so that fdep + frock = 1. This theoretical mixing was quantified by applying a Monte Carlo simulation, where end-member parameter values were randomly sampled from their independently observed regional parameter distributions (obtained for example from a literature review, see below) to create 10 000 different theoretical initial conditions (i.e., the assumed stream water isotopic composition before MSR). A Rayleigh fractionation model was then applied to calculate the residual fraction of sulfur concentration after reduction (fred ). The model is based on the initial isotopic composition of the stream water (δ0 ; here represented by the 10 000 theoretical predictions of δsample ) and the residual isotopic composition in the stream water (δR ; represented by the observed isotopic value of stream waterδstream ), according to: