Significance testing on TFBS load data was non-trivial, as their distributions are sparse (especially in the case of human data), with the majority of TFBSs having a load of zero. In statistical terms, these data present a case of zero-inflation, in which the observed zeros are a mixture of missing data (that is, mutations that are not observed due to a limited number of available genotypes) and 'real' zeroes (mutations that never occur because their deleterious effect is prohibitively strong). To overcome this problem, we have initially used generalized additive models (gam) based on zero-inflated distributions of the response variable (ZAGA for Drosophila and BEINF0 for human implemented in the R package gamlss [73]; not shown). However, gam P-values may be difficult to interpret, especially when the model includes random effects [73] (in our case, the TF identity). We have therefore eventually turned to permutation tests, permuting motif load values separately for each TF to avoid bias associated with specific properties of individual factors. To test the significance of trends, we used a permutation statistic based on [74]: the dot product of the normalized data vector × and the index vector (1,..., N), where N is the length of X.
