What this calculator does
Mutation frequency is the proportion of a population carrying a mutation: mutants divided by total tested. It is a straightforward division, and the reason it gets its own calculator is the scaling. Frequencies are typically so small that the raw fraction is unreadable.
One worthwhile distinction: frequency is not the same as mutation rate. Frequency counts what is present now, which includes mutations that arose many generations ago and have been carried along since. Rate measures how often new mutations appear per generation. A single lucky early mutation can inflate frequency enormously without the rate changing at all.
The formula
The number of mutants is divided by the total tested to give a plain fraction, which is also expressed as a percentage. The per-million and per-hundred-million figures rescale the same number into ranges that are easier to read and compare, since mutation frequencies routinely fall below one in a million.
| Term | Meaning |
|---|---|
| Mutation frequency | Mutants divided by total individuals tested, at a point in time. |
| Mutation rate | New mutations arising per cell division or per generation. A different quantity requiring a different experimental design. |
| Jackpot culture | A culture where a mutation arose early and was amplified by subsequent growth, giving a high frequency unrelated to the rate. |
| Fluctuation test | The Luria-Delbruck experimental design that separates rate from frequency. |
The inputs explained
| Field | What to enter |
|---|---|
| Mutants observed (count) | Number of mutants observed. |
| Total organisms/cells tested (count) | Total individuals or colonies tested. |
When to use it
Reporting a screening result
Mutant counts against a total screened is the raw output of a selection experiment, and frequency is how it gets reported.
Comparing treatments
A mutagen treatment against an untreated control is compared as a ratio of frequencies, which requires both to be calculated the same way.
Estimating resistance in a population
The frequency of pre-existing resistant organisms determines how likely a treatment is to fail, and it is why combination therapy is used against organisms that mutate readily.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
What frequency does each mutant count give?
A range of mutant counts from the same total tested.
| Mutants observed | Mutation frequency | Per million tested | Per 100 million tested |
|---|---|---|---|
| 1 | 0.000001 | 1.00 | 100.0 |
| 12 | 0.000012 | 12.00 | 1,200.0 |
| 100 | 0.0001 | 100.00 | 10,000.0 |
| 1,000 | 0.001 | 1,000.00 | 100,000.0 |
Questions
What is the difference between mutation frequency and mutation rate?
Frequency is a snapshot of how many mutants are present; rate is how often new ones arise per generation. A culture where a mutation happened early and then grew has a high frequency and an ordinary rate. Separating the two requires a fluctuation test rather than a single measurement.
What is a typical mutation frequency?
It depends entirely on the organism, the locus and whether a mutagen was applied. Spontaneous frequencies for a specific gene in bacteria commonly fall between one in a million and one in a hundred million, which is why the scaled columns cover that range.
Why report per million rather than as a percentage?
Because percentages round to zero at these scales. One mutant in a million is 0.0001%, and one in a hundred million is 0.000001%, neither of which is readable or comparable at a glance. Per-million units keep the significant figures visible.
How many individuals do I need to test?
Enough to expect several mutants rather than zero or one, since a count of zero gives no usable estimate and a count of one has enormous uncertainty. If the expected frequency is one in a million, testing ten million is a reasonable target.
For allele frequencies in a population, see the allele frequency calculator. For microbial population growth, see the bacterial growth calculator.