  Motivation: Stochastic reaction networks are a widespread model to describe
biological systems where the presence of noise is relevant, such as in cell
regulatory processes. Unfortu-nately, in all but simplest models the resulting
discrete state-space representation hinders analytical tractability and makes
numerical simulations expensive. Reduction methods can lower complexity by
computing model projections that preserve dynamics of interest to the user.
Results: We present an exact lumping method for stochastic reaction networks
with mass-action kinetics. It hinges on an equivalence relation between the
species, resulting in a reduced network where the dynamics of each
macro-species is stochastically equivalent to the sum of the original species
in each equivalence class, for any choice of the initial state of the system.
Furthermore, by an appropriate encoding of kinetic parameters as additional
species, the method can establish equivalences that do not depend on specific
values of the parameters. The method is supported by an efficient algorithm to
compute the largest species equivalence, thus the maximal lumping. The
effectiveness and scalability of our lumping technique, as well as the physical
interpretability of resulting reductions, is demonstrated in several models of
signaling pathways and epidemic processes on complex networks. Availability:
The algorithms for species equivalence have been implemented in the software
tool ERODE, freely available for download from https://www.erode.eu.
