Model selection in binary trait locus mapping

Abstract

Quantitative trait locus (QTL) mapping methodology for continuous normally distributed traits is the subject of much attention in the literature. Binary trait locus (BTL) mapping in experimental populations has received much less attention. A binary trait by definition has only two possible values, and the penetrance parameter is restricted to values between zero and one. Due to this restriction, the infinitesimal model appears to come into play even when only a few loci are involved, making selection of an appropriate genetic model in BTL mapping challenging. We present a probability model for an arbitrary number of BTL and demonstrate that, given adequate sample sizes, the power for detecting loci is high under a wide range of genetic models, including most epistatic models. A novel model selection strategy based upon the underlying genetic map is employed for choosing the genetic model. We propose selecting the "best" marker from each linkage group, regardless of significance. This reduces the model space so that an efficient search for epistatic loci can be conducted without invoking stepwise model selection. This procedure can identify unlinked epistatic BTL, demonstrated by our simulations and the reanalysis of Oncorhynchus mykiss experimental data.

Figure 1.—

Genetic map of markers for two-locus simulations where markers are denoted M_i and BTL are denoted G_i. (a) Simulation 1: r₁ is the recombination rate between M₁ and G₁, r₂ is the recombination rate between M₂ and G₂, θ₁ is the recombination rate between M₁ and M₂, and M₃ is an unlinked marker. (b) Simulation 2: r₁ is the recombination rate between M₁ and G₁ on linkage group 1, r₂ is the recombination rate between M₇ and G₂ on linkage group 2, and θ₁ is the recombination rate between M₁ and M₇.

Figure 1.—

Genetic map of markers for two-locus simulations where markers are denoted M_i and BTL are denoted G_i. (a) Simulation 1: r₁ is the recombination rate between M₁ and G₁, r₂ is the recombination rate between M₂ and G₂, θ₁ is the recombination rate between M₁ and M₂, and M₃ is an unlinked marker. (b) Simulation 2: r₁ is the recombination rate between M₁ and G₁ on linkage group 1, r₂ is the recombination rate between M₇ and G₂ on linkage group 2, and θ₁ is the recombination rate between M₁ and M₇.

Figure 2.—

Plots of a penetrance model from each of three simulated groups for two loci. (a) Group 1, additive; (b) group 2, recessive (rec.) epistasis 1; (c) group 2, rec. epistasis 3; (d) group 3, epistasis 1. Solid line, locus 1, allele type 1; dashed line, locus 1, allele type 2, with p_gj representing the penetrance of genotype g_j.

Figure 3.—

Plots of a penetrance model from each of three simulated groups for three loci. (a) Group 1, additive; (b) group 2, rec. epistasis 1; (c) group 3, epistasis 1. Solid line, locus 2, allele type 1; dashed line, locus 2, allele type 2, with p_gj representing the penetrance of genotype g_j.

Figure 4.—

Power for correct two-locus model for each of the simulated penetrance group genetic models when markers M₁ and M₂ are unlinked to each other. (a) Power with recombination between M₁ and G₁ (r₁) on the x-axis is averaged over recombination between M₂ and G₂. (b) Power with recombination between r₂ on the x-axis is averaged over r₁. Penetrance group (1–3) and genetic model are given in the inset.

Figure 4.—

Power for correct two-locus model for each of the simulated penetrance group genetic models when markers M₁ and M₂ are unlinked to each other. (a) Power with recombination between M₁ and G₁ (r₁) on the x-axis is averaged over recombination between M₂ and G₂. (b) Power with recombination between r₂ on the x-axis is averaged over r₁. Penetrance group (1–3) and genetic model are given in the inset.

Figure 5.—

Model selection: proportion of times the correct two-locus model was selected using the AIC when markers M₁ and M₂ are unlinked to each other. (a) Recombination between M₁ and G₁ (r₁) on the x-axis is averaged over recombination between M₂ and G₂. (b) Recombination between M₁ and G₁ (r₂) on the x-axis is averaged over r₁. Penetrance group (1–3) and genetic model are given in the inset.

Figure 5.—

Model selection: proportion of times the correct two-locus model was selected using the AIC when markers M₁ and M₂ are unlinked to each other. (a) Recombination between M₁ and G₁ (r₁) on the x-axis is averaged over recombination between M₂ and G₂. (b) Recombination between M₁ and G₁ (r₂) on the x-axis is averaged over r₁. Penetrance group (1–3) and genetic model are given in the inset.