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Equation 4 · Part 5 · Seventy-Five Thousand Generations of E. coli, and Counting

=

wopen(t)=1+a tβw_{\text{open}}(t) = 1 + a\,t^{\beta}
=

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

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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

which approaches a fixed value of 1 + a/b as t grows without bound, and wopen(t)=1+a tβw_{\text{open}}(t) = 1 + a\,t^{\beta}. for an exponent β\beta between 0 and 1, which keeps rising — more and more slowly, but without any asymptote — for every value of t . Wiser and colleagues derived the second form theoretically from a model combining clonal interference with diminishing-returns epistasis among beneficial mutations, and reported that across 50,000 generations of real data, “mean fitness appears to increase without bound, consistent with a power law” [ 2 ] . The decelerating rate that Lenski’s 1991 paper had already observed over the first 2,000 generations turns out to be compatible with no ceiling at all: a…

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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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