Globalization has led to the introduction of thousands of alien species worldwide. With growing impacts by invasive species, understanding the invasion process remains critical for predicting adverse effects and informing efficient management. Theoretically, invasion dynamics have been assumed to follow an "invasion curve" (S-shaped curve of available area invaded over time), but this dynamic has lacked empirical testing using large-scale data and neglects to consider invader abundances. We propose an "impact curve" describing the impacts generated by invasive species over time based on cumulative abundances. To test this curve's large-scale applicability, we used the data-rich New Zealand mud snail Potamopyrgus antipodarum, one of the most damaging freshwater invaders that has invaded almost all of Europe. Using long-term abundance and environmental data collected across 306 European sites, we observed that P. antipodarum abundance generally increased through time, with slower population growth at higher latitudes and with lower runoff depth. Fifty-nine percent of these populations followed the impact curve, characterized by first occurrence, exponential growth, then long-term saturation. This behaviour is consistent with boom-bust dynamics, as saturation occurs due to a rapid decline in abundance over time. Across sites, we estimated that impact peaked approximately two decades after first detection, but the rate of progression along the invasion process was influenced by local abiotic conditions. The S-shaped impact curve may be common among many invasive species that undergo complex invasion dynamics. This provides a potentially unifying approach to advance understanding of large-scale invasion dynamics and could inform timely management actions to mitigate impacts on ecosystems and economies.

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Aim: Invasive alien species are a growing problem worldwide due to their ecological, economic and human health impacts. The "killer shrimp" Dikerogammarus villosus is a notorious invasive alien amphipod from the Ponto-Caspian region that has invaded many fresh and brackish waters across Europe. Understandings of large-scale population dynamics of highly impactful invaders such as D. villosus are lacking, inhibiting predictions of impact and efficient timing of management strategies. Hence, our aim was to assess trends and dynamics of D. villosus as well as its impacts in freshwater rivers and streams.Location: Europe. Methods:We analysed 96 European time series between 1994 and 2019 and identified trends in the relative abundance (i.e. dominance %) of D. villosus in invaded time series, as well as a set of site-specific characteristics to identify drivers and determinants of population changes and invasion dynamics using meta-regression modelling.We also looked at the spread over space and time to estimate the invasion speed (km/year) of D. villosus in Europe. We investigated the impact of D. villosus abundance on recipient community metrics (i.e. abundance, taxa richness, temporal turnover, Shannon diversity and Pielou evenness) using generalized linear models.Results: Population trends varied across the time series. Nevertheless, community dominance of D. villosus increased over time across all time series. The frequency of occurrences (used as a proxy for invader spread) was well described by a Pareto distribution, whereby we estimated a lag phase (i.e. the time between introduction and spatial expansion) of approximately 28 years, followed by a gradual increase before new occurrences declined rapidly in the long term. D. villosus population change was associated with decreased taxa richness, community turnover and Shannon diversity. Main Conclusion:Our results show that D. villosus is well-established in European waters and its abundance significantly alters ecological communities. However, the multidecadal lag phase prior to observed spatial expansion suggests that initial introductions by D. villosus are cryptic, thus signalling the need for more effective early detection methods.