S-Leaping: An Adaptive, Accelerated Stochastic Simulation Algorithm, Bridging \(\tau \)-Leaping and R-Leaping

  • Jana Lipková
  • Georgios Arampatzis
  • Philippe Chatelain
  • Bjoern Menze
  • Petros KoumoutsakosEmail author
Special Issue: Gillespie and His Algorithms


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.


Stochastic simulation algorithms Stiff systems Accelerated simulation 



PK and GA gratefully acknowledge support from the European Research Council (ERC) Advanced Investigator Award (No. 341117). The authors thank both anonymous reviewers for their insightful comments that have helped us to improve the content of the paper.


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© Society for Mathematical Biology 2018

Authors and Affiliations

  1. 1.Department of InformaticsTechnical University of MunichMunichGermany
  2. 2.Institute of Mechanics, Materials and Civil EngineeringUniversité catholique de LouvainLouvain-la-NeuveBelgium
  3. 3.Computational Science and Engineering LaboratoryETH ZurichZurichSwitzerland

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