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We present an accelerated algorithm to forward-simulate origin-fixation models. Our algorithm requires, on average, only about two fitness evaluations per fixed mutation, whereas traditional algorithms require, per one fixed mutation, a number of fitness evaluations on the order of the effective population size, Ne. Our accelerated algorithm yields the exact same steady state as the original algorithm but produces a different order of fixed mutations. By comparing several relevant evolutionarydoi:10.6084/m9.figshare.4675786.v1 fatcat:kq2eghmmpbfuvameuhtze4pzza