  The genetic code refers to a rule that maps 64 codons to 20 amino acids.
Nearly all organisms, with few exceptions, share the same genetic code, the
standard genetic code (SGC). While it remains unclear why this universal code
has arisen and been maintained during evolution, it may have been preserved
under selection pressure. Theoretical studies comparing the SGC and numerically
created hypothetical random genetic codes have suggested that the SGC has been
subject to strong selection pressure for being robust against translation
errors. However, these prior studies have searched for random genetic codes in
only a small subspace of the possible code space due to limitations in
computation time. Thus, how the genetic code has evolved, and the
characteristics of the genetic code fitness landscape, remain unclear. By
applying multicanonical Monte Carlo, an efficient rare-event sampling method,
we efficiently sampled random codes from a much broader random ensemble of
genetic codes than in previous studies, estimating that only one out of every
$10^{20}$ random codes is more robust than the SGC. This estimate is
significantly smaller than the previous estimate, one in a million. We also
characterized the fitness landscape of the genetic code that has four major
fitness peaks, one of which includes the SGC. Furthermore, genetic algorithm
analysis revealed that evolution under such a multi-peaked fitness landscape
could be strongly biased toward a narrow peak, in an evolutionary
path-dependent manner.
