Distribution of fitness effects of beneficial mutations
In plain words
Extreme-value statistics, the mathematics of the largest values in a random sample, predicts that rare improving mutations in a well-adapted organism follow a simple exponential law. Experiments give mixed support, and which statistical class real mutations follow is unsettled.
Precise statement
If the wild type is near the top of the fitness distribution of its mutational neighbors, extreme-value theory predicts exponentially distributed beneficial selection coefficients s (Gumbel domain), with Weibull (bounded) or Frechet (heavy-tailed) alternatives. Determine the domain of attraction from large mutant libraries (deep mutational scanning, barcoded lineage tracking) across organisms and environments, and how it depends on distance from the optimum.
What would settle it
Large-library measurements of beneficial effects with tail-shape estimation across several organisms and environments.