On estimation and identifiability issues of sex-linked inheritance with a case study of pigmentation in Swiss barn owl (Tyto alba)

Abstract

Genetic evaluation using animal models or pedigree-based models generally assume only autosomal inheritance. Bayesian animal models provide a flexible framework for genetic evaluation, and we show how the model readily can accommodate situations where the trait of interest is influenced by both autosomal and sex-linked inheritance. This allows for simultaneous calculation of autosomal and sex-chromosomal additive genetic effects. Inferences were performed using integrated nested Laplace approximations (INLA), a nonsampling-based Bayesian inference methodology. We provide a detailed description of how to calculate the inverse of the X- or Z-chromosomal additive genetic relationship matrix, needed for inference. The case study of eumelanic spot diameter in a Swiss barn owl (Tyto alba) population shows that this trait is substantially influenced by variation in genes on the Z-chromosome ([Formula: see text] and [Formula: see text]). Further, a simulation study for this study system shows that the animal model accounting for both autosomal and sex-chromosome-linked inheritance is identifiable, that is, the two effects can be distinguished, and provides accurate inference on the variance components.

Keywords: Approximate Bayesian animal model; barn owl (Tyto alba); integrated nested Laplace approximation; quantitative genetics; sex chromosome; sex-linked additive genetic effects.

Figure 1

Results from simulation studies showing performance of animal models for estimating Z-linked additive genetic effects. (A) Boxplot of simulated values of ΔDIC (limit ΔDIC = 10 indicated as a horizontal solid line) against the value of (AZI) used in the simulations (together with and ). (B) Posterior mean (filled squares/solid lines) with 95% credible interval (dashed line) for (AZI) from the simulation study (together with and ), power of the model selection test using ΔDIC >10 as limit (x'es/solid line) estimated using the simulation approach, and a 1:1 function of true vs. estimated parameter values (gray line). (C) Posterior mean (open triangles/solid line) for (AI) (gray) with 95% credible interval (dashed lines) and for (AZI) (open squares, black) with 95% credible interval (dashed lines) from the simulation study (together with and ), power of the model selection test, and 1:1 function as described in panel (A). (D) Posterior mean (solid lines) for (AI) (gray) with 95% credible interval (dashed lines) and for (AZI) (black) with 95% credible interval (dashed lines) from the simulation study against the value of used in the simulations (together with ) and power function as described in (A).

Figure 2

(A) Posterior mean of mean additive genetic effect for spot diameter of all individuals in the pedigree for each cohort (i.e., hatch year) 1996–2007 for autosomal loci (black) and Z-linked loci (gray) (solid lines) with 95% credible intervals (dashed lines). The mean spot diameter was standardized to have mean 0 and variance 1. (B) Posterior of difference between cohorts 1996 and 2007 in mean additive genetic effects for autosomal loci (solid lines) and Z-linked loci (dashed lines) for spot diameter in Swiss barn owls.