To assess the environmental factors associated with the presence and abundance of Potamopyrgus and sympatric native mollusks, in July 2014 and 2015 we surveyed biotic (abundances of co-occurring mollusks) and abiotic conditions (temperature, conductivity, ion concentrations, pH, stream velocity, and stream width) across an environmental gradient created by sampling sites above and below geothermal inputs (Table 1) in each of three (2015) to five (2014) rivers in the Greater Yellowstone Area (Suppl. material 1) where Potamopyrgus had occurred in the past. Although there are other approaches to assessing the environmental variables associated with the presence of Potamopyrgus, we focused on rivers where Potamopyrgus occurred and took advantage of variation in occurrence between sites above and below geothermal inputs to discern the environmental conditions associated with their occurrence and abundance.

At each site where we collected samples, we measured temperature, conductivity, pH, ion concentrations, stream width, and stream velocity using standard procedures for stream sampling. We measured temperature and conductivity at three locations (along each shoreline and in the middle of the stream) at each site using a sonde (Yellow Springs Instruments, model 85). We measured stream width at the greatest width at the water surface for each sampling site. We used the float method (Newbury and Bates 2017) three times/site to measure stream velocity. At each site, we collected two water samples (shoreline and mid-stream) to measure pH, cations, and anions. We filtered each sample using Whatman Grade GF/A glass microfiber 0.4 µm filters and cooled samples on ice. Within 12 hours of collection, we measured pH (Corning 430 pH meter) and acidified the sample for cation analysis with 0.5 M HCl until the pH dropped below 2. We refrigerated the cation samples and froze the anion samples until we analyzed them using ion chromatography (Thermo Fisher Scientific ICS 5000) at the Geochemical Analytical Laboratory (Geology and Geophysics Department, University of Wyoming).

We used a stovepipe (0.032 m²) to sample abundance of mollusks at each site. We elutriated each stovepipe sample using 500-µm sieves to remove most cobbles, gravel, and other substrates and preserved each sample immediately in 95% ethanol. In July 2014, we collected 3–5 samples/site at 5 rivers along a single transect at a minimum of 50 meters from the geothermal hot spring. In July 2015, we sampled 10 replicates/site along 1 or 2 transects in 3 of the rivers sampled in 2014, increasing the replicate number to obtain a more robust estimate of sample variance (Suppl. material 1). In 2015, we also omitted two of the rivers that we sampled in 2014: the Firehole River because the frequency and intensity of geothermal activity precluded a gradient in conductivity and the Gibbon River because we found only one live snail and no Potamopyrgus and our study design required Potamopyrgus to occur. At sites dominated by bedrock or high stream velocities, we collected longitudinal rather than transverse transects (Suppl. material 1). In the laboratory, we sorted samples, identified mollusks to the genus level (Brown 1991), and counted snails to assess the abundance of each taxonomic group. The native mollusks that we found were Pyrgulopsis (Call & Pilsbry, 1886), Physa (Draparnaud, 1801), Galba (Schrank, 1803) and Sphaerium (Scopoli, 1777) clams. We did not analyze abundance of Galba because they occurred in samples from only three of fourteen sites (Table 2).

We used principal component analysis (PCA) to reduce the 11 abiotic independent variables (Table 1) to two uncorrelated principal components. Because we made multiple measurements for all variables except stream width, we analyzed mean values for each site (and year, for rivers with data from two years) such that each independent variable in the PCA resulted from 14 values (two sites at four rivers in 2014 [the Gibbon River was excluded from all analyses because of mollusk rarity] and two sites at three rivers in 2015). We used scaled and standardized independent variables in the PCA (resulting in all metrics having a mean of zero and a standard deviation of 1). Based on the limited number of sample sites in our study and the broken stick model (Legendre and Legendre 2012) we selected the principal components that explained more variance than random chance and the equilibrium circle of descriptors method (Legendre and Legendre 2012) to assess which principal component loadings were important for describing the principal components.

Because we had count data that was zero-inflated (all mollusk taxa were absent from > 27% of the samples) and overdispersed (Zuur et al. 2009), we used Zero-Inflated Negative Binomial (ZINB) regression models (using zeroinfl function with a log link for count models and a logit link for zero-inflated models in the pscl package in R; Zeileis et al. 2008) to address the extent that principal components predicted abundance (Count Model) and occurrence (presence or absence: Zero-Inflation Model) of each mollusk taxon. Zero-inflated models are mixture models which address both occurrence and abundance of organisms and are ideal for analyzing count data with many zeros (Zuur et al. 2009). Zero-inflated models combine logistic regression to analyze occurrence (zeros v. non-zeros; Zero-Inflation Model) and negative binomial GLM to analyze counts (zero and non-zeros; Count Model; Zuur et al. 2009). We included only first order terms in our analyses because evaluating interactions in principal component analyses is precluded (Aiken and West 1991). We combined data from two years for three of the rivers (Marmot, Polecat, Crayfish) because the auto-correlation function (ACF; Zuur et al. 2009) revealed no significant auto-correlations for any of the native mollusks and very slight auto-correlation in 10% of the cases for Potamopyrgus. Following Zuur et al. (2009), and given the limited number of observations in our study, we did not include an auto-correlation structure in any of the models.

We assessed whether abundance of Potamopyrgus affected the abundance or occurrence of each native mollusk taxon using zero-inflated negative binomial (ZINB) regressions with abundance of Potamopyrgus as the independent variable and the abundance of each of the native mollusk taxa (tested individually) as the dependent variable. We conducted all analyses and made all plots using R statistical package (Version RStudio 4.1.2, 2021 R Foundation for Statistical Computing, Vienna).

Potamopyrgus increased in abundance with increasing stream width and conductivity and specifically with chloride, sulfate, sodium, and potassium ions. Also, Potamopyrgus were slightly more abundant and more likely to occur at sites with relatively more calcium and relatively lower water velocity and pH. By assessing the abundance of this invasive snail across a gradient of water and stream conditions, our survey reveals the ideal environmental conditions required for the clonal lineage US1 (Dybdahl and Drown 2011) of Potamopyrgus in the Western U.S.A. However, diverse genotypes in the native range in New Zealand (water velocity: Holomuzki and Biggs 1999) and other invasive genotypes (water velocity: Kefford and Lake 1999; conductivity: Levri et al. 2020; salinity: Jacobsen and Forbes 1997; Gerard et al. 2003) show similar responses to many of the same environmental conditions. By revealing the conditions required for the invasive snail to occur and thrive, our results can be used to predict sites that are suitable for secondary spread and invasion success of Potamopyrgus.

Positive associations between abundance of Potamopyrgus and conductivity and specifically with sodium, chloride, sulfate, and potassium ions (PC1; Fig. 2, Table 4) are consistent with many studies (Kerans et al. 2005; Herbst et al. 2008; Clements et al 2011; Moffitt and James 2012; Spyra and Strzelec 2014; Spyra et al. 2015; Szocs et al. 2015; Halabowski et al. 2020; Levri et al. 2020, reviewed in Geist et al. 2022). For freshwater mollusks, ion concentrations must be high enough to permit locomotion, growth (Brodersen and Madsen 2003; Dalesman and Lukowiak 2010), and shell integrity (Brodersen and Madsen 2003). Consequently, laboratory experiments revealed stunted growth (< 100 µS/cm; Herbst et al. 2008; Larson et al. 2020) and high mortality (< 50 µS/cm; Herbst et al. 2008; Vazquez et al. 2016; Larson et al. 2020) of Potamopyrgus at relatively low conductivities. Although Murria and colleagues (2008) found a negative relationship between conductivity and Potamopyrgus abundance in streams in Spain, high pollutant levels (POM, DOC, and ammonium) probably contributed to this contrasting result.

In addition to adding to many studies showing that conductivity is important to the fitness of Potamopyrgus (Kerans et al. 2005; Herbst et al. 2008; Clements et al. 2011; Moffitt and James 2012; Spyra and Strzelec 2014; Spyra et al. 2015; Szocs et al. 2015; Halabowski et al. 2020; Levri et al. 2020, reviewed in Geist et al. 2022), our study also addresses six specific ions (magnesium, calcium, potassium, chloride, sodium and sulfate) contributing to conductivity. In a recent comprehensive review of the autecology of Potamopyrgus, Geist and authors (2022) stated the need for more knowledge and understanding of how water chemistry affects Potamopyrgus. Our study addresses this knowledge gap by measuring concentrations of specific ions and revealing four ions (sodium, chloride, sulfate, and potassium) that directly affected abundance of Potamopyrgus.

Abundance of Potamopyrgus also increased with stream width (PC1; Fig. 2, Table 4). Stream width may increase snail abundance because habitat diversity often increases with habitat size. Densities of invasive zebra mussels (Dreissena polymorpha) increase with lake size possibly because larger lakes possess more habitat and available substrate (Naddafi et al. 2011). Stream width can also affect quantity of food for grazers. Relative to narrow streams with high canopy cover (and substantial allochthonous subsidies), primary production (Hill et al. 1995; Quinn et al. 1997; Kiffney et al. 2004; Stovall et al. 2009; Wootton 2012; Lesutiene et al. 2014; Warren et al. 2016) and consequently food quantity, is often higher with low canopy cover and high light penetration. Finally, stream width is often correlated with stable, less stressful environments for snails because water velocity is often inversely related to stream width (Dodds and Whiles 2010). Consistent with this relationship, we found that higher relative water velocities reduced the occurrence of Potamopyrgus.

The relationship between Potamopyrgus abundance and PC1 (stream width and conductivity and specifically with chloride, sulfate, sodium, and potassium ions), although statistically strong (p < 0.001), was uneven (Fig. 2). Relatively large variation in abundance of Potamopyrgus at low (negative) values of PC1 suggests that Potamopyrgus is tolerant of a large range of conductivity, especially chloride, sulfate, sodium, and potassium ions, and stream width. Wide environmental tolerance is consistent with our findings for pH (discussed below) and with a recent review of the autecology of Potamopyrgus (Geist et al. 2022). Future studies that include a wider range of environments, similar to intermediate values of PC1 (intermediate stream width, conductivity, and specific ions), will clarify the specific nature of this relationship.

Consistent with previous field studies and experiments (Jowett et al. 1991; Holomuzki and Biggs 1999; Kefford and Lake 1999; Shimada and Urabe 2003; Lysne and Koetsier 2006; Holomuzki and Biggs 2007; Murria et al. 2008; McKenzie et al. 2013; Schossow et al. 2016), Potamopyrgus were slightly more abundant and were more likely to occur in relatively low water velocities (PC2; Table 4). Potamopyrgus can dislodge from substrates at stream velocities > 0.12 m/s (Schossow et al. 2016) with most snails dislodging at > 0.70 m/s (Holomuzki and Biggs 1999; Kefford and Lake 1999). Additionally, Potamopyrgus locomotion decreases and rate of dislodgement increases with increasing water velocity (Sepulveda and Marczak 2012). Also, Potamopyrgus produce slightly fewer offspring in environments with high (lotic) versus low (lentic) water velocity (Verhaegen et al. 2021). Therefore, high water velocity conditions are stressful for Potamopyrgus by decreasing motility and fitness and increasing the likelihood of dislodgement.

Potamopyrgus were somewhat more abundant and more likely to occur at sites with relatively low pH. Multiple studies show effects of pH on mollusk presence or abundance (Lewin and Smolinski 2006; Spyra 2010; Sowa et al. 2019; Levri et al. 2020) and the direction of the relationship depends on the range of pH across the study sites and the taxa of mollusks. For example, most studies showing abundance or occurrence of mollusks increasing with pH included multiple mollusk taxa or sites with acidic (< 7 pH) water (Spyra 2010; Sowa et al. 2019; Levri et al. 2020, but Lewin and Smolinski 2006 is an exception). In contrast, the water at all of our survey sites was basic (pH 7.4–8.5, Table 1), which probably explains why we found that Potamopyrgus was more likely to occur where pH was relatively lower. However, Potamopyrgus can occur in acidic to alkaline waters (pH 5.6–6.0, Blakely and Harding 2005; pH 4.0–9.0, Spyra 2010; pH 5.7–9.0, Levri et al. 2020) suggesting that Potamopyrgus tolerates a large range of pH.

Potamopyrgus were slightly more abundant and were more likely to occur where calcium levels were relatively high (range in our study 0.0–4.3 mg/L). In freshwater mollusks, calcium is used to form shells (calcium carbonate) and, is required for muscle contractions and nerve impulses (Thomas and Lough 1974; Madsen 1987; Dillon 2000; Zalizniak et al. 2009). Consistent with our results, calcium concentrations altered mollusk fitness in previous studies. Growth, reproduction, and locomotion of diverse snails increased with calcium concentrations in laboratory experiments (Thomas and Lough 1974; Madsen 1987; Dillon 2000; Zalizniak et al. 2009) and low calcium concentrations can reduce growth and thin mollusk shells (Glass and Darby 2009).

Densities of the snails can increase with substrate complexity, perhaps by providing refuge from predation and stress from high stream velocity, or increasing access to forage (Stewart and Garcia 2002). Because we did not account for differences in substrate among samples, this omission probably increased the error of our estimates of abundance of all mollusks.

All native mollusks differed substantially from Potamopyrgus in the physicochemical conditions associated with abundance and occurrence. We found strong evidence that abundance of Physa and weak evidence that abundance of Sphaerium clams responded oppositely to PC1 (stream width, conductivity, specifically sodium, chloride, sulfate, and potassium ions) than Potamopyrgus. Abundance of both native mollusks decreased with increasing stream width and conductivity, specifically with sodium, chloride, sulfate, and potassium ions (PC1). We found no physicochemical attributes that predicted abundance of Pyrgulopsis. The limited sample size of Pyrgulopsis populations in our survey, only 34% of sites possessed Pyrgulopsis yet 74% of sites had Potamopyrgus, could explain or contribute to this result. Also, none of the physical or chemical attributes describing PC1 and PC2 predicted occurrence of any of the native mollusks. Possibly we were unable to identify the physicochemical attributes of water bodies that predict occurrence of these native taxa because the sites that we sampled do not represent the full range of physicochemical attributes where native mollusks occur and achieve high population abundance. We designed our field survey to target rivers with sites where Potamopyrgus were known to occur rather than sampling rivers based on the known distributions of any of the native mollusks. Thus, our findings about the physicochemical attributes associated with the occurrence and abundance of native mollusks are limited for the native mollusks.

Also, the Zero-Inflation models portion of ZINB, indicating no predictors of the occurrence of native mollusks should be interpreted with caution because our data were more likely to contain false negatives for the native taxa than for Potamopyrgus. This is because all native mollusks were much less common at our study sites than Potamopyrgus and less common taxa are more likely missed when the sampling area is too small (design error; Zuur et al. 2009). The sampling area may have been too small to detect some uncommon native taxa (area = 0.10–0.32 m² in combined samples/year). Consequently, the physicochemical conditions associated with the occurrence of Potamopyrgus are more likely to be robust than for the native mollusks simply because the natives were less common than the invasive snail. For this reason, and because we targeted our sampling at sites where Potamopyrgus were known to occur, rather than where specific native taxa occurred, we have less confidence in the habitat associations for native mollusks than for Potamopyrgus.

Even with the limitations of our data regarding the physicochemical attributes associated with presence and abundance of native mollusks, the different response of native mollusk taxa to physical attributes of their environments may inform management and conservation of native mollusks. For example, in habitats that are less hospitable to Potamopyrgus (e.g. above geothermal inputs), some native mollusks probably have higher fitness than the invasive snail. Consequently, variation among habitats within and among rivers could permit native mollusks to persist at a larger geographic scale. Also, because Potamopyrgus populations can decline rapidly after reaching high population densities (Moore et al. 2012; Gerard et al. 2018; Greenwood et al. 2020), and Potamopyrgus can compete with native mollusks (Lysne and Koetsier 2008; Riley et al. 2008; Thon 2010; Larson and Black 2016), the ability to thrive in distinct environmental conditions could allow native mollusk taxa, and other native taxa, to persist and possibly rebound when Potamopyrgus populations decline (e.g. Moore et al. 2012; Gerard et al. 2018; Greenwood et al. 2020).

Abundance of Potamopyrgus had variable effects on abundance and occurrence of native mollusks. Abundance of Potamopyrgus was moderately negatively associated with abundance of Physa but did not affect the likelihood of Physa presence (Table 5, Fig. 3b). A negative association between the abundance of the two taxa is consistent with our finding that stream width and conductivity (PC1) had opposing effects on abundance of the two mollusk taxa: abundance of Potamopyrgus strongly increased with stream width and conductivity whereas Physa abundance weakly decreased in these same conditions. Opposite relationships between the two mollusk taxa and the environmental attributes could be caused by differences between the two taxa in habitat use or by competition, the most likely interaction between non-native and native taxa occupying the same trophic level (Levine et al. 2003), or by an interaction between both the physical environment and competition (Shea and Chesson 2002). However, because our sampling design targeted rivers supporting populations of Potamopyrgus at some sites, rather than targeting habitats where Physa were known to occur, the physicochemical attributes associated with the abundance of Physa probably do not fully represent the range of sites where these native mollusks occur and achieve high population abundance. Although the negative relationship between Potamopyrgus and Physa may appear to be driven by two sampling sites where Potamopyrgus were very abundant and Physa were uncommon (Fig. 3b), omitting data from these two sites, increased the negative relationship between the abundance of the two taxa (increasing from strong evidence to very strong evidence, sensu Muff et al. 2021). Thus, abundance of Physa was depressed even at relatively low abundance and density of Potamopyrgus. In contrast, Cope and Winterbourn (2004) found reproduction and growth of Physella acuta (synonym Physa acuta) could be facilitated by the presence of Potamopyrgus. Although high densities of Potamopyrgus can reduce abundance of native mollusks by altering nutrient cycling (Hall et al. 2003), dominating secondary production (Hall et al. 2006), or attracting fish predators (Bowler 1991), to our knowledge, possible negative effects of Potamopyrgus on abundance of Physa have not been previously documented.

Similar to Physa, abundance of Potamopyrgus had no effect on the occurrence of Pyrgulopsis (Table 5). However, abundance of Pyrgulopsis weakly (p = 0.07) increased with Potamopyrgus (Table 5, Fig. 3a) but was completely driven by one sample (highest abundance for Pyrgulopsis; Fig. 3a) with the highest co-occurring abundance of Pyrgulopsis and Potamopyrgus. Thus, we suspect that the slight effect is not biologically relevant; both because of the outlier and because a positive relationship between the two taxa contrasts with experimental conditions where Potamopyrgus strongly limited growth of Pyrgulopsis (Riley et al. 2008).

Abundance of Potamopyrgus moderately increased the likelihood that Sphaerium clams occurred at a site (Table 5). Although we found no evidence that the abundance of Potamopyrgus affected the abundance of Sphaerium clams, our results contrast with Gerard et al. (2018) who suggested that possible competition between Potamopyrgus and Sphaerium clams may have driven population declines of Potamopyrgus.