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We implement LSD via approximate Bayesian computation and demonstrate, via simulations, that LSD (a) has high power to identify selected loci across a large range of demographic-selection regimes, (b) outperforms commonly applied genome-scan methods under complex demographies and (c) accurately infers the directionality of selection for identified candidates. Using the same simulations, we further characterize the behaviour of isolation-with-migration models conducive to the study of local adaptation under regimes of selection. Finally