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Number of mutations and mutated sequences

Expected number of mutations in a single sequence: $$p_{m} = \frac{N_{mutations}}{L_{Sequence}} = N_{generations} * r_{mutation} = t_{total} * \Phi * r_{mutation}$$

The expected share of sequences that shows at least one mutation in $L_{Sequence}$ bp is the probability that $L_{sequence}$ basepairs stay unchanged when $\frac{N_{mutations}}{L_{Sequence}}$ mutations are expected: $$p_{M} = \frac{N_{mutated}}{N_{Sequences}} = 1 - p(N_{mutations}=0) = 1 - (1-p_{m})^{L_{Sequence}} $$

With this equation we can also calculate the number of sequences $N_{Sequences}$ that have to be sequenced in order to find a mutated one with a probability of $p(N_{mutated} > 0)$. $$ N_{Sequences} = \frac{p(N_{mutated} > 0)}{p_{M}} $$

The probability to find at least one mutated sequence under the given conditions is $$p(N_{mutated}>0) = 1 - (1-p_{M})^{N_{sequences}}$$ which gives $$N_{Sequences} = \frac{ln(1-p(N_{mutated}>0))}{ln(1-p_{M})}$$

Set $\Phi$ to zero to use the number of generations for the calculation. If $\Phi$ and the number of generations are given, $\Phi$ is used.

Consider $L_{Sequence}$ as the number of basepairs that is expected to be mutated. If half of the sequence you are interested in, is highly conserved choose a lower $L_{Sequence}$.

$p_{m} =$ %(bp/bp).

$N_{mutations} =$ bp per sequence.

The share of sequences that shows at least one mutation in $L_{Sequence}$ bp is $p_{M}=$ % of sequences

Get your mutations

Mutation rate $r_{mutation} [bp/generation]$
Flow troughLagoon $\Phi_{lagoon} [Volumes/h]$
Total time
in lagoon $t_{total} [h]$
Number
of generations $N_{generations}$
Length of sequence that can mutate $L_{Sequence} [bp]$
Number of sequences that are sequenced $N_{Sequences}$
Probability to get at least one mutated result $p(N_{mutated}>0) $