Assessing nonlinearities in the GFP random mutagenesis landscape using the Power Transform

Epistasis, a non-additive contribution of mutations to fitness, complicates genotype-to-phenotype prediction and is often confounded by nonlinearities in phenotype measurements. The Power Transform method, particularly Box-Cox, has been used to reduce epistasis in small, combinatorially complete datasets by linearizing phenotypic scales. However, its applicability to large landscapes, especially those generated by (quasi-)random mutagenesis, remains unclear. Here, we apply both Box-Cox and Yeo-Johnson Power Transforms to the extensively characterized green fluorescent protein (GFP) fitness landscape, which contains hundreds of thousands of two- and three-dimensional combinatorially complete datasets. Surprisingly, when applied to individual hypercubes, Box-Cox reduces pairwise epistasis by 19.4% on average, whereas Yeo-Johnson - despite accommodating negative values - slightly increases epistasis (by 4.45%). Moreover, in a notable fraction of hypercubes, both methods increase the magnitude of epistatic coefficients, indicating that Power Transform does not universally reduce nonlinearity at the local scale. In contrast, applying Yeo-Johnson to the largest connected component of the GFP landscape (20,872 genotypes) successfully reduces both pairwise (by 3.86%) and third-order epistasis (by 11.6%), with the majority of coefficients decreasing in magnitude. These results demonstrate that Power Transform can be extended to large, real-world landscapes generated by random mutagenesis, but only when applied to connected sublandscapes. Our findings highlight a critical distinction between global and local linearization and caution against assuming that Power Transform always diminishes epistasis.