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Equation 1 · Part 5 · Seventy-Five Thousand Generations of E. coli, and Counting

=

wceiling(t)=1+a t1+b tw_{\text{ceiling}}(t) = 1 + \frac{a\,t}{1 + b\,t}
=

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

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 wceiling(t)=1+a t1+b tw_{\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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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the article section

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