Understand the relationship
The reasoning behind the result
Direct rates need event and opportunity counts
μ = E/O
The numerator must represent independently identified mutational events, not all descendant mutant cells. The denominator must count the declared opportunities at which those events could occur.
Pooling adds events and opportunities before division. The quotient is an event rate for the visitor-defined opportunity unit and may exceed one when that unit can contain multiple independent events; it is not silently restricted to a Bernoulli probability.
The zero class estimates event number
P₀=e⁻ᵐ; m=−ln(P₀)
Under the ideal zero-class fluctuation model, the fraction of parallel cultures with no mutants is the zero term of a Poisson distribution for mutation events per culture.
The simple method discards much of the mutant-count distribution and is useful only in a limited range.
Cell divisions provide the stated opportunity denominator
μ = m/(Nₜ−N₀)
The entered binary-growth approximation treats final minus initial cells as divisions per culture, with no death and a mutant-free inoculum. If those conditions fail, this denominator is inappropriate.
The calculator reports both m and the rate so they are not conflated.
Endpoint mutant frequency is not a rate
An early event can produce many descendants and a late event few. Averaging endpoint mutant fractions is especially sensitive to jackpots.
Modern full-distribution estimators, phenotypic lag corrections and plating fractions require dedicated analysis outside this limited arithmetic.
Follow the numbers
Calculate a P₀ zero-class scenario
- Twelve of twenty cultures contain zero observed mutants, so P₀ = 12/20 = 0.6.
- The expected mutation events per culture are m = −ln(0.6) = 0.510826.
- The entered division approximation is 100,000,000 − 100 = 99,999,900 divisions per culture.
- The point estimate is μ = 0.510826/99,999,900 = 5.10826 × 10⁻⁹ per division.
- Because P₀=0.6 lies within the disclosed 0.1–0.7 working interval, the simple zero-class arithmetic is not range flagged.
The result is conditional on the ideal parallel-culture, detection and division assumptions and is not an endpoint mutant frequency.
Quick guide
How to use this calculator
- Choose direct mode only when independent events and their opportunities were established externally.
- Use P₀ mode only for a compatible parallel-culture fluctuation design and inspect the stated zero-class range and assumptions.
- Do not substitute endpoint mutant counts for independent mutation events.
Calculation method
Calculation and interpretation
Keep independent mutation events, observed mutant descendants and opportunity denominators separate.
Direct: μ = Σ independent events/Σ opportunities. P₀ scenario: m = −ln(P₀), P₀ = zero cultures/total cultures, μ = m/(Nₜ−N₀)
Worked example
Calculate a P₀ zero-class scenario
The result is conditional on the ideal parallel-culture, detection and division assumptions and is not an endpoint mutant frequency.
Direct: μ = Σ independent events/Σ opportunities. P₀ scenario: m = −ln(P₀), P₀ = zero cultures/total cultures, μ = m/(Nₜ−N₀)
Supported inputs
Precision and limits
Independent events required
Direct mode assumes the event counts were resolved externally; descendant mutant counts are not interchangeable. Because the visitor defines the opportunity unit, the result is an event rate and is not capped at one.
Limited P₀ method
The zero-class calculation is a simple point estimate. It flags P₀ outside 0.1–0.7 and does not replace a full fluctuation-test likelihood.
Binary-growth denominator
Nₜ−N₀ assumes initially mutant-free cultures, negligible death and one added cell per division.
Detection remains external
Phenotypic lag, plating fraction, selection, recovery and classification error are not corrected.
Numerical support
Use 1–30 direct records with safe whole event/opportunity counts, or 1–1,000,000 cultures and safe whole per-culture cell counts with Nₜ>N₀.
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