Tracking a killer shrimp: Dikerogammarus villosus invasion dynamics across Europe

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.


| INTRODUC TI ON
Humans have translocated thousands of invasive alien species beyond their native ranges (Seebens et al., 2021). Their establishment and spread have been recognized as a leading cause of biodiversity loss and a growing socio-economic burden worldwide (Bellard et al., 2016;Diagne et al., 2021). It is therefore imperative to understand and predict large-scale invasion patterns, identify future invaders (i.e. introduced species that become invasive ;Fournier et al., 2019;Pyšek et al., 2020) and assess their impacts . With the ongoing global increase in invasion rates (Seebens et al., 2021) and a growing threat to ecosystems and economies (Pyšek et al., 2020), there is an urgent need to characterize population dynamics at large scales to inform effective detection, The form of population dynamics may differ among invaders, invasion pathways, biogeographical regions, abiotic or biotic gradients and spatio-temporal scales (Arim et al., 2006;Haubrock et al., 2020). Characterization of population dynamics of invasive alien species at a broad spatio-temporal scale has been limited by insufficient long-term data. However, advances in availability in long-term biodiversity monitoring (Dornelas et al., 2018;Mirtl et al., 2018) and data analysis approaches for biodiversity time series (Bowler et al., 2017;Dornelas et al., 2014;Pilotto et al., 2020) have been made. These and other initiatives have collated large datasets for diverse taxonomic groups and examined biodiversity and ecosystem function trends at regional and global scales (Seebens et al., 2019. Large-scale, community-level data can also be used to examine distribution and abundance patterns of invasive alien species, as well as their potential effects on ecological communities over time (Dornelas et al., 2014;Haubrock et al., 2020).
Invaders may take considerable time before becoming established, detected and disruptive (Crooks, 2005;Spear et al., 2021), and such time lags are very difficult to predict (Coutts et al., 2018).
Furthermore, the invaders may not remain disruptive or could become less so, owing to population declines (e.g. reflecting boomand-bust cycles and/or community adjustment; Strayer et al., 2017).
Finally, the type and magnitude of ecological impacts an invader causes are dependent, in part, on its abundance (Sofaer et al., 2018;Yokomizo et al., 2009), and thus can change through time according to the invader's population dynamics. Given that the long-term population dynamics of even widespread conspicuous invaders are often poorly characterized (Strayer et al., 2006), this gap challenges our ability to (i) predict in which situations the invader's impacts on invaded ecosystems will be maximal and (ii) decide if/when management should intervene. However, species having well-documented invasion histories within large contiguous regions offer temporally highly resolved data whose collation and analysis could reveal essential information to guide risk assessment and management prioritization.
One such species is the "killer shrimp" Dikerogammarus villosus, an invasive alien freshwater amphipod listed among the "100 worst" invaders in Europe (Nentwig et al., 2018). The confirmed native range of D. villosus is the northern margins of the Ponto-Caspian region (i.e. Black Sea, Caspian Sea and Azov Sea; Dedyu, 1980;Mordukhai-Boltovskoi, 1960). This voracious predator has spread rapidly through European inland waterways and the Baltic Sea, aided by canalization and anthropogenic vectors De Ventura et al., 2017), and also poses an invasion risk to the North American Great Lakes (Kramer et al., 2017). Facilitated by the known influence of streams on the spread of D. villosus, it has substantial impacts on biodiversity in invaded regions, causing marked declines in native macroinvertebrates via predation and competition (Dick et al., 2002;Dick & Platvoet, 2000). It also potentially impacts egg and embryonic stages of large, ecologically important crustaceans, fish and amphibians (Roje et al., 2021;Taylor & Dunn, 2017;Warren et al., 2021), causing disruptions across multiple trophic levels (i.e. trophic cascades; Van Riel, . Its displacement of native species (MacNeil et al., 2011;MacNeil & Platvoet, 2013) also facilitates the establishment of other invasive alien species (Bollache et al., 2004;Leuven et al., 2009). Notably, it is the only invasive amphipod with documented monetary costs . Yet, information on this invader's effects on native species assemblages over time is still scarce.
Dikerogammarus villosus invasion success has been promoted by its suitability for transport by anthropogenic vectors (e.g. ships; Anderson et al., 2014), wide thermal and salinity tolerances , aggressive competitive behaviours (Kobak et al., 2016), effective anti-predator strategies ) and high growth rates and fecundity (Holdich & Pöckl, 2007;Pöckl, 2009), as one female can carry nearly 200 eggs (Pöckl, 2009). Accordingly, this invader's potential to successfully establish after introduction -from even a single gravid female -into a novel environment is substantial Lockwood et al., 2005). Reflecting its impacts on recipient ecosystems (e.g. extirpation of native species and changes in biotic indices; Kouba et al., 2021;, D. villosus has been the focus of various management actions, although measures for management post-establishment are undeveloped, and prevention of initial introduction has been advocated (Bradbeer et al., 2020;Wood et al., 2021). Moreover, understanding the population dynamics of this species remains limited at large spatial scales regarding temporal and climatic gradients (e.g. time since invasion; variability in temperature and precipitation), hindering quantification of impact and population trends that could inform management strategies. For example, earlier invasions, such as those detected in Hungary (Bij de Vaate et al., 2002: in 1926Huber et al., 2015Huber et al., in 1970 Figure 1), might already be regressing from their peak abundance to a stable, intermediate level or exhibiting "boom-bust" dynamics (Rolla, Consuegra, Hall, & Garcia de Leaniz, 2020;Strayer et al., 2017) and therefore be expanding to new areas more slowly than populations with a more recent invasion history (Seebens et al., 2018). More recent invasions may be at an early stage of spread, potentially preceding future exponential population increases. In addition, invasion success and exerted impacts are intertwined with anthropogenic stressors such as hydromorphological alterations and dam construction, which can influence spread rates (Colautti et al., 2006;MacNeil & Platvoet, 2013).
To characterize the population dynamics of D. villosus across time series, we collated European riverine macroinvertebrate biomonitoring data containing this species. We hypothesized that the (i) dominance of D. villosus populations is increasing within time series, whereas the number of new occurrences is declining in the long-term, indicating a deceleration in the invasion; (ii) recent invasions exhibit more rapid population growth, whereas populations originating from earlier invasions are stable or declining; (iii) population dynamics of D. villosus are mediated by site-specific climatic and spatial characteristics, with populations affected by warming and the presence of anthropogenic barriers such as dams. Lastly, we hypothesized (iv) changes in recipient communities to be associated with D. villosus population dynamics.

| Data compilation
To investigate the population dynamics of D. villosus and the response of recipient communities across Europe, we considered 1816 time series (Peter Haase, unpublished data) reporting the abundance of macroinvertebrate taxa in streams and rivers across 22 European countries. Macroinvertebrates were sampled using different methods and protocols (see Table S1

| Trend identification and metaregression modelling
To synthesize and describe the directionality and the trends in the number of sampled D. villosus individuals, we used a metaregression modelling approach, which synthesizes the slopes of individual regressions (as in our case from different time series).
For this, we used the "rma.mv" function of the R package metafor (Viechtbauer, 2010), using the time-series Mann-Kendall trend test (S-statistics) and respective variance as the effect size. The Mann-Kendall trend test is a non-parametric test to evaluate a monotonic increase or decrease in trends. In particular, we used the trends calculated by modified Mann-Kendall trend tests with variance correction to account for temporal auto-correlation (Hamed & Rao, 1998;Maire et al., 2019). To correct the spatial autocorrelation between time series, we used a random effect model, specifying the geographic coordinates as a random effect according to a Gaussian correlation structure (Cressie, 1993;Maire et al., 2019). This approach uses a regression model and enables comparability of time series by analysing the individual time series abundance trends (i.e. its slope) rather than the raw abundances.
These models account for the variance of each individual temporal trend and treat each population as an individual spatial unit associated with scale and sampling protocol (Viechtbauer et al., 2015).

| Effects of site-specific characteristics on D. villosus
To investigate the spatial and climatic drivers of D. villosus trends, we used site-specific characteristics of each time series. Climatic regions (i.e. Köppen-Geiger climate zone) were extracted from Beck et al. (2018). Biogeographical regions were defined following the European Environment Agency classification map and estimated visually using the site-specific coordinates (EEA, 2021). We further classified the type of ecosystem of each time series based on Strahler order (i.e. stream <8 or large rivers ≥8) to evaluate differences in the degree of invasions between both. We obtained site-specific runoff data, expressed as the annual Q (mm), from the TerraClimate dataset at 4-km spatial resolution (Abatzoglou et al., 2018). We extracted the elevation of each site from the MERIT Hydro digital elevation model (Yamazaki et al., 2019) at 90-m spatial resolution and used the Hydrography90m  stream network, catchments and sub-catchments (catchments between network nodes) as underlying spatial units. For each site, we computed the stream slope using the r.stream.slope function. We extracted land cover data from the European Space Agency Climate Change Initiative (ESA CCI) Land Cover time series v2.0.7 dataset, at 300-m spatial resolution (ESA, 2017), as the percentage cover of a given land cover category within the sub-catchment. We used the Global Reservoir and Dam Database (GRanD) v1.3 to identify dams along the river network. We then measured the distance to the nearest dam to investigate the effect of instream barriers. We extracted mean daily temperature and total daily precipitation data from a gridded European scale observation-based dataset (spatial resolution: 0.1°; Cornes et al., 2018) and calculated the average annual temperature and precipitation for each sampled assemblage in each sampling year , as well as their respective S-statistics (i.e. the Mann-Kendall trend test statistic, see above), as indicators of climatic changes. Precipitation in particular can be used as a proxy for river discharge (Higashino & Stefan, 2019) and was included as it affects the availability of water and nutrients as well as the habitat suitability for many species (Gallardo et al., 2012;Shi et al., 2010).
We then calculated the mean maximum and minimum temperature and precipitation and each respective S-statistic. Dikerogammarus villosus slopes (to investigate factors determining D. villosus' rate of change over time) and relative abundances (as a proxy of D. villosus' dominance in invaded ecosystems over time) were analysed as a function of these spatial, temporal, and site-specific characteristics, to identify significant drivers of temporal trends (see Table S2).
We used generalized linear models (GLMs) via the MASS R package (Ripley et al., 2013). We used a Gaussian distribution for continuous data and quasibinomial distribution (to account for high variance of the dataset) for proportion data (i.e. relative abundances) after visually inspecting their respective residual distributions for normality through histograms.
To identify the best model, we first tested for collinearity among the numerical variables using the variance inflation factor (VIF) for continuous predictors using the "corvif" function (Zuur et al., 2009).
We selected VIF >5 as the threshold, and those variables with high VIF values for each model were assessed for their ecological relevance based on expert knowledge (Table S3; Dorman et al., 2013;Zuur et al., 2009). Regarding the four categorical variables (country, biogeographical region, Köppen-Geiger classification and ecosystem type), we used chi-square tests to investigate the collinearity, and retained only the biogeographical region (Table S4). We considered each model and the respective predictors, using expert-based opinion to determine if the inclusion predictors would make sense from an ecological perspective (Table S5). Hence, the model consisted of a single response variable (i.e. the Mann-Kendall trend test slopes of D. villosus abundances or the relative proportion of D. villosus) and site-specific characteristics (see above; Table S2). Following the alphabetical order, the Alpine region was used as a reference factor (i.e. as intercept), and therefore, we do not infer any results about this region.

| Modelling occurrence frequency and invasion speed
We combined the first occurrence of D. villosus in each time series in our data with those occurrences (as coordinates and year of records) in the Global Biodiversity Information Facility database (GBIF, 2021).
Eight GBIF occurrences were removed due to insufficient information (e.g. no recorded year), resulting in 400 records.
We excluded those sample years from the dataset of 400 records that reported relatively high occurrence frequencies, that is, any number of occurrences that was greater than Q 3 + 3 × IQR, where Q 3 is the upper quartile and IQR is the interquartile range of the dataset. A single outlier was found with 120 occurrences in the year 2009, and thus, it was removed. We modelled the remaining 280 occurrences to represent invader spread, using a logistic distribution and a two-tailed Pareto distribution. A key difference between these distributions is the decay rate at the end tails: the logistic distribution decays exponentially fast (thin tails), and for the Pareto distribution, the decay is much slower according to an inverse power law (fat tails; Nolan, 2020). Moreover, Pareto distributions with distinct parameters were considered (i.e. two-tailed) for the early and late phases of the invasion. Both distributions were fitted against the occurrence data using the non-linear regression tool lsqcurvefit in Matlab. The better-fitting model was determined based on lower number of parameters and higher R 2 value (see Note S2).
Further, we estimated the frequency of occurrences f 0 at the time of first sampling (t = 0) the time of introduction t intro , and the duration of the lag phase t lag that is, the period before D. villosus was observed in additional assemblages, evaluated at 10% of the largest recorded occurrence frequency f*.
As a complementary analysis, we computed the distance between the locations of every sampled site from the first invaded site using site location data (GPS coordinates recorded as latitude and longitude) over the years 1994-2021. An estimate for the invasion speed (km/ year) was obtained by computing the mean distance (i.e. total distance averaged over the number of occurrences per year) over time and modelled using a linear equation (Bagnara et al., 2022). We also calculated the differences between the first record of D. villosus in our data and sTWIST database (the most comprehensive source of first records of alien species, integrating several databases and merging them into a single database; Seebens et al., 2018).

| Impacts of D. villosus on community metrics
To assess the effect of D. villosus abundance on recipient communities (proxied by the S-statistic of D. villosus trends), we computed five common metrics for each community and year within each time series: total abundance (i.e. individuals), taxon richness (i.e. the total number of taxa), temporal turnover (i.e. the proportion of species either gained or lost over time relative to the total number of species observed; Carvalho et al., 2012), the Shannon diversity index (Shannon & Weaver, 1949) and Pielou's evenness (Pielou, 1966). The metrics were calculated considering all species in the community except D. villosus, potentially including both native and other non-native species. For evenness, we followed the formula: H/ln(S) (where H is the Shannon Index and S is the taxon richness of a community). Metrics were calculated using the "diversity" function in the R package vegan (Oksanen et al., 2013) and the "turnover" function in the R package codyn (Hallett et al., 2016). In analysing these metrics as response variables in metaregression models, we included the middle point of each time series (see above) in addition to the rate change of D. villosus to infer the effects of temporal variability in changing temporal trends (i.e. slopes) over time and evaluate the change of sampled individuals of D. villosus individuals to test its associated effect on community metrics.
All models used restricted maximum likelihood estimation (REML). We also quantified the proportion of variance in the model not attributed to sampling error by using the I 2 statistic. In addition, we evaluated the results of the meta-regression by a graphical representation (i.e. forest plots) using the "forest" function of the R package metafor ( Figure S2; Viechtbauer, 2010). To inspect potential biases that may alter the results, we checked the symmetry of the data using funnel plots and statistically evaluated this symmetry using the Egger's test (Egger et al., 1997; see Figure S3; Table S6).
The reproducible R script is available with the manuscript and lists all R packages that were used.

| Trends of D. villosus across Europe
Across the sampling sites in Europe included in this study, the abun-

| Effect of site-specific characteristics on D. villosus trend
We did not identify a change in individuals of D. villosus sampled over time, despite a positive tendency (i.e. change in the S-statistics; GLM: 0.59 ± 0.45; p = .19; Figure 3a; Table S7). The rate of change in the trend of D. villosus increased significantly across the Mediterranean biogeographic region (p < .05). The average minimum temperature and the rate change of the maximum temperature had positive effects on the rate of change of D. villosus individuals (p < .05), while the distance to the next barrier had negative effects (p < .05; Figure 3b; Table S7).
Regarding the relative abundance of D. villosus over time, we identified a significant increase (p < .05; Figure 3c; Table S7). This increase was shown in all biogeographic regions (relative to Alpine), as well as with increasing distance to the next barrier and the elevation of the stream (p < .01; Figure 3d; Table S7). The relative abundance decreased in streams relative to large rivers (p < .01; Figure 3d; Table S7).

| Modelling occurrence frequency and invasion speed at the European level
The mean ± SD for the number of D. villosus occurrences was 13.33 ± 19.07, with the maximum recorded occurrence frequency f* = 78 in the year 2008 (t* = 14). The occurrence frequency of D. villosus was best described by a two-tailed Pareto distribution (R 2 = .90 for t ≤ t* and R 2 = .98 for t ≥ t* see Figure 4a), which fits better than the logistic distribution (R 2 = .86; see Note S2). Moreover, the Pareto distribution depends on fewer parameters. On considering an occurrence frequency of 1 (i.e. first invaded site), we predicted the time of introduction t intro = −20.67 years prior to the first sampling event.
The estimated number of occurrences at the time of first sampling was f 0 = 3.37. The duration of the lag phase was 27.64 years after t intro . Beyond t*, occurrence frequency rapidly declined, reaching low levels 45-50 years after t intro , indicating low levels of spread for D.

villosus.
We estimated the invasion speed of D. villosus at the time of first sampling as 80.27 km/year, with deceleration at a rate of 2.83 km/ year 2 , eventually reaching minimum speed at time t = 28.34 years (see Figure 4b). The estimation of null speed corresponds to a cessation in the frequency of occurrences at approximately the same time (49.03 years after t intro , Figure 4a).

| Impact of D. villosus on community metrics trends
We did not find a significant trend over time for community metrics ( Table 1). The rate of change in the number of D. villosus individuals sampled over time (i.e. its slope) had a significant negative effect on trends in taxon richness, temporal turnover and Shannon diversity ( Figure 5; Table 1). We did not find a significant effect of the number of sampled D. villosus individuals on total community abundance and Pielou's evenness trends (Table 1; Figure 5).

Response variable Predictor Estimate
For example, in France, all temporal trends (i.e. S-Statistics) were positive, whereas most trends were negative in Hungary. The sustained dominance of D. villosus in recipient ecosystems increased over time, which could reflect its ability to rapidly reach high population densities in combination with its capacity to predate, eliminate and replace native and alien species (Dick & Platvoet, 2000;Nentwig et al., 2018;Warren et al., 2021). In addition, the difference between the first record of D. villosus in sTWIST and our database was ~10.8 years. Yet, after excluding Switzerland and Austria-which had a difference of ~14 years between both databases likely due to the scarce time series from that country (n = 2)-the difference among both databases shrank to ~2.8 years only, underlining the accuracy of our data.  In addition, contrary to our fourth hypothesis, we observed no difference in the growth rates of earlier and more recently invading populations, suggesting that the time since invasion does not influ-

| Occurrence frequency and invasion speed of D. villosus
We estimated that the introduction of D. villosus occurred on average 21 years before the first sampling event suggesting current monitoring of European streams is insufficient for early detection of invasive alien species. Following their introduction, such species often have low abundance during an initial establishment phase before increasing or becoming detected (Crooks et al., 1999), although lag phases are rarely measured in freshwater systems (but see Karatayev et al., 2011). Here, after a considerably long lag phase of 28 years from the time of introduction, D. villosus then only took another seven years to reach peak abundance. A lengthy lag period could reflect nonmutually exclusive phenomena including, inter alia, limits on the organism's reproductive rate in the early phase of exponential growth (e.g. Allee effects); (ii) multiple failed introductions prior to colonization success; (iii) genotypic selection of locally adapted organisms; and (iv) sudden population growth triggered by disturbance, environmental stochasticity or interspecific interactions (Crooks et al., 1999;Crooks, 2005;Sakai et al., 2001;Spear et al., 2021). Although reporting efforts may be increased over time, this lag phase may explain the rapid decrease in new occurrences 35 years after an assemblage was first invaded (Ricciardi, 2013;Rouget et al., 2016). Nevertheless, records extracted from GBIF have to be taken with caution, as the taxonomic validity cannot always be ensured, simultaneously suggesting that many observations may be missing (Nekola et al., 2019: Shirey et al., 2019. Predicting future trends in the abundance of D. villosus is hampered by context dependencies, which may cause sudden shifts in population dynamics at different temporal scales, for example reflecting boom-bust dynamics (Strayer et al., 2017). (t * ,f * ) (Bacela-Spychalska et al., 2013). Furthermore, dams can be used as refuges and "stepping stones" for further spread, but also limit the spread upstream. Therefore, invasive alien species can accumulate near these barriers (Rahel, 2013). For invasive alien species, climatic variables -in particular temperature -can be the most important environmental variables determining the survival, reproduction and establishment in recipient ecosystems (Müller & Baur, 2011).

| The influence of site-specific characteristics on D. villosus
Temperature is also well-known for its influence on life cycle characteristics such as fecundity in D. villosus (Pöckl et al., 2003). In congruence with Kobak et al. (2017), D. villosus preferred warm water and exhibited a stronger tendency to select extreme temperatures.
The dominance of D. villosus increased over time. This increase can be explained by propagule/colonization pressures, such as by the species exploiting increasing anthropogenic invasion corridors such as canals (MacIsaac et al., 2001;Lockwood et al., 2005). Reduced abiotic and biotic resistance resulting from degradation of ecosystems directly or indirectly by humans could also promote invasion (Hufbauer et al., 2012). The more rapid increase in D. villosus population growth at higher elevations nevertheless contradicts other studies that show lower elevation as high bioclimatic suitability for D. villosus (Gallardo et al., 2012), but suggests the species is invading higher elevated regions as a potential response to the ongoing climate change (Pauchard et al., 2016). Lastly, the dominance of D.
villosus was lower in streams in comparison to the major European rivers. This result may be partially explained by fast water flow or lower temperature in streams (Allan & Castillo, 2007;Grabowski et al., 2009), but also larger rivers having a greater level of confluence with smaller streams, functioning as shipping canals and therefore being prone to higher invasion rates. These results could be also affected by differences in sampling effort and the sampling methods among time series, which could have created biases and delays in detecting D. villosus at local and regional scales.

| Impact of D. villosus on community metrics
Understandings of how invasive alien species impact the recipient ecosystems and the potential synergistic effects of anthropogenic stressors (abiotic and biotic factors) have become priorities in invasion science .  (Dick et al., 2002). Invasive amphipods have also been shown to display lower levels of omnivory than native species (Cuthbert, Kotronaki, Hütt, et al., 2022). This predatory capacity can reduce or replace functionally equivalent species via intraguild predation (e.g. native Gammarus duebeni by alien G. tigrinus; Rewicz et al., 2014). Dikerogammarus villosus also has negative effects on ecosystem functioning, including alteration of habitat structure, leaf litter decomposition and energy flows through food webs, potentially causing large-scale trophic cascades (Koester et al., 2016;MacNeil et al., 2011;Piscart et al., 2011;. These impacts can create vacant niches that increase community susceptibility to other invasions and exacerbate the collective impacts of invasive alien species (Boets et al., 2010(Boets et al., , 2011. However, we stress that changes in community trends cannot be attributed exclusively to the effect of D. villosus, as correlation does not indicate causation, and were likely also altered by other anthropogenic and natural stressors not included in our models, including changes in water quality, disturbance events or even other invasive alien species (Didham et al., 2005;Haubrock et al., 2020;Pilotto et al., 2020). The combination of invasive alien species and other human impacts can promote the local extirpation of native species, reducing community diversity and driving biotic homogenization (Dormann et al., 2007;Ekroos et al., 2010;McKinney, 2004;McKinney & Lockwood, 1999), but can also promote or prevent invasions and/or increases in invader populations (Simberloff & Von Holle, 1999;Beaury et al., 2020).

| Implications and conclusions
The scope of our study was limited by the time series represented in our database. Invasive alien species, such as D. villosus, can affect food webs through either bottom-up or top-down regulation, potentially triggering trophic cascades that cause major disturbances in invaded ecosystems . The greater effects of D. villosus following steeper increases in its abundance suggest that the main effects on invaded communities are driven by high population densities, which overwhelm the ecological resistance of the recipient community. Surprisingly, the data from GBIF and our time series do not overlap in some cases, highlighting areas for future abundance survey efforts. Dikerogammarus villosus was first recorded in Italy in 1992 (Seebens et al., 2018), Belgium in 1998 (Seebens et al., 2018), France at the beginning of the 2000s (Devin et al., 2001) and the United Kingdom in 2010 (Bacela-Spychalska et al., 2013;Seebens et al., 2018), but D. villosus was not present in any time series from these countries, perhaps because our data are restricted to lotic systems. Our study was therefore limited by our focus on rivers and streams. Dikerogammarus villosus also occurs in lentic freshwaters including lakes, ponds, and brackish waters, and has marked impacts on these ecosystems (Bacela-Spychalska et al., 2013;Bollache et al., 2004;Minchin et al., 2019). Its occurrence in other countries could also be underestimated, resulting in relatively few time series, for example the Netherlands or Switzerland (Altermatt et al., 2014;Bij de Vaate & Klink, 1995).
As such, further research would be needed to comprehensively characterize D. villosus impacts across all European freshwaters.
Notwithstanding these data gaps, our results allow broad-scale inference of impacts using standardized time series across a range of invaded lotic European freshwaters.
Overall, our results show that D. villosus is well-established across the vast majority of Europe. Considering that D. villosus has invaded many freshwater and brackish ecosystems beyond those sites covered by the time series we considered in our analyses, it remains impossible to conclude anything about the capacity of D.
villosus to expand further in Europe. Nonetheless, our documentation of D. villosus highlights the need for greater effort to reduce delays in the detection of invasive alien species to implement management techniques in an early stage of invasion, when such methods can be more effective Lodge et al., 2016) and less expensive Fantle-Lepczyk et al., 2022;Hulme et al., 2009). These measures are especially important in those regions currently uninvaded, such as the North American Great Lakes that can act as "stepping stones" to assist further spread across the continent. Our use of long-term, largescale time series also emphasizes the importance of long-term data in ecology (Crooks et al., 1999). Further long-term studies are necessary to increase our understanding of the population dynamics of D. villosus and other aquatic invaders across the breadth of ecosystems, and the context-dependencies that differentiate such dynamics, to provide better management information for stakeholders and governments. Open Access funding enabled and organized by Projekt DEAL.

CO N FLI C T O F I NTE R E S T
The authors declare no competing interests.

DATA AVA I L A B I L I T Y S TAT E M E N T
The data that support the findings of this study are openly available in a GitHub reposit at https://github.com/IsmaS A/Diker ogamm arusvillo sus-popul ation -dynam ics.git.

PEER R E V I E W
The peer review history for this article is available at https://publo ns.com/publo n/10.1111/ddi.13649.