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Figure S1. Comparison between simulated walk length distribution walk distance distribution and the analytical estimates by Flyvbjerg and Lautrup (1992) for a random walker.

Figure S2. Comparison between simulated walk distance distribution of a greedy walker and two analytical estimates.

Figure S3. Simulated walk distance distribution for a random walker under sudden or slow switching on purely random landscapes.

Figure S4. Simulated walk distance distribution for a greedy walker under sudden or slow switching on purely random landscapes.

Figure S5. Simulated probability of reverse evolution at each genetic distance for a random walker on purely random landscapes.

Figure S6. Simulated probability of reverse evolution at each genetic distance for a greedy walker on purely random landscapes.

Figure S7. Similar to Figure 3 in the main text, but the fitness landscapes were constructed using the Kauffman NK model (Kauffman and Weinberger 1989), with either uniform or normal distributions for the underlying fitness values.

Figure S8. Similar to Figure 3 in the main text, but the initial additive (nonepistatic) landscapes were constructed differently.

Figure S9. In small populations with large-effect mutations (sb >> 1), slowly switching between environments facilitates reverse evolution even after multiple rounds of switching.

Figure S10. Similar to Figure S9, but with small-effect mutations (sb << 1).

Figure S11. We propose a phenomenological model to simulate the effect of clonal interference in large populations, and use individual-based simulations to confirm the rough consistency of this phenomenological model on a simple fitness landscape.

Figure S12. Under our phenomenological model of clonal interference slowly switching between environments no longer facilitates reverse evolution for very large populations that are subject to extensive clonal interference.

Figure S13. Average distance evolved in the new environment for individual-based Wright--Fisher simulations.

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