Functional diversity (FD) is a key facet of biodiversity used to address central questions in ecology. Despite recent methodological advances, FD remains a complex concept and no consensus has been reached either on how to quantify it, or on how it influences ecological processes. Here we define FD as the distribution of trait values within a community. When and how to account for intraspecific trait variability (ITV) when measuring FD remains one of the main current debates. It remains however unclear to what extent accounting for population-level ITV would modify FD quantification and associated conclusions. In this paper, we address two critical questions: (1) How sensitive are different components of FD to the inclusion of population-level ITV? (2) Does the omission of ITV obscure the understanding of ecological patterns? Using a mixture of empirical data and simulation experiments, we conducted a sensitivity analysis of four commonly used FD indices (community weighted mean traits, functional richness, Rao's quadratic entropy, Petchey and Gaston's FD index) and their relationships with environmental gradients and species richness, by varying both the extent (plasticity or not) and the structure (contingency to environmental gradient due to local adaptation) of population-level ITV. Our results suggest that ITV may strongly alter the quantification of FD and the detection of ecological patterns. Our analysis highlights that 1) species trait values distributions within communities are crucial to the sensitivity to ITV, 2) ITV structure plays a major role in this sensitivity and 3) different indices are not evenly sensitive to ITV, the single-trait FD from Petchey and Gaston being the most sensitive among the four metrics tested. We conclude that the effects of intraspecific variability in trait values should be more systematically tested before drawing central conclusions on FD, and suggest the use of simulation studies for such sensitivity analyses.