Title: $S$-Leaping: An adaptive, accelerated stochastic simulation algorithm, bridging $τ$-leaping and $R$-leaping,
Abstract: We propose the $S$-leaping algorithm for the acceleration of Gillespie's
stochastic simulation algorithm that combines the advantages of the two main
accelerated methods; the $\tau$-leaping and $R$-leaping algorithms. These
algorithms are known to be efficient under different conditions; the
$\tau$-leaping is efficient for non-stiff systems or systems with partial
equilibrium, while the $R$-leaping performs better in stiff system thanks to an
efficient sampling procedure. However, even a small change in a system's set up
can critically affect the nature of the simulated system and thus reduce the
efficiency of an accelerated algorithm. The proposed algorithm combines the
efficient time step selection from the $\tau$-leaping with the effective
sampling procedure from the $R$-leaping algorithm. The $S$-leaping is shown to
maintain its efficiency under different conditions and in the case of large and
stiff systems or systems with fast dynamics, the $S$-leaping outperforms both
methods. We demonstrate the performance and the accuracy of the $S$-leaping in
comparison with the $\tau$-leaping and $R$-leaping on a number of benchmark
systems involving biological reaction networks.