The probability ofkor more events occurring
inthetimeintervalisthen
PðX≥kÞ¼ 1 Qðk;lÞwhich can be solved forlnumerically using
the inverse incomplete regularized gamma
function,
l¼Q^1 ½ 1 PðX≥kÞ;kThe total time to acquirekor more mu-
tations is thenlΤ.
The probability of acquiring at leastk=4
improbable mutations given a rate parameter
of 1 improbable mutation every 12 weeks is
plotted as a function of time in fig. S19C. For
P(X≥4) = 0.99, the number of 12-week inter-
vals is 10.05 to acquire at least four improbable
mutations. Thus, mice would need to be im-
munized biweekly for ~120 weeks in order to
achieve 99% probability of acquiring at least
four improbable mutations.
Quantification and statistical analysis
The statistical analyses for this paper were per-
formed in SAS 9.4 to calculate exact Wilcoxon
tests for group comparisons. Due to the ex-
ploratorynatureofthisresearchandthesmall
sample size, we are using an alpha level of
0.05 as a descriptive level for significance
and have not made any adjustments to con-
trol for multiple testing. For group sizes less
than 5, no paired-sample comparisons were
performed due to the small sample size; only
descriptive statistics are provided in these
instances.
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