fraction

The passage around this formula

Against that record, Wiser, Ribeck and Lenski fit fitness trajectories from all twelve populations across 50,000 generations against two competing functional shapes for how relative fitness might grow with time. One is a form that saturates — fitness rising quickly at first and then flattening toward a fixed asymptote, the kind of ceiling a “diminishing returns” reading of Lenski’s 1991 result would predict. The other is a power-law form, with no fixed limit: growth continues indefinitely, at an ever-slowing rate that nonetheless never reaches zero. Schematically, the contrast is between something like $w_{\text{ceiling}}(t) = 1 + \frac{a\,t}{1 + b\,t}$. which approaches a fixed value of 1 + a/b as t grows without bound,…

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