Accurate predictions about plant invasions require estimation of demographic and dispersal parameters in low-density, expanding populations. We used inverse modelling on the spatial distribution of seedlings to estimate the effective reproductive rate and dispersal parameters in expanding populations of native Pinus sylvestris L. and non-native Pinus nigra Arnold in the Causse Méjean, southern France. The objective was to compare the ability of these two species to colonize these calcareous grasslands. Four empirical models of dispersal were compared. The mixed discrete dispersal kernels had the best fit (lower Aikake information criterion), whereas other candidate models underestimated the tail of the dispersal curve. However, the alternative functions performed quite similarly. The models showed clear differences between P. sylvestris and P. nigra, with the latter species having a higher net reproductive rate and higher effective dispersal. Our results based on the effective dispersal of seedlings over 4 years of age predict a faster spread rate for the non-native P. nigra compared with native P. sylvestris. Our results suggest that P. nigra may expand rapidly into the Causse Méjean grasslands in the forthcoming decades.