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 (1979-2020) 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.

Carnegie Mellon University Institute for Green Science Pittsburgh Pennsylvania USA

Center for Applied Mathematics and Bioinformatics Department of Mathematics and Natural Sciences Gulf University for Science and Technology Hawally Kuwait

Christian Albrechts University Kiel Institute for Natural Resource Conservation Department of Hydrology and Water Resources Management Kiel Germany

Department of Animal Sciences and Aquatic Ecology Ghent University Ghent Belgium

Department of Aquatic Sciences and Assessment Swedish University of Agricultural Sciences Uppsala Sweden

Department of Biology Carleton University Ottawa Canada

Department of Botany and Zoology Faculty of Science Masaryk University Brno Czech Republic

Department of Ecoscience Lake Ecology Aarhus University Aarhus Denmark

Department of Hydrobiology University of Pécs Pécs Hungary

Department of Plant Biology and Ecology Faculty of Science and Technology University of the Basque Country Leioa Spain

Department of Tisza Research Institute of Aquatic Ecology Centre for Ecological Research Debrecen Hungary

EDF R and D Laboratoire National d'Hydraulique et Environnement Chatou France

Environment Agency Wallingford UK

Environmental Research and Innovation Belvaux Luxembourg

Finnish Environment Institute Freshwater Centre Oulu Finland

Flanders Environment Agency Aalst Belgium

Freshwater Ecology Hydrology and Management Departament de Biologia Evolutiva Ecologia i Ciències Ambientals Facultat de Biologia Institut de Recerca de l'Aigua Barcelona Spain

Freshwater Ecology Hydrology and Management Departament de Biologia Evolutiva Ecologia i Ciències Ambientals Facultat de Biologia Institut de Recerca de la Biodiversitat Barcelona Spain

Geography Department Faculty of Mathematics and Natural Sciences Humboldt Universität zu Berlin Berlin Germany

GEOMAR Helmholtz Zentrum für Ozeanforschung Kiel Kiel Germany

INRAE UR RiverLy centre de Lyon Villeurbanne Villeurbanne France

Institute of Technology Centre for Freshwater and Environmental Studies Dundalk Ireland

Leibniz Institute of Freshwater Ecology and Inland Fisheries Department Community and Ecosystem Ecology Berlin Germany

MARE Marine and Environmental Sciences Centre Department of Life Sciences University of Coimbra Coimbra Portugal

Marine Institute Newport Ireland

RECOVER Research Unit National Research Institute for Agriculture Food and Environment Aix en Provence France

School of Biological Sciences Queen's University Belfast Belfast UK

School of Natural Resources University of Nebraska Lincoln Lincoln Nebraska USA

School of Science and Technology Nottingham Trent University Nottingham UK

Section for Nature Based Solutions Norwegian Institute for Water Research Oslo Norway

Senckenberg Research Institute and Natural History Museum Frankfurt Department of River Ecology and Conservation Gelnhausen Germany

University of Duisburg Essen Faculty of Biology Essen Germany

University of Koblenz Landau Institute for Environmental Sciences Landau Germany

University of Natural Resources and Life Sciences Institute of Hydrobiology and Aquatic Ecosystem Management Vienna Austria

University of South Bohemia in České Budějovice Faculty of Fisheries and Protection of Waters South Bohemian Research Center of Aquaculture and Biodiversity of Hydrocenoses Vodňany Czech Republic

Yale University School of the Environment New Haven Connecticut USA

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