely combined. The joint consideration of multiple crosses among related taxa (whether species or strains) not only allows more precise mapping of the genetic loci (called quantitative trait loci, QTL) that contribute to important quantitative traits, but also offers the opportunity to identify the origin of a QTL allele on the phylogenetic tree that relates the taxa. We describe a formal method for combining multiple crosses to infer the location of a QTL on a tree. We further discuss experimental design issues for such endeavors, such as how many crosses are required and which sets of crosses are best. Finally, we explore the method's performance in computer simulations, and we illustrate its use through application to a set of four mouse intercrosses among five inbred strains, with data on HDL cholesterol.

Figure 1

Illustration of the basic concepts behind the mapping of a QTL to a phylogenetic tree. On the left is an example tree relating four taxa. The locations of possible origins of a diallelic QTL are indicated by the numbers 1–5. In the table on the right, we indicate the presence or absence of a QTL in each of the six possible crosses among pairs of taxa, according to the location of the QTL on the tree. Each possible QTL location on the tree corresponds to a partition of the taxa into two groups.

Figure 2

A phylogenetic tree with six taxa (A) and three possible choices of five crosses among the six taxa, with nodes denoting taxa and edges denoting crosses (B–D).

Figure 3

Estimated receiver operating characteristic (ROC) curves for the naive method (solid curves), the proposed method, with power indicating that the true partition is contained within the 95% credible set (dashed curves), and the proposed method, with power indicating that the 95% credible set contains only the true partition (dotted curves), in the case of four taxa, with each of the six possible intercrosses having a sample size of 75, and a QTL responsible for 10% of the phenotypic variance in the crosses in which it is segregating. The red and blue curves correspond to the case that the true partition is $\text{A}|\text{BCD}$ and $\text{AB}|\text{CD}$, respectively. Points indicate the power and false positive rates for a 5% significance threshold. The results are based on 10,000 simulation replicates.

Figure 4

Estimated power (top), “exact” power (middle), and false-positive rates (bottom) in the case of four taxa with a total sample size of 450, as a function of the percentage phenotypic variance explained by the QTL. The black dashed curves correspond to the use of all six possible crosses. The other curves are for the various choices of a minimal set of three crosses, with the curves in blue, red, and green corresponding to cases in which three, two, and one of the crosses are segregating the QTL, respectively. The results are based on 10,000 simulation replicates, with analyses considering all possible partitions of the taxa.

Figure 5

Detailed results on the estimated power (top), “exact” power (middle), and false positive rates (bottom), for individual choices of crosses, in the case of four taxa with a total sample size of 450, and with the QTL being responsible for 10% of the phenotypic variance in crosses in which it is segregating. Blue, red, and green correspond to cases in which three, two, and one of the crosses are segregating the QTL, respectively. The results are based on 10,000 simulation replicates, with analyses considering all possible partitions of the taxa. The black vertical line segments indicate 95% confidence intervals.

Figure 6

Analysis results for selected chromosomes for the data from Li et al. (2005): LOD curves for individual crosses (left), LOD curves for the top five partitions (middle), and approximate posterior probabilities for each partition (right). The partitions corresponding to the five LOD curves in the middle are indicated on the right. The labeled points on the right indicate the partitions included in the 95% Bayesian credible sets. On the left and in the middle, dashed horizontal lines are plotted at the 5% significance thresholds.