A mechanistic understanding of how individual- and environment-level factors influence species demography and range dynamics is paramount to our ability to accurately project future biodiversity. Such knowledge is particularly crucial for invasive species, which expansion may have far-reaching consequences for native ecosystems. Here, we experimentally examine how survival and dispersal respond to multiple individual- and environment-level factors in the red swamp crayfish Procambarus clarkii, one of the most invasive species worldwide, along an invasion gradient. Crayfish survival probability was (i) positively dependent on body size-dependent at high (but not low) crayfish density and on temperature, and was (ii) negatively dependent on body condition and crayfish density. Dispersal probability was positively dependent on body-size, body condition and temperature. In contrast, survival and dispersal probabilities were similar among range-core and range-edge crayfish, suggesting no evolution of the range-expansion potential along the invasion gradient. Our study highlights in an invasive aquatic species that alterations of body-size structure, population density and temperature, as driven by global anthropogenic changes, may lead to demographic reorganizations that will ultimately shift demographic ranges and determine future biodiversity patterns. From a management perspective, our results show that range expansion in P. clarkii will be promoted by future climate warming, and should be most efficiently hindered by selectively removing large-bodied individuals.