Variation in mutational (co)variances

Abstract

Because of pleiotropy, mutations affect the expression and inheritance of multiple traits and, together with selection, are expected to shape standing genetic covariances between traits and eventual phenotypic divergence between populations. It is therefore important to find if the M matrix, describing mutational variances of each trait and covariances between traits, varies between genotypes. We here estimate the M matrix for six locomotion behavior traits in lines of two genotypes of the nematode Caenorhabditis elegans that accumulated mutations in a nearly neutral manner for 250 generations. We find significant mutational variance along at least one phenotypic dimension of the M matrices, but neither their size nor their orientation had detectable differences between genotypes. The number of generations of mutation accumulation, or the number of MA lines measured, was likely insufficient to sample enough mutations and detect potentially small differences between the two M matrices. We then tested if the M matrices were similar to one G matrix describing the standing genetic (co)variances of a population derived by the hybridization of several genotypes, including the two measured for M, and domesticated to a lab-defined environment for 140 generations. We found that the M and G were different because the genetic covariances caused by mutational pleiotropy in the two genotypes are smaller than those caused by linkage disequilibrium in the lab population. We further show that M matrices differed in their alignment with the lab population G matrix. If generalized to other founder genotypes of the lab population, these observations indicate that selection does not shape the evolution of the M matrix for locomotion behavior in the short-term of a few tens to hundreds of generations and suggests that the hybridization of C. elegans genotypes allows selection on new phenotypic dimensions of locomotion behavior.

Keywords: Caenorhabditis elegans; G-matrix; M-matrix; experimental evolution; locomotion behavior; multivariate selection; transition rates.

Fig. 1.

Background effects and mutational bias in locomotion behavior. Each plot shows the transition rates between backward (B), forward (F), and still (S) movement states, with left-to-right letter ordering indicating the direction of movement. Red circles show the mean for the N2 and PB306 ancestor genotypes before and after MA. Gray dots show the uncorrected measurements and black the best linear unbiased predictors of the MA line means obtained from equation (3). Error bars in the ancestor genotypes are the standard error of the mean. See Table 1 for the statistical support in genotype background effects and mutation bias.

Fig. 2.

M-matrices for N2 and PB306 genotypes. a) Genetic variance estimates for each transition rate. Lettering indicates backward (B), forward (F) and still (S) movement states. The posterior means are compared to the 95% CI of the randomized null M matrices (orange bars). We detect significant genetic variance for all traits in the N2 background and for 3 out of 6 traits in the PB306 background (stars indicating significance at $\alpha <0.05$). b) Genetic covariances estimates between transition rates. (Co)variances estimates are non-null if the 95% CI of the distribution does not overlap zero (stars indicating significance at $\alpha <0.05$). Mean and CI interval values of genetic (co)variances can be found in Supplementary Table S1 as well as the 95% CI of the null distributions.

Fig. 3.

M matrix comparison between N2 and PB306. a) Shown is the total amount of genetic variance as measured by the trace of the M matrices. For both N2 and PB306, the total genetic variance is different from the randomized null distribution (gray, mean $\pm$95% CI), but there is no difference between N2 and PB306 (colored, 83% CI). b) Spectral decomposition of the M-matrices indicate that the phenotypic dimension encompassing most genetic variance (measured by the $\lambda$ eigenvalue of the first eigenvector $m_{max}$), is different from the null distribution for both N2 and PB306 (gray, mean $\pm$95% CI), but N2 and PB306 do not differ in this $m_{max}$ dimension (colored, 83% CI). C. The normalized projection of the M matrices on the other background’s $m_{max}$ axis ranges from 0 to 1 (with 1 meaning perfect alignment, see Methods). For each matrix from our posterior distribution, we compute $\mathrm{\Pi }$ (dots and 83% and 95% bars; see equation (6)) and the null expectation (${\mathrm{\Pi }}_0$, 83%, and 95% bars with star; see equation (7)). For each background, there is more variance projected than under a null expectation because the mean estimates do not overlap the 95% null CI (Supplementary Table S2).

Fig. 4.

Standing and mutation genetic (co)variances for locomotion behavior. Lettering indicates backward (B), forward (F), and still (S) movement states, left to right indicating the direction of movement. The bottom six entries are the diagonal genetic variance estimates for each transition rate, while top 15 entries the off-diagonal genetic covariances estimates between transition rates. Green for the lab-adapted population (A6140), cyan for the N2 genotype, blue for the PB306 genotype. Dots show the mean of posterior distribution with bars being the 95% credible intervals. Distributions can be differentiated whenever their 83% credible intervals do not overlap (colored bars). All estimates are standardized by on a common scale by dividing each genetic (co)variance by the total phenotypic variance in each population (equation (9)).

Fig. 5.

Standing versus mutation genetic (co)variances for locomotion behavior. a) Eigentensor decomposition of the 3 matrices, 2 M matrices from the N2 and the PB306 genotypes, and the G matrix from the A6140 lab-adapted population (from Fig. 4). The genetic variance explaining differences between matrices are shown as the mode and 95% credible interval of the posterior distributions of the first ($E_1$) and second ($E_2$) eigentensors, along with the expected distributions by sampling alone (line and dashed, respectively). b) In the first eigentensor ($E_1$), the coordinates of the three matrices. The lab-adapted population has the largest absolute values, which drives most of the differentiation seen in panel A. c) The first eigenvector ($e_{11}$) of the first eigentensor ($E_1$) is the one where most genetic differences between the lab-adapted population and the N2 and PB306 genotypes are found (71% of the variance found in E1). d) The normalized projection of the M-matrices on the $g_{max}$ of the domesticated population (dots and 83% and 95% colored bars). Here only the PB306 M-matrix has more genetic variance along $g_{max}$ than under a null expectation (${\mathrm{\Pi }}_0$, asterisks, and bars; see equation (7)). Moreover, the N2 genotype is not more aligned with the G matrix than expected by chance and has significantly less aligned variance than the PB306 genotype (using the 83% CI criteria; Supplementary Table S3). The angles between the two $m_{max}$ and $g_{max}$ show the same trend between the two backgrounds (Supplementary Fig. S2).