Detecting genomic footprints of selection is an important step in the understanding of evolution. Accounting for linkage disequilibrium in genome scans increases detection power, but haplotype-based methods require individual genotypes and are not applicable on pool-sequenced samples. We propose to take advantage of the local score approach to account for linkage disequilibrium in genome scans for selection, cumulating (possibly small) signals from single markers over a genomic segment, to clearly pinpoint a selection signal. Using computer simulations, we demonstrate that this approach detects selection with higher power than several state-of-the-art single marker, windowing or haplotype-based approaches. We illustrate this on two benchmark data sets including individual genotypes, for which we obtain similar results with the local score and one haplotype-based approach. Finally, we apply the local score approach to Pool-Seq data obtained from a divergent selection experiment on behavior in quail, and obtain precise and biologically coherent selection signals: while competing methods fail to highlight any clear selection signature, our method detects several regions involving genes known to act on social responsiveness or autistic traits. Although we focus here on the detection of positive selection from multiple population data, the local score approach is general and can be applied to other genome scans for selection or other genome-wide analyses such as GWAS.