Equation 1 · 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 equation states an equality: the expressions on both sides have the same value under the article’s assumptions. 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 w_ceiling
eiling is part of the quantity the equation computes from the expression on the right.
Symbol t
t is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.
Symbol a
a occurs above the fraction bar. The numerator is divided by the entire denominator below it.
Symbol b
b occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →subscript
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
Denominator: 1 + bt
The complete quantity below the fraction bar; it must be nonzero for this division.
How to interpret it
With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
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 . which approaches a fixed value of 1 + a/b as t grows without bound,…
Read the full surrounding passage
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 . which approaches a fixed value of 1 + a/b as t grows without bound, and
Sources cited in the article section
- [3] Historical contingency and the evolution of a key innovation in an experimental population of Escherichia coli ↗
- [14] They're back! ↗
- [2] Long-Term Dynamics of Adaptation in Asexual Populations ↗
- [13] The E. Coli Long-Term Evolution Experiment Is The Longest-Running Study Of Its Kind, And It's Been Going For 80,000 Generations ↗
These citations give research context. Read each source to check which claims it supports.
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