Table S1.

Environmental patterns allowing accessibility

Pattern or concatenated pattern	Occurrence
A
ERERRR*	42
ERRRRR†	30
REERRR‡	29
REEERR	12
REER=R‡	11
ERERER*	6
ERER=R*	4
ERRERR	4
REERER‡	4
EREERR	4
ERRR=R†	2
B
RE	—
ER	32
RER	52
ERE	—
RERE	—
ERER	56
RERER	15
ERERE	—
RERERE	—
ERERER	10

For each of the 720 direct mutational trajectories from MK:acca to YQ:tggt, we analyzed for each mutational step the environmental conditions that allow fixation of the mutation. R indicates that an environment without IPTG (repression) is required for the fixation of the mutation. E indicates that an environment with IPTG (induction) is required; = indicates that there are no requirements (mutation fixation can occur in both environments). Under A are patterns of environmental requirement sorted by occurrence (i.e., the number of accessible direct paths corresponding to the given pattern of environmental requirements). Under B are statistics on the concatenated patterns. To classify the patterns regardless of the time spent in each environment, the same environmental episodes are concatenated. For example, the first pattern under A is concatenated as ERER, because there are only three environmental changes. The concatenated patterns are sorted by length. When both environments allow fixation, = is counted one time as R and one time as E; — indicates that no occurrence of the corresponding pattern of requirement is observed.

^{*, †, ‡}Indicated groups are to show which other patterns a pattern containing = could be associated with if one were to differentiate = as either R or E; for instance, patterns ERERRR and ERERER are specific instances of pattern ERER=R.