Biological invasions have reached an unprecedented level and the number of introduced species is still increasing worldwide. Despite major advances in invasion science, the determinants of success of introduced species, the magnitude and dimensions of their impact, and the mechanisms sustaining successful invasions are still debated. Empirical studies show divergent impacts of non-native populations on ecosystems and contrasting effects of biotic and abiotic factors on the dynamics of non-native populations; this is hindering the emergence of a unified theory of biological invasions. We propose a synthesis that merges perspectives from population, community, and ecosystem levels. Along a timeline of ecosystem transformation driven by non-native species, from historical to human-modified ecosystems, we order invasion concepts and theories to clarify their chaining and relevance during each step of the invasion process. This temporal sorting of invasion concepts shows that each concept is relevant at a specific stage of the invasion. Concepts and empirical findings on non-native species may appear contradictory. However, we suggest that, when mapped onto an invasion timeline, they may be combined in a complementary way. An overall scheme is proposed to summarise the theoretical dynamics of ecosystems subjected to invasions. For any given case study, this framework provides a guide through the maze of theories and should help choose the appropriate concepts according to the stage of invasion.

With the advent of the Anthropocene, biological invasions have reached an unprecedented level, and the number of species introductions is still increasing in an everchanging world. Despite major advances in invasion science, significant debate and lack of clarity remain surrounding the determinants of success of introduced species, the magnitude and dimensions of their impact, and the mechanisms sustaining successful invasions. Empirical studies show divergent impacts of alien populations on ecosystems and contrasting effects of biotic and abiotic factors on the dynamics of alien populations, which hinders the creation of a unified theory of biological invasions. Compounding these issues is the plethora of hypotheses that aim to explain invasion success, which can be unclear and contradictory. We propose a synthesis that categorizes hypotheses along a timeline of invasion. We sorted invasion hypotheses along the invasion timeline, and considered population, community and ecosystem levels. This temporal sorting of invasion concepts shows that each is relevant at a specific stage of

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