All published methods for learning about demographic history make the simplifying assumption that the genome evolves neutrally, and do not seek to account for the effects of natural selection on patterns of variation. This is a major concern, as ample work has demonstrated the pervasive effects of natural selection and in particular background selection (BGS) on patterns of genetic variation in diverse species. Simulations and theoretical work have shown that methods to infer changes in effective population size over time (Ne(t)) become increasingly inaccurate as the strength of linked selection increases. Here, we introduce an extension to the Pairwise Sequentially Markovian Coalescent (PSMC) algorithm, PSMC+, which explicitly co-models demographic history and natural selection. We benchmark our method using forward-in-time simulations with BGS and find that our approach improves the accuracy of effective population size inference. Leveraging a high-resolution map of BGS in humans, we infer considerable changes in the magnitude of inferred effective population size relative to previous reports. Finally, we separately infer Ne(t) on the X chromosome and on the autosomes in diverse great apes without making a correction for selection and find that the inferred ratio fluctuates substantially through time in a way that differs across species, showing that uncorrected selection may be an important driver of signals of genetic difference on the X chromosome and autosomes.Trevor Cousins, Daniel Tabin, Nick Patterson, David Reich, Arun DurvasulabioRxiv 2024.01.18.576291; doi: https://doi.org/10.1101/2024.01.18.576291