The Genetic Architecture of Quantitative Traits Cannot Be Inferred from Variance Component Analysis

Abstract

Classical quantitative genetic analyses estimate additive and non-additive genetic and environmental components of variance from phenotypes of related individuals without knowing the identities of quantitative trait loci (QTLs). Many studies have found a large proportion of quantitative trait variation can be attributed to the additive genetic variance (VA), providing the basis for claims that non-additive gene actions are unimportant. In this study, we show that arbitrarily defined parameterizations of genetic effects seemingly consistent with non-additive gene actions can also capture the majority of genetic variation. This reveals a logical flaw in using the relative magnitudes of variance components to indicate the relative importance of additive and non-additive gene actions. We discuss the implications and propose that variance component analyses should not be used to infer the genetic architecture of quantitative traits.

Fig 1. Additive genetic variance V_A is a major determinant of total genetic variance.

Under additive (a), dominant (b), or additive by additive (c, d) models, the proportion of total genetic variance explained by the additive genetic variance V_A and dominance genetic variance V_D are estimated either analytically (a, b) or numerically by simulation (d).

Fig 2. Relationship between gene actions and variance components.

(a) Ideally, the variance generated by each type of gene actions is mutually exclusive therefore variance components provide a measure of relative importance of gene actions. (b) In the classical V_A + V_D + V_I variance partition, additive genetic variance V_A has contribution from all of additive, dominant, and epistatic gene actions in most circumstances. With the alternative parameterizations, all types of gene actions contribute to $V_D^{\prime }$ (c) and $V_{AA}^{\prime \prime }$ (d) in most circumstances.

Fig 3. Least squares regression interpretation of V_A.

This representation is adapted from Fig. 7.2 of Reference [2]. Grey circles indicate the genotypic value of each genotype, which is coded as 0, 1, 2 for aa, Aa, and AA respectively. A regression line (red line) is fitted to the data, on which the fitted values are indicated by white circles. The fitted line must pass through the center of the data, as indicated by the cross. The fitted values are equivalent to breeding values. The arrows between the breeding values and the genotypic values are the dominance deviations, which are the same as residuals of the regression. Note that the data points are weighted by their frequencies in the population. A dominance model is used so that the dominance deviation can be illustrated.

Fig 4. Least squares regression interpretation of VD′.

Grey circles indicate the genotypic value of each genotype, which is coded as 0, 2, 2 for aa, Aa, and AA respectively. A regression line (red line) is fitted to the data, on which the fitted values are indicated by white circles. The fitted line must pass through the center of the data, as indicated by the cross. The fitted line must also pass through the circle (half grey and half white to indicate the overlap of the genotypic and fitted values) denoting genotype aa. The fitted values are equivalent to dominance values as defined in this parameterization. The arrows between the dominance values and the genotypic values are the residuals of the regression, which we define as “additive deviation”, therefore the residual variance is $V_A^{\prime }$. Note that the data points are weighted by their frequencies in the population. An additive model is used so that the additive deviation can be illustrated.

Fig 5. Alternative parameterizations capture the majority of genetic variance.

Using an alternative parameterization that emphasizes dominant gene action, a newly defined dominance variance $V_D^{\prime }$ and additive deviation variance $V_A^{\prime }$ are estimated analytically under dominant (a) and additive (b) models. Using an alternative parameterization that emphasizes additive by additive gene action, a newly defined interaction variance $V_{AA}^{\prime \prime }$ is estimated numerically under additive by additive (c) and additive (d) models.

Fig 6. Conventional and alternative parameterizations capture the majority of polygenic genetic variance.

Simulation is used to generate data sets with the additive (A), dominant (D), and additive by additive (AxA) genetic models and V_A, $V_D^{\prime }$ and $V_{AA}^{\prime \prime }$ are estimated using linear mixed models. The results are presented as the proportion of heritability explained by the genetic variance component; $h_a^2$ corresponds to V_A (a), $h_{d\prime }^2$ to $V_D^{\prime }$ (b), and $h_{aa\prime \prime }^2$ to $V_{AA}^{\prime \prime }$ (c).

Fig 7. Variance component analyses of human height data.

Phenotypic variation of height (in cm) observed in the GENEVA study is partitioned into genetic variance components as indicated (color-coded bars) and environmental variance (V_e, grey bar). The colors of bars correspond to the colors of the text indicating the variance components. Error bars indicate standard errors of the variance component estimates provided by GCTA. Proportions of the components are also indicated.