The availability of large-scale population genomic sequence data has resulted in an explosion in efforts to infer the demographic histories of natural populations across a broad range of organisms. As demographic events alter coalescent genealogies, they leave detectable signatures in patterns of genetic variation within and between populations. Accordingly, a variety of approaches have been designed to leverage population genetic data to uncover the footprints of demographic change in the genome. The vast majority of these methods make the simplifying assumption that the measures of genetic variation used as their input are unaffected by natural selection. However, natural selection can dramatically skew patterns of variation not only at selected sites, but at linked, neutral loci as well. Here we assess the impact of recent positive selection on demographic inference by characterizing the performance of three popular methods through extensive simulation of data sets with varying numbers of linked selective sweeps. In particular, we examined three different demographic models relevant to a number of species, finding that positive selection can bias parameter estimates of each of these models-often severely. We find that selection can lead to incorrect inferences of population size changes when none have occurred. Moreover, we show that linked selection can lead to incorrect demographic model selection, when multiple demographic scenarios are compared. We argue that natural populations may experience the amount of recent positive selection required to skew inferences. These results suggest that demographic studies conducted in many species to date may have exaggerated the extent and frequency of population size changes.KEYWORDS population genetics; positive selection; demographic inference T HE widespread availability of population genomic data has spurred a new generation of studies aimed at understanding the histories of natural populations from a host of model and nonmodel organisms alike. In particular, genomescale variation data allows for inference of demographic factors such as population size changes, the timing and ordering of population splits, migration rates between populations, and the founding of admixed populations (Pool et al. 2010;Pickrell and Pritchard 2012;Sousa and Hey 2013). Such efforts can refine our picture of demographic events inferred from the archaeological record (e.g., Fagundes et al. 2007;Goebel et al. 2008), or reveal such events in species where no archaeological data are available, and can aid conservation efforts by complementing census data (e.g., Hájková et al. 2007;Garrick et al. 2015).Population genomic data sets are well suited for this task simply because demographic changes leave their mark on patterns of genetic variation. Recent population growth, for example, will result in an excess of rare variation compared to equilibrium expectations (Fu 1997), while population contraction will result in an excess of intermediate frequency alleles (Maruyama and Fuerst 198...