1. Invasive species usually exhibit different spatial population dynamics in their native and invaded range. This is often attributed to demographic differences, but may be due to differences in dispersal as well. 2. Regardless of how these dispersal and demographic differences from the native range arose, studying how they contributed to increases in population spread rates will increase our understanding of what has made these species invasive. Here we investigate which vital rates and dispersal parameters of the invasive thistle Carduus nutans drive the increases in spread rate in different invaded ranges compared to that in the native range in Eurasia. 3. We construct and analyse spatial integrodifference models that combine structured, local population models with mechanistic (WALD) models of seed dispersal by wind across a homogeneous landscape. Published and new demographic and dispersal data for single populations from the native (France) and invaded (Australia, New Zealand, Kansas and Pennsylvania) ranges were used for the parameterization. 4. We developed a variance decomposition method ( c *-LTRE) to analyse the contributions of the changes in the vital rates and dispersal parameters to the increases in the invasion wave speed ( c *) estimates for the different invaded ranges compared to that for the native range. 5. The c *-LTRE analysis showed that the net contribution of the dispersal parameters to c * increases varied among the populations from 51% (Australia), to 79% (Kansas), to 80% (New Zealand) and to 85% (Pennsylvanian experiment). Escape from natural enemies that reduce seed set by floral herbivory was important in all invaded ranges. Large positive contributions were also made by increases in rapid growth of seedlings and small rosettes, increases in flowering probabilities and potential seed production, as well as by increased plant height and lower falling velocities of the plumed seeds. 6. Synthesis . By incorporating amechanistic dispersal model with a structured population model, and by linking this joint model to field data from several continents, we demonstrate the relative importance of dispersal and demography to invasion success. This approach can be used to analyse which aspects of an invader's life history have changed most importantly from the native range.