Most adaptive traits are controlled by large number of genes that may all together be the targets of selection. Adaptation may thus involve multiple but not necessarily substantial allele frequency changes. This has important consequences for the detection of selected loci and implies that a quantitative genetics framework may be more appropriate than the classical selective sweep paradigm. Preferred methods to detect loci involved in local adaptation are based on the detection of outlier values of the allelic differentiation FST. A quantitative genetics framework is adopted here to review theoretical expectations for how allelic differentiation at quantitative trait loci (FSTQ) relates to (i), neutral genetic differentiation (FST) and (ii), phenotypic differentiation (QST). We identify cases where results of outlier-based methods are likely to be poor and where differentiation at selected loci conveys little information regarding local adaptation. A first case is when neutral differentiation is high, so that local adaptation does not necessitate increased differentiation. A second case is when local adaptation is reached via an increased covariance of allelic effects rather than via allele frequency changes, which is more likely under high gene flow when the number of loci is high and selection is recent. The comparison of theoretical predictions with observed data from the literature suggests that polygenic local adaptation involving only faint allele frequency changes are very likely in some species such as forest trees and for climate-related traits. Recent methodological improvements that may alleviate the weakness of FST-based detection methods are presented< Leer menos