1. Understanding how functional traits, which are key for plant functioning, relate to demographic parameters of populations is central to tackle pending issues in plant ecology such as the forecast of the fate of populations and communities in a changing world, the quantification of community assembly processes or the improvement of species distribution models. We addressed this question in the case of species from a Mediterranean rangeland of southern France. 2. Changes in species abundance in response to management intensification (fertilization and increased grazing pressure) were followed over a 28-year period. Probabilities of presence, and elasticities of the changes in the probability of space occupancy to colonization and survival, which are analogues of demographic parameters, were calculated for 53 species from the time series of abundance data using a space occupancy model. Nine quantitative traits pertaining to resource use, plant morphology, regeneration and phenology were measured on these species and related to demographic parameters. 3. The long-term dynamics of species in response to management intensification was associated with major changes in functional traits and strategies. Changes in the probability of occurrence – analogous to population growth rate - were correlated with traits describing the fast-slow continuum of leaf functioning. The elasticity of population growth rate to colonization was significantly related to reproductive plant height and seed mass, and to a lower extent, to leaf carbon isotopic ratio. 4. Synthesis. The functional response of species to management intensification corresponds to a shift along the second axis of a recently identified global spectrum of plant form and function, which maps, to some extent, onto the fast-slow continuum of life-history strategies. By contrast, the elasticity of colonization relates to the global spectrum axis capturing the size of organs. Seed mass contributes to this axis and is assumed to relate to one of the important traits structuring the reproductive strategy axis of life histories as well, namely net reproductive rate. While this mapping between functional and life-history traits is appealing, further tests in contrasting types of communities are required to assess its degree of generality.