Summary
Neutral mutation frequency is similar across distance fitness peaks within a given protein (1). This was observed in GFP.
1.
Sarkisyan KS, Bolotin DA, Meer MV, Usmanova DR, Mishin AS, Sharonov GV, et al. Local fitness landscape of the green fluorescent protein. Nature. 2016;533(7603):397–401. Available from: https://doi.org/10.1038/nature17995