BIO
In the literature: open
Does fitness in long-term evolution increase without limit?
In plain words
In an experiment running since 1988, twelve populations of E. coli have kept getting fitter for more than 70,000 generations. Whether their fitness approaches a ceiling or rises forever is open.
Precise statement
For the E. coli long-term evolution experiment (12 populations in constant glucose-limited medium), relative fitness $w(t)$ up to 50,000 generations was fit better by a power law $w = (1 + b t)^a$ (unbounded) than by a hyperbola $w = 1 + c t/(t + d)$ (bounded) (Wiser, Ribeck and Lenski, 2013). Decide from later data whether $w(t)$ is bounded, and derive the trajectory from clonal-interference theory with diminishing-returns epistasis.
What would settle it
Fitness assays across the full archive of frozen samples, with model comparison between bounded and unbounded forms.