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Figure S1. Correlated phenotypic neighbourhood---Mean adaptation time as a function of the probability of environmental perturbation, ε.

Figure S2. Variation in size of phenotypic neighbourhood---plots show populations of N = 10,000 individuals, with μ = 0.001, P = 100, &Kbar; = 5, q = 0.5, φH = 0.9, φL = 0.1 and πH = 0.5 with s = 2 (red line) and s = 8 (blue line).

Figure S3. Nonlethal deleterious mutations---plots show populations of N = 10,000 individuals, with μ = 0.001, P = 100, K = 10, q = 0.2, φH = 0.9, φL = 0.1 and πH = 0.5, d = 0.2 with s = 0.5 (red line) and s = 3 (blue line).

Figure S4. Deleterious low robustness adaptive genotype---plots show populations of N = 10,000 individuals, with μ = 0.001, P = 100, K = 5, q = 0.5 and s = 0.05.

Figure S5. Mean adaptation time as a function of the probability of environmental perturbation, &epsi;, in the regime 1&plus;s/K < φHφL/1 − φL.

Figure S6.The mean adaptation time as a function of mutational robustness, q.

Figure S7. Most realistic selective regime with s/K = 0.2, πH = 0.5 and πL = 0.5.

Figure S8. Less realistic selective regime with s/K = 1.2, πH = 0.5 and πL = 0.5.

Figure S9. Most realistic selective regime with s/K = 0.2, πH = 0.5 and πL = 0.1.

Table S1. Model parameters.

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