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Relaxation of selective strength, manifested as a reduction in the efficiency or intensity of natural selection, can drive evolutionary innovation and presage lineage extinction or loss of function. Mechanisms through which selection can be relaxed range from the removal of an existing selective constraint to a reduction in effective population size. Standard methods for estimating the strength and extent of purifying or positive selection from molecular sequence data are not suitable for detecting relaxed selection, because they lack power and can mistake an increase in the intensity of positive selection for relaxation of both purifying and positive selection. Here, we present a general hypothesis testing framework (RELAX) for detecting relaxed selection in a codon-based phylogenetic framework. Given two subsets of branches in a phylogeny, RELAX can determine whether selective strength was relaxed or …