Journal: Molecular Systems Biology

Article Title: Canalisation and plasticity on the developmental manifold of Caenorhabditis elegans

doi: 10.15252/msb.202311835

Figure Lengend Snippet: The z scores of the three rescaled logistic fit parameters are shown in a 3d scatterplot (blue dots). These points lie close to a curved 2d manifold (mesh grid), which was found by performing nonlinear principal component analysis (NLPCA). The flattened manifold is shown in (D). On this manifold, φ 1 seems to separate the environmental conditions as shown in by the marginal distribution over bacterial food sources. In contrast, the marginal distributions over the C. elegans strains shows separation in φ 2 . Marginal distributions were computed with a kernel density estimator implemented with the ksdensity function in MATLAB. The principal component weights for first two nonlinear principal components φ 1 and φ 2 for each C. elegans shown as a scatterplot. The colour of each point indicates that worm's development time, t dev , as indicated by the colour bar. The mean φ 1 and φ 2 for each condition are shown as a combination of symbols ( C. elegans strain) and colour (Bacterial food source). This separation in φ 1 and φ 2 can be quantified by computing the F‐statistic for a linear regression model taking genotype and environment as regressors. φ 1 regresses primarily on environment and φ 2 on genotype. Interestingly, both genotype and environment together are generally required to explain the variance in the three logistic fit parameters and the developmental time alone. To determine the effect of varying φ 1 on the shape of the growth curve, φ 2 was fixed to 0 and φ 1 was varied through a range, as indicated by the colour bar, with coordinates being converted back from the unit‐less quantities. In this case, there appears to be a trade‐off between fast growth (blue curves) and larger adult size (green curves). Similarly, when φ 1 is fixed and φ 2 varied, the resulting growth curves change from slower growth and smaller adult size (green) to faster growth and larger adult size (blue). Source data are available online for this figure.

Article Snippet: Here, we use Gaussian distributions as our Kernel function. f x est x = 1 nh ∑ i = 1 n K x − x i h with: K x = 1 2 π exp − x 2 2 The parameter h is called the bandwidth and is optimally chosen on the basis of the number of data points n . We use the ksdensity implementation of this estimator in MATLAB.

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