| Abstract: |
| Cancer results from somatic mutations disrupting cell division, with the number of required mutations varying by cancer type. The waiting time for m mutations in a cell is a key parameter in carcinogenesis models, which are theoretically complex due to interactions of mutation, drift, and selection, and computationally expensive to simulate due to large cell populations and low mutation rates.
We present an efficient algorithm to simulate the waiting time under a population genetics model of cancer. Our hybrid method combines an exact algorithm for small populations with a coarse-grained
$\tau$-leaping approximation for large populations. Comparisons with exact simulations for small populations and asymptotic results for large populations confirm the algorithm`s accuracy and computational efficiency. We applied it to study waiting times for up to 20 mutations in a Moran model with variable population sizes. This algorithm may facilitate the study of realistic carcinogenesis models incorporating variable mutation rates and fitness effects. |
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