Equation 6 · Seventy-Five Thousand Generations of E. coli, and Counting
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for an exponent 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 population’s fitness gains can keep shrinking, generation after generation, without the sum of those…
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for an exponent 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 population’s fitness gains can keep shrinking, generation after generation, without the sum of those gains ever stopping. That is a specific, falsifiable claim about the shape of adaptation, not a synonym for “still improving.”
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