Motivation: Cancer is well known to be the end result of somatic mutations that disrupt normal cell division. The number of such mutations that have to be accumulated in a cell before cancer develops depends on the type of cancer. The waiting time T(m) until the appearance of m mutations in a cell is thus an important quantity in population genetics models of carcinogenesis. Such models are often difficult to analyze theoretically because of the complex interactions of mutation, drift and selection. They are also computationally expensive to simulate because of the large number of cells and the low mutation rate.
Results: We develop an efficient algorithm for simulating the waiting time T(m) until m mutations under a population genetics model of cancer development. We use an exact algorithm to simulate evolution of small cell populations and coarse-grained τ-leaping approximation to handle large populations. We compared our hybrid simulation algorithm with the exact algorithm in small populations and with available asymptotic results for large populations. The comparison suggested that our algorithm is accurate and computationally efficient. We used the algorithm to study the waiting time for up to 20 mutations under a Moran model with variable population sizes. Our new algorithm may be useful for studying realistic models of carcinogenesis, which incorporates variable mutation rates and fitness effects.