Estimating the proportion of adaptive substitutions (α) is of primary importance to uncover the determinants of adaptation in comparative genomic studies. Several methods have been proposed to estimate α from patterns polymorphism and divergence in coding sequences. However, estimators of α can be biased when the underlying assumptions are not met. Here we focus on a potential source of bias, i.e., variation through time in the long term population size (N) of the considered species....