The relative importance of natural selection and genetic drift in maintaining genetic diversity is key to explain current diversity and future adaptive potential. By comparing allelic frequencies, expected and observed heterozygosity or haplotype homozygosity within and between populations, we can disentangle selection and demography in statistical inferences. Finding regions under selection is central to understanding the processes of adaptation and speciation. Recent developments include haplotype-based methods to infer selection within populations. We benchmark iHS, nSL and H12 in simulated data with selection on a polygenic trait, and show that these methods work best when the traits are mildly polygenic. We also test their power on known regions under selection using Heliconius butterflies. In a second step, we study the impact of demographic history, through a simulation study based on the history of Central African human populations.This is a good model since it is settled by agricultural and hunter-gatherer populations having experienced different adaptive histories and for which demographic histories have been inferred. We analyse genomic diversity by simulating the split of an ancestral human population into agriculturalists (AGR) and hunter-gatherers (HG), where the AGR population has been expanding during the last 20000 years. We consider several scenarios, in which a quantitative trait has been under selection since agriculture emerged 5000 years ago in the AGR population. Either all populations were in mutation-drift equilibrium, or they are under background selection together with selection on the quantitative trait on the AGR population only. We benchmark common statistics (Fst, dxy, iHS, nSL and H12) on the loci that code for the quantitative trait under selection in order to analyse the impact of demography and selection on their power and false positive rates. Lastly, we show the impact of differing demographic histories on the genetic load of both populations.