Predicting the Evolution of Sexual Dimorphism in Gene Expression

Abstract Sexual dimorphism in gene expression is likely to be the underlying source of dimorphism in a variety of traits. Many analyses implicitly make the assumption that dimorphism only evolves when selection favors different phenotypes in the two sexes, although theory makes clear that it can also evolve as an indirect response to other kinds of selection. Furthermore, previous analyses consider the evolution of a single transcript or trait at a time, ignoring the genetic covariance with other transcripts and traits. We first show which aspects of the genetic-variance–covariance matrix, G, affect dimorphism when these assumptions about selection are relaxed. We then reanalyze gene expression data from Drosophila melanogaster with these predictions in mind. Dimorphism of gene expression for individual transcripts shows the signature of both direct selection for dimorphism and indirect responses to selection. To account for the effect of measurement error on evolutionary predictions, we estimated a G matrix for eight linear combinations of expression traits. Sex-specific genetic variances in female- and male-biased transcription, as well as one relatively unbiased combination, were quite unequal, ensuring that most forms of selection on these traits will have large effects on dimorphism. Predictions of response to selection based on the whole G matrix showed that sexually concordant and antagonistic selection are equally capable of changing sexual dimorphism. In addition, the indirect responses of dimorphism due to cross-trait covariances were quite substantial. The assumption that sexual dimorphism in transcription is an adaptation could be incorrect in many specific cases.


Relationship between modules and bias-specific eigenvectors
identified 241 transcriptional modules in their data. To determine the relationship between these modules and the eigenvectors used to summarize the variation for the quantitative genetic analysis, we split the module data into the male-female-and relativelyunbiased classes. For each class, we formed a vector of indicator variables for each gene, with a one for each gene in the module and zeroes otherwise, then standardized the elements of this vector to have mean 0. We then calculated the vector correlation between this module-indicator vector and the absolute value of each eigenvector. Nominal significance of these correlations was evaluated relative to a null distribution of each indicator vector with 1000 random vectors with elements drawn from a normal distribution. We investigated correlations with modules that had 50 or more genes.

Choosing composite traits for quantitative genetic analysis
To choose informative traits, we extracted three submatrices from G*: male expression of male biased genes (MB), female expression of female biased genes (FB), and the sex-averaged expression of the remaining genes, termed relatively unbiased (UB). We then conducted a principal components analysis of submatrix. Male and female expression of each line was then scored on the first two PCs in the MB and FB subsets, and the first four in the UB subset, so k=8 in each sex.
Analyses of genetic variation of the k=8 data showed that the best fitting model had eight variable dimensions vectors out of 16 possible (and fit more than 3.6 AICc units better than the 7-or 9-dimensional models). The covariance and correlation matrices estimated using this model are shown in Supplementary Table S2. The average information matrix contained very small elements that prevented estimation of standard errors for all model terms, suggesting that the overall fit of the model was poor.
To help diagnose the trait combinations lacking significant genetic variation, we examined the estimates of trait variances, shown in Supplementary Table S3. Sex-specific variances are substantially different for the biased expression classes (MB and FB). Note that these biased traits as well as trait UB1 have very large asymmetries in the sex-specific genetic variances, making d (equation 3) substantially less than 1. This indicates that dimorphism is much more likely to evolve under both SAS (equation 3) and SCS (equation 4) than under the assumption of equal variances.
We conjectured that the female variances for the male-based traits and the male variances for the female-biased traits are not distinguishable from 0. To test this, we dropped the female expression of male-biased traits and the male expression of female-biased traits from the data set, and repeated estimation of the genetic variance for the remaining 12 variables. The best model now had nine significant genetic dimensions, although this was just 0.91 AICc units better than the eight-dimensional model. This supports the hypothesis that there is no significant genetic variation in females for male-biased genes or in males for female biased genes.

Relationship between transcriptional modules and bias-specific eigenvectors
We assessed similarity of the transcriptional modules inferred by Ayroles et al. (2009) with the sex-bias class PCs used as traits in the quantitative genetic analysis, producing the results shown in Table S4. While there are many nominally significant correlations, few of them are of substantial size. Overall, there is little tendency for the modules to line up clearly with the PC traits used in our analysis, reflecting the differences in the algorithms used. The two transcriptional modules identified as male-biased and female-biased by Ayroles et al. (2009) are particularly illuminating. Male biased module 7 had highly significant but very small correlations with the two male-biased PC traits, but was also significantly correlated with female-biased and relatively unbiased trait PCs. Female-biased module 18 likewise had one slightly higher correlation with a female-biased trait PC, but was also correlated with all the remaining trait PCs. The single apparent exception is module 50, which had a correlation of 0.62 with FB2, and low correlations with unbiased trait PCs. Overall, the pattern of genetic covariance among genes is structured quite differently from that of the modules recovered by