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Phenotypic plasticity has long been suspected to allow invasive species to expand their geographic range across large-scale environmental gradients. We tested this possibility in Australia using a continental scale survey of the invasive tree Parkinsonia aculeata (Fabaceae) in twenty-three sites distributed across four climate regions and three habitat types. Using tree-level responses, we detected a trade-off between seed mass and seed number across the moisture gradient. Individual trees plastically and reversibly produced many small seeds at dry sites or years, and few big seeds at wet sites and years. Bigger seeds were positively correlated with higher seed and seedling survival rates. The trade-off, the relation between seed mass, seed and seedling survival, and other fitness components of the plant life-cycle were integrated within a matrix population model. The model confirms that the plastic response resulted in average fitness benefits across the life-cycle. Plasticity resulted in average fitness being positively maintained at the wet and dry range margins where extinction risks would otherwise have been high ("Jack-of-all-Trades" strategy JT), and fitness being maximized at the species range centre where extinction risks were already low ("Master-of-Some" strategy MS). The resulting hybrid "Jack-and-Master" strategy (JM) broadened the geographic range and amplified average fitness in the range centre. Our study provides the first empirical evidence for a JM species. It also confirms mechanistically the importance of phenotypic plasticity in determining the size, the shape and the dynamic of a species distribution. The JM allows rapid and reversible phenotypic responses to new or changing moisture conditions at different scales, providing the species with definite advantages over genetic adaptation when invading diverse and variable environments. Furthermore, natural selection pressure acting on phenotypic plasticity is predicted to result in maintenance of the JT and strengthening of the MS, further enhancing the species invasiveness in its range centre.