Equation 5 · Seventy-Five Thousand Generations of E. coli, and Counting
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
Read it piece by piece
Symbol β
β is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
How to interpret it
Read this expression with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
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…
Read the full surrounding passage
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.”
Sources cited in the surrounding passage
These citations give research context. Read each source to check which claims it supports.
Return to Seventy-Five Thousand Generations of E. coli, and Counting