BIO In the literature: partially resolved

Accessibility of fitness peaks in large sequence spaces

In plain words

For evolution to reach the best genome, there must be a route of single mutations along which fitness never decreases. How often such routes exist in real landscapes with many sites is unknown.

Precise statement

In random-field models (house-of-cards, rough Mount Fuji, NK), the number of fitness-monotonic paths from a genotype to the global optimum in a sequence space of $L$ sites (binary or four-letter) varies with $L$ in ways set by ruggedness, including path-percolation transitions. Determine from combinatorially complete or near-complete empirical landscapes ($L\ge10$ to 15 sites) which model class applies, and extrapolate the probability that the global peak is accessible as $L$ grows.

What would settle it

Complete fitness maps of at least 10 to 15 interacting sites with path statistics compared against the random-field model classes.

Status in the literature

A combinatorially complete $4^9$ DHFR landscape (2023) was rugged (514 peaks) yet its highest peaks were accessible (Science, doi 10.1126/science.adh3860); extrapolation to larger $L$ is open.