Inheritance beyond plain heritability: variance-controlling genes in Arabidopsis thaliana

Abstract

The phenotypic effect of a gene is normally described by the mean-difference between alternative genotypes. A gene may, however, also influence the phenotype by causing a difference in variance between genotypes. Here, we reanalyze a publicly available Arabidopsis thaliana dataset [1] and show that genetic variance heterogeneity appears to be as common as normal additive effects on a genomewide scale. The study also develops theory to estimate the contributions of variance differences between genotypes to the phenotypic variance, and this is used to show that individual loci can explain more than 20% of the phenotypic variance. Two well-studied systems, cellular control of molybdenum level by the ion-transporter MOT1 and flowering-time regulation by the FRI-FLC expression network, and a novel association for Leaf serration are used to illustrate the contribution of major individual loci, expression pathways, and gene-by-environment interactions to the genetic variance heterogeneity.

Figure 1. Comparison of p-values (a) and proportions of the phenotypic variance explained (b) for loci detected in the GWAS and vGWAS.

Wilcoxon and Brown-Forsythe tests were applied for the GWAS and vGWAS analyses, respectively. Plotted GC-corrected p-values are for the association of all SNPs with MAF for all the quantitative traits with -value inflation . The red dashed lines indicate the Bonferroni-corrected significance threshold. The scatterplots are heat maps for the logarithm of the number of dots in each mesh cell. A sub genome-wide significance threshold of is marked in (a), and a cutoff of 15% is marked in (b). The value in each block shows the ratio of the number of points in the block to the total number of points in the subfigure.

Figure 2. Dissection of the variance for the two most significant variance-controlling loci.

The variance due to mean shift (additive variance) and variance heterogeneity are shown in blue and yellow, respectively. The cumulative bar for each locus shows the contributions of the two components of the variance at the observed low-variance allele frequency (LAF). The dotted curves illustrate the change in the variance partitioning as LAF changes.

Figure 3. Detection of the molybdenum transporter MOT1 as a variance-controlling gene using vGWAS.

a: Manhattan plot for genetic association with the Molybdenum concentration in the plant. The yellow dots in the front are the genomic controlled p-values from the Wilcoxon (difference in mean) test. The other colored dots are the genomic controlled p-values from the Brown-Forsythe (difference in variance) test, where the colors are used to separate the 5 chromosomes. The horizontal dashed line corresponds to a nominal 5% significance threshold with Bonferroni correction. b: Molybdenum concentration distributions for the ecotypes with alternative homozygous genotypes for the only SNP typed in the exon of MOT1. The density curves were smoothed using a standard Gaussian kernel. The box plots in the density shades shows the real data distribution for the genotype.

Figure 4. Detection of a variance-controlling locus (Variance in Serration - VS) affecting Leaf serration at 16°C.

a: Manhattan plot for genetic association with Leaf serration at 16°C in the plant. The yellow dots in the front are the genomic controlled p-values from the Wilcoxon (difference in mean) test. The other colored dots are the genomic controlled p-values from the Brown-Forsythe (difference in variance) test, where the colors are used to separate the 5 chromosomes. The horizontal dashed line corresponds to a nominal 5% significance threshold with Bonferroni correction. b: Two overlapping histograms showing the phenotypic distributions per genotype of the VS locus. c: The distribution of LD across the VS locus. d: Association signals around the VS locus where the annotated genes are illustrated by shades in red (gene-name available) or gray (gene-name unavailable).

Figure 5. Propagation of variance heterogeneity in the FRI-FLC pathway.

a: The horizontal bars show the variance in FRI-expression, FLC-expression and flowering times under four different conditions (short (SD)/long (LD) days, with (V) or without (−) vernalization) as the phenotypic mean +/− 1 S.D. within the two alternative genotypes at the FRI-locus. Deletion represents homozygosity for the loss of function allele and A homozygosity for the wild-type allele. The mean and the variance are significantly larger for all traits among the inbred lines with the functional A genotype (Table 2). The pathway is adapted from . b: Scatterplots and Spearman's rank correlation coefficients are given for the deviation of FRI, FLC, and the flowering traits in (a) from the median of each phenotype. *** indicates that the corresponding correlation coefficient is significantly different from zero with -value less than . (c): For all the phenotypes in the pathway, the values for individuals are connected by lines. The color of the line for an individual is assigned based on its level of FRI expression. Individuals with FRI expression below the 25% quantile are in blue, between the 25% and 75% quantiles in green, and above the 75% quantile in red.

Figure 6. The effect of the FRI Vernalization interaction on flowering-time in Arabidopsis thaliana .

The columns show the phenotypic distributions for each FRI genotype x Vernalization combination. FRI:- represents the loss of function genotype and FRI:A the wild-type genotype. Flowering-time was measured under long days without (0W)/with 2 (2W)/4 (4W)/8 (8W) weeks of vernalization.