Efficient step size selection for the tau-leaping simulation method

Abstract

The tau-leaping method of simulating the stochastic time evolution of a well-stirred chemically reacting system uses a Poisson approximation to take time steps that leap over many reaction events. Theory implies that tau leaping should be accurate so long as no propensity function changes its value "significantly" during any time step tau. Presented here is an improved procedure for estimating the largest value for tau that is consistent with this condition. This new tau-selection procedure is more accurate, easier to code, and faster to execute than the currently used procedure. The speedup in execution will be especially pronounced in systems that have many reaction channels.