{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"3fe71898daa2848a6bc343c079f808caaa11f962b2cc9ad5d93a84b7a5fa2556","created":"2026-10-03T07:17:57Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"f055b7c3b737b0a907a29f02bff08c62eade7557d0e72a869fde54bf4b616869","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"bio.fitness-landscapes.unbounded-fitness","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"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.","posed_since":"2013","precise":"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.","problem_ref":null,"references":"","settled_by":"Fitness assays across the full archive of frozen samples, with model comparison between bounded and unbounded forms.","status_note":"","title":"Does fitness in long-term evolution increase without 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