On the Probability of Reaching High Peaks in Fitness Landscapes by Adaptive Walks

Adaptive evolution can be described by an uphill walk in a fitness landscape. However, climbing the global peak in a multipeak landscape is improbable because of the high chance of being trapped at a local peak. Nonetheless, over three-quarters of simulated adaptive walks in the fitness landscape of the Escherichia coli dihydrofolate reductase (DHFR) gene were reported to end at the highest 14% of peaks, suggesting that biological systems may be substantially more evolvable than commonly thought. To investigate the cause and generality of this observation, we estimate in empirical and theoretical fitness landscapes the probability of reaching high peaks by adaptive walks (PHP), where high peaks refer to the highest 1, 5, 14, or 25% of all peaks. We find that (i) PHP varies substantially among landscapes, (ii) PHP in empirical landscapes is generally comparable to or smaller than that in same-size Rough Mount Fuji landscapes of similar ruggedness, and (iii) lowering landscape ruggedness boosts PHP. As observed in DHFR, we find in every examined landscape a positive correlation between the fitness of a peak and its basin size, which is the number of genotypes that can reach the peak through adaptive walks. Yet, this correlation does not guarantee a large PHP because of the influences of other factors. We conclude that evolvability depends on the specific fitness landscape and that the large PHP in the DHFR landscape is not a general property of empirical or theoretical fitness landscapes.