New genomic approaches open the interesting perspective of identifying genes or genome regions under selection. In particular, genes involved in recent adaptive events should show the signs of recent selective sweeps, which include reduced genetic diversity, high levels of surrounding LD, long range haplotype homozygosity, increased genetic differences between populations, etc… However, it is still unclear if these effects cannot be obtained by chance at neutral loci under certain demographic scenarios, like a recent spatial expansion. We are therefore interested to study the neutral pattern of diversity arising after a complex demographic history in order to obtain better and more realistic null models of neutral evolution, and to develop more powerful tests of selection. We are also interested in studying the joint effect of selection and demographic in realistic models of past human evolution.