Extended Data Fig. 4: Growth curves relating expression levels and relative fitness among environments.
Figure 3c uses a weighted linear least squares regression (LOESS curve) to describe the relationship between TDH3 expression and fitness in each environment. This method fits a line to the same data without assuming a particular shape of the relationship, but it does not enable statistical comparisons of this relationship among environments. To enable such comparisons, we fit both linear and quadratic models to the data in each environment, determined which model fit better in each case, and then tested for significant differences in fit among environments. (a) Fit of linear (blue, dotted) and quadratic (red, solid) models to the data in each environment, with predicted 95% confidence intervals. Datapoints show mean relative expression and fitness for each TDH3 promoter allele. In each case, the quadratic model better described the relationship between expression and relative fitness, though the improvement in fit was only marginally significant in ethanol (ANOVA, Glucose: F = 156.62, P < 2.2 *10−16; Galactose: F = 168.65, P = < 2.2 *10−16; Glycerol: F = 126.46, P = 6.34*10−15; Ethanol: F = 4.18, P = 0.047). (b) Comparison of inferred models for the four environment-specific datasets. Datapoints show mean relative expression and fitness for each TDH3 promoter allele in each environment. To test whether the quadratic fitness functions varied among environments, we compared a quadratic model in which parameters were estimated separately for each of the four environments to a quadratic model in which the fitness function was estimated jointly for all environments. We found that the more complex model (that is, fitting a distinct quadratic model to data from each environment) provided a significantly better fit to the data (AIC: -1378.53 vs -1289.27; ANOVA F = 14.82, P < 2.2 *10−16), suggesting that different environments have distinct, non-linear fitness functions. The estimated optimal expression level (scaled to the expression level of the unmutated reference) ± the standard deviation from the inferred quadratic models in each of the four environments were 1.27 ± 0.04 for glucose (blue), 0.92 ± 0.03 for galactose (green), 1.33 ± 0.05 for glycerol (pink), and 2.44 ± 0.8 for ethanol (red).
