Fig. 5

Interactions among top six alleles show evidence of epistasis. Genotypes and fitness measurements were obtained from 359 intermediate clones generated during the construction of the final strain containing the six best alleles (Additional file 7). Each clone was genotyped using MASC-PCR and doubling time was measured during allele validation experiments and final strain construction. a Individual model coefficients for the top six alleles, as well as three significant interaction terms identified during combinatorial construction. These values are from a linear model with interaction terms between each pair of alleles. The error  bars signify the standard error of the mean of the model coefficients and the significance codes for a non-zero effect size are: *** p < 0.001, ** 0.001 ≤ p < 0.01, * 0.01 ≤ p < 0.05, n.s. not significant. All three interactions coefficients remain significant after a family-wise error rate (FWER) of \( \upalpha \) = 0.05/C(6,2) = 0.003. b Each data point represents the amount of fitness recovered when adding the allele specified to an identical starting genotype background. Horizontal error bars correspond to the standard deviation of fitness defect among all clones with this starting genotype. Vertical error bars represent the standard deviation of all differences between clones with and without the respective allele. For each plot, the thick colored line represents a simple linear fit through the points, corresponding to the r and p values given in each plot. The dotted line corresponds to the predicted fit for a simple multiplicative model of fitness where the allele always recovers a constant percent of the remaining fitness defect regardless of the background. For all alleles except A4102449G (pink), adding the allele to C321 showed a recovery of the fitness defect (>0 on the y axis), with the percentage of defect recovered decreasing as other alleles are also reverted, consistent with a first-order multiplicative model. In some cases, the fitness improvement drops more rapidly than predicted by the multiplicative model (i.e. points below the dotted lines), suggesting diminishing returns epistasis. This is supported by the negative-coefficient interaction terms in panel (a). In the case of A4102449G there appears to be a negative effect with the mutation alone, but an increase in the presence of other alleles, suggesting possible sign epistasis