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Projecting future response of biological systems to global change requires a mechanistic understanding of how climate and ecology jointly drive species demography and range dynamics. Such knowledge is particularly crucial when it comes to invasive species, which expansion may have far-reaching consequences for recipient ecosystems. Here, we use mark-recapture in replicated outdoor mesocosms to examine how survival and dispersal, two key drivers of population and range dynamics, respond to climate and ecology in the invasive red swamp crayfish (Procambarus clarkii) along an invasion gradient. We show that crayfish survival probability increased with (i) increasing body size at high (but not low) crayfish density and (ii) with warmer temperatures, and decreased (i) with increasing body condition and (ii) under higher crayfish density. Overland dispersal probability by crayfish increased with increasing (i) body-size, (ii) body condition and (iii) temperatures. In contrast, crayfish from range-edge and range-core habitats had similar survival and overland dispersal probabilities, suggesting no evolution of the crayfish expansion potential along the invasion gradient. Our results highlight that species population dynamics and range shifts in a changing world are driven by joint contributions from both climate and ecology. In P. clarkii, global warming will simultaneously promote both a demographic increase and a geographic range expansion, especially in populations dominated by large-bodied individuals.