Estimation of variance components of quantitative traits in inbred populations

Abstract

Use of variance-component estimation for mapping of quantitative-trait loci in humans is a subject of great current interest. When only trait values, not genotypic information, are considered, variance-component estimation can also be used to estimate heritability of a quantitative trait. Inbred pedigrees present special challenges for variance-component estimation. First, there are more variance components to be estimated in the inbred case, even for a relatively simple model including additive, dominance, and environmental effects. Second, more identity coefficients need to be calculated from an inbred pedigree in order to perform the estimation, and these are computationally more difficult to obtain in the inbred than in the outbred case. As a result, inbreeding effects have generally been ignored in practice. We describe here the calculation of identity coefficients and estimation of variance components of quantitative traits in large inbred pedigrees, using the example of HDL in the Hutterites. We use a multivariate normal model for the genetic effects, extending the central-limit theorem of Lange to allow for both inbreeding and dominance under the assumptions of our variance-component model. We use simulated examples to give an indication of under what conditions one has the power to detect the additional variance components and to examine their impact on variance-component estimation. We discuss the implications for mapping and heritability estimation by use of variance components in inbred populations.

Figure 1

15 Possible identity states for individuals A and B, grouped according to their nine condensed states. Lines indicate alleles that are IBD (adapted from the work of Lynch and Walsh [1998]).

Figure 2

Plot of Δ₈ vs. , for the 324,415 pairs of individuals in the Hutterite sample, where the labeled clouds of points are described in table 1. The horizontal lines are at values Δ₈=.25 and Δ₈=.5.

Figure 3

Example pedigrees 1 (A) and 2 (B) from the Hutterite sample

Figure 4

Histograms of (A) (kinship coefficient) for the 324,415 pairs of individuals in the Hutterite sample and (B) inbreeding coefficient for the 806 individuals in the Hutterite sample.

Figure 5

Plot of inbreeding coefficient versus year of birth for the 806 individuals in the Hutterite study sample

Figure 6

Histograms of (A) , (B) Δ₂, (C) combined with , (D) Δ₄ combined with Δ₆, (E) , (F) , and (G) Δ₉, for the 324,415 pairs of individuals in the Hutterite sample.