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Competing theoretical models make different predictions on which life history strategies facilitate growth of small populations. While ‘fast’ strategies allow for rapid increase in population size and limit vulnerability to stochastic events, ‘slow’ strategies and bet‐hedging may reduce variance in vital rates in response to stochasticity. We test these predictions using biological invasions since founder alien populations start small, compiling the largest dataset yet of global herpetological introductions and life history traits. Using state‐of‐the‐art phylogenetic comparative methods, we show that successful invaders have fast traits, such as large and frequent clutches, at both establishment and spread stages. These results, together with recent findings in mammals and plants, support ‘fast advantage’ models and the importance of high potential population growth rate. Conversely, successful alien birds are bet‐hedgers. We propose that transient population dynamics and differences in longevity and behavioural flexibility can help reconcile apparently contrasting results across terrestrial vertebrate classes.

Why some organisms become invasive when introduced into novel regions while others fail to even establish is a fundamental question in ecology. Barriers to success are expected to filter species at each stage along the invasion pathway. No study to date, however, has investigated how species traits associate with success from introduction to spread at a large spatial scale in any group. Using the largest data set of mammalian introductions at the global scale and recently developed phylogenetic comparative methods, we show that human-mediated introductions considerably bias which species have the opportunity to become invasive, as highly productive mammals with longer reproductive lifespans are far more likely to be introduced. Subsequently, greater reproductive output and higher introduction effort are associated with success at both the establishment and spread stages. High productivity thus supports population growth and invasion success, with barriers at each invasion stage filtering species with progressively greater fecundity.