The role of waterway connections and downstream drift of veliger larvae in the expanding invasion of inland lakes by zebra mussels in Minnesota , USA

Zebra mussel spread to inland waters in Europe and North America is often attributed to overland transport by trailered boats and water-related equipment. Much less attention is paid to spread between lakes connected by streams that may serve as conduits for larval dispersal. Previous studies have produced few data on the magnitude and distance of downstream drift of veliger larvae. Here we present an evaluation of the contribution of streamflow connections to zebra mussel spread, and new data on the numbers of larvae transported from infested lake stream outlets. We studied lake/stream connections in Minnesota (MN) and found that lakes connected to upstream infested lakes are 27 times more often infested than unconnected lakes. In 4 lake/stream systems and at increasing distances downstream of infested source lakes, we estimated recruitment and larval “flux” (numbers per unit time), and found recruitment to be localized, in most cases to within 1 km from source lakes. A short distance from lake outlets, larval flux reached 109 larvae per day or more at peak times in the 2 systems with the highest supply. In all 4 systems, flux dropped steeply and exponentially with distance. Nevertheless, flux reached 0 (observed) through the entire season, and/or was below a low-risk threshold (estimated) at the downstream inlet (as far as 64 km downstream) in only 1 system. Spread risk by downstream drift is so high that prevention and treatment efforts should be focused on upstream lakes in pristine watersheds. At the same time, localized recruitment confirms that zebra mussel populations are unlikely to persist far from source waters, limiting impact to unionids and other native species in small streams.


Introduction
In 2000, IUCN listed zebra mussels (Dreissena polymorpha Pallas, 1771) among the 9 worst aquatic invertebrate invasive species in the world, due to their extensive economic and ecological impacts (Lowe et al. 2000).In their North American invaded range, these animals cost tens of millions to a billion dollars per year to power generation, water treatment, boating and water-related recreational industries (Connelly et al. 2007;IEAB 2010;Lovell and Stone 2005;Pimentel et al. 2005).Dreissena polymorpha infestations are also known to alter water chemistry and clarity, remove massive amounts of phytoplankton biomass and reduce zooplankton densities (Higgins and Vander Zanden 2010).They cause population declines and local extinctions of native mussels (Bogan 1993;Ricciardi et al. 1998), reduce populations of other invertebrates, or increase them in the vicinity of zebra mussel beds (Higgins and Vander Zanden 2010), reduce fish populations in some systems (Strayer et al. 2004), and profoundly alter energy and nutrient flow through aquatic food webs (Mayer et al. 2014;Strayer 2010).
Zebra mussels spread throughout much of their present North American range in about 3-5 years following their introduction (presumably in the ballast of trans-Atlantic ships) to the Great Lakes in the late 1980's.It is now widely accepted that the secondary spread to inland lakes, rivers and streams that followed is mostly associated with human activity-via veliger larvae carried within trailered boat compartments, and juvenile and adult mussels attached to plants, and boating and other equipment, moved between water bodies (Buchan and Padilla 1999;Johnson et al. 2001).
Receiving far less scrutiny is the spread of planktonic larvae and mussels between water bodies interconnected by streamflow via downstream drift.Studies of spread in the US prior to 1998 showed that connection downstream of infested lakes increased the probability for a lake being infested 10-fold (Bobeldyk et al. 2005).Larvae can drift over several kilometers downstream, but their survival declines with distance, potentially reducing risk to downstream water bodies (Horvath and Lamberti 1999a, b).Furthermore, recruitment is localized; for example in Michigan and Indiana watersheds adult zebra mussel densities dropped sharply between 1 and 10 river kilometers (rkm) in streams downstream of source lakes (Bobeldyk et al. 2005;Horvath et al. 1996), and on artificial substrates, recruitment also declined steeply with distance (Horvath and Lamberti 1999b).These findings led to the so-called "source-sink" model (Bobeldyk et al. 2005;Horvath et al. 1996), which proposes that small streams (< 30 m wide) connecting lakes act as conduits for spread to lakes short distances downstream (ca. 10 rkm).Zebra mussel populations in these streams, moreover, are not selfsustaining and depend on upstream source lakes for recruitment; hence they operate as sinks for reproductive output and larval supply.Despite the intuitive appeal of this model and the confirmed role of connected waterbodies in the spread of zebra mussels, the issue has seldom been revisited [two recent studies of dispersal downstream of reservoirs (Churchill and Quigley 2017;Smith et al. 2015) are exceptions].Whatever risk larval drift poses for infestation of lakes and how far it extends dowstream is unknown for the many infested systems in which management could benefit from this information.
Our goal in this study was to provide additional information on the spatial scale and magnitude of drift of veliger larvae within a region-Minnesota (MN)-currently experiencing rapid spread of zebra mussels to inland lakes.Every year since 2009, new lakes have been infested with zebra mussels in MN.The number of new infestations in 2016 (Minnesota Department of Natural Resources 2016) is similar to those seen (at peak) 10-15 years ago or more in the other 6 Great Lakes states containing the majority of US invaded waters [New York NY, Ohio OH, Indiana IN, Illinois IL, Michigan MI, and Wisconsin WI: (Johnson et al. 2006;Mallez and McCartney 2018)].We (i) examined the influence of stream connections on probability of invasion in MN and (ii) determined the scale of downstream dispersal in several lake/stream systems by estimating the number of veligers and recruiting juveniles at increasing distances downstream.We focused on lake/stream systems in two lake-rich regions of MN that together contained 45% of the invaded lakes in MN by the end of 2016.These are: (1) the Central Lakes region near Brainerd MN (2 rivers) and (2) the Detroit Lakes/Pelican Rapids Region in western MN (1 river).We also studied a stream near the Twin Cities Metropolitan (Metro) area that flows from the largest, most highly infested Metro-area lake (Lake Minnetonka) potentially creating a risk for invasion of lakes in the Minneapolis Parks.

Field study sites
Four coupled lake/stream systems-the Pine River, Gull River, Pelican River and Minnehaha Creek systems (Figure 1)-were selected to study downstream patterns of veliger transport and juvenile recruitment, due to their high potential for downstream dispersal.A brief description of the lake/stream systems is presented below.For expanded details on each system, see Appendix.
The Pine River (Figure 2) rises at the outlet of Pine Mountain Lake in Crow Wing County, then flows to the southeast 91.6 rkm to the confluence with the Mississippi River, 10.5 km NW of Ironton MN.In route, it flows through the Whitefish Chain of Lakes, which includes 13 water bodies.The river bottom is mainly gravel with boulders, and the water shows high clarity through much of its length.At a distance 8.7 rkm upstream of the Mississippi confluence, Pelican Brook flows 8.6 rkm into the Pine River from its origin at the outlet of Ossawinnamakee Lake, which was the earliest infested (2003) natural inland lake in MN.
The Gull River (Figure 2) originates at the outlet of Gull Lake then flows 22.9 rkm through Cass and Crow Wing counties to the confluence with the Crow Wing River, just 6.4 rkm upstream of where the Crow Wing flows into the Mississippi.The river bottom is sand, gravel and cobble in the upper reaches with high water clarity and abundant native mussels.Gull Lake is part of the Gull Chain of Lakes, which includes 7 infested lakes.
Minnehaha Creek (Figure 3) originates from the outlet at the southeast end of Lake Minnetonka, then flows 35 rkm southeast where, after passing over Minnehaha Falls, it empties into the Mississippi River 5.2 rkm upstream of its confluence with the Minnesota River.This small tributary stream flows through the highly-urbanized landscape of Hennepin County through the cities of Minnetonka, Hopkins, St. Louis Park, Edina and Minneapolis.
The Pelican River headwaters are north of Floyd Lake in Campbell Creek (not shown).From there, the Pelican River (Figure 4) flows south through 6 infested lakes and joins the Otter Tail River near Fergus Falls MN, 58 rkm from the most downstream source lake.The upper reaches of the river are highly sinuous and show very clear water, with mostly sand bottom with limited hard substrate (gravel and cobble) and abundant streamside vegetation.Below Pelican Rapids (sites PR-5 through PR-8), the river curves less.It becomes highly colored due to runoff from agriculture or by flow over clay soils of prairie grassland.The Pelican and Otter Tail watersheds exhibit one of the highest rates of spread in the state.

Lake/stream interconnections and zebra mussel infestations in MN
To evaluate the effect of hydrologic connectivity between lakes on the likelihood of infestation by zebra mussels, we adopted an approach modified from Bobeldyk et al. (2005).We focused on the 91 inland lakes that were confirmed infested by the end of 2015 (Minnesota Department of Natural Resources 2016), and used ArcGIS ArcMap 10.3.1 to examine connections and distance between infested waters and other water bodies.The ArcGIS shapefiles and data layers were downloaded from the Minnesota Geospatial Commons (2017) website.
Overland straight-line distances were measured between the centroid of the focal infested lake and the centroids of all other inland lakes > 10 acres (40,468 m 2 ) in surface area.Lakes < 30 km from the focal lake were selected for further analysis.These Brook that, along with the red shaded portion of the Mississippi River, we consider to be at increased risk of infestation from downstream drift.The green shaded portion of the Mississippi is upstream of and not at risk from veligers from the Pine River.Sampling sites for veligers and recruitment in the Pine and Gull (e.g.GR-1) are marked with green dots.Lakes labeled in red text were infested with zebra mussels as of December 2015.
were coded as infested or not (as of end-2015) and as directly connected up or downstream, or not connected, to the focal lake.Water flow direction was obtained from the US Geological Survey's National Hydrography Database (USGS 2017).For downstream connected waterbodies, we used the tool "Stream Routes with Kittle Numbers and Mile Measures" in ArcMap to hand-measure stream distances.For lakes in clusters, stream flow paths often pass through lakes, so distances along stream channels were also added to the total length of the downstream flow path (preferable to ignoring stream courses through lakes entirely).
Lakes were tallied as infested or not, and connected or not, and a 2 × 2 table was constructed.A G-test of independence (adjusted using Williams' correction: Sokal and Rohlf 1994) was used to examine whether infestation incidence was dependent upon whether a lake was connected or not to an infested lake.Similarly, location with respect to stream flow was evaluated in connected water bodies, first by performing a G-test of independence to determine whether infestation incidence was dependent upon being up or downstream of a connected infested lake.Then, the influence of stream distance was evaluated for all water bodies connected and downstream of infested focal lakes.Because the distribution of stream distances was highly right-skewed and no transformation was found to restore normality, we used a non-parametric Wilcoxon 2-sample test to compare stream distances to un-infested downstream lakes and stream distances to infested downstream lakes.

Veliger sampling
On each of these 4 systems, we established stations at increasing distances downstream from the stream outlet at the infested source lake (or lakes: Supplementary material Table S1).Only the Pelican system has more than one source lake at the upstream outlet (Figure 4); in this case, 1 station per lake was placed just downstream of Pelican, Lizzie and Prairie Lake outlets and then several were placed at increasing distances downstream of Prairie.To collect veliger larvae, we pumped water (using a Honda WX10 gasoline-powered water pump) for approximately 1.5-2 min at each of 3 depths (0, 0.5, and 1 m), until we collected 147 L total.Water was pumped through a 50 µm Nitex mesh plankton net into a large PVC drum.The filtered material was fixed on site in 100 ml total volume of 70% ethanol and stored on ice, then transported to our laboratory for storage at 4 C.
Veligers were counted within a subsampled volume (or when necessary the entire sample volume), under cross polarized light, using a Huvitz H7-APO stereomicroscope.Veliger concentrations were expressed as numbers per liter.Veliger flux (the number of veligers passing through a stream cross sectional area at any position downstream, per unit time) was calculated by multiplying concentration by river discharge on the day that samples were taken.Discharge estimates were obtained from gauging stations where present (see Table S1 for sources of discharge data).Where no gauges were available, we used a Price AA current meter (Rickly Hydrological Co., Columbus OH) mounted on a wading rod and standard methods for estimating stream discharge (Buchanan and Somers 1969).
Regression analysis was used to examine the decline in veliger concentration with rkm downstream.We found that non-linear regression of a simple 2-parameter negative exponential (2P Exp) decay function [ , where y = flux (veligers/s) and x = distance downstream (rkm)] fit several of the data series well.Fit to the 2P Exp was compared to fit to a linear function using the Akaike Information Criterion, corrected for small sample size (AICc).We then used the AICc weight values (the normalized AICc values) to compare linear to non-linear fits.We also estimated the distance downstream (and Figure 4. Expanded map of the Pelican River system.For labeling of map elements, see Figure 2 legend.In this system, downstream waters under risk of infestation (red-shaded) include the Pelican River, Lakes Lizzie and Prairie, and the Otter Tail River downstream including three reservoirs.Of these water bodies, only Breckenridge Reservoir was not infested as of December 2015.Several lakes in this region are also infested but not connected downstream; Crystal and North and South Lida are labeled on the map. the upper 95% confidence limit) at which veliger flux dropped to a low-risk threshold using inverse prediction of rkm.Our low risk threshold was 0.1 veliger per second, which corresponds to 8.64 × 10 3 veligers/day.Sprung (1989) estimated that 0-0.7% of early-stage ("D-stage") larvae reach settlement stage, and Lewandowski (1982) estimated 1% survival during the settlement transition.Together, survival to the post-larval stage, when multiplied by the threshold flux, yields < 1 surviving larva settled per day.We use this threshold as a heuristic, and emphasize that it has no verified basis in predicting the likelihood of infestation.
Finally, we obtained samples of veligers from plankton tows in each of the source lakes for the 4 systems studied.Vertical tows of the entire water column (minus 1 m to prevent fouling with sediment and to a maximum depth of 10 m) were taken with a 50 µm-mesh net, 30 cm in diameter and 120 cm in length.Four to six sites per lake, including one a short distance from the stream outlet, were sampled to characterize variation in veliger densities throughout the lake.One of the samples in each month (June, July, August) was taken within a week of the river veliger counts.Lake tow samples were processed and counted as described above.Non-parametric correlations (Kendall's ) were calculated to examine whether veliger counts in stream stations at lake outlets were related to veliger counts in source lakes; the latter judged by (1) veliger counts at sites in lakes nearest the outlet, and (2) mean veliger counts across all tow sites within lakes.

Recruitment
Recruitment of zebra mussel juveniles was estimated over the entire reproductive season of 2014 and 2015, using cinder block samplers placed on the stream bed at the same sites where veligers were sampled (except for GR-4 in 2014 and PR-8 in 2015, due to unsafe pumping or difficulty in recovering blocks).Three 2-hole cement cinder blocks (39 cm L × 19 cm D × 19 cm H; 4389 cm 2 settlement surface area) were placed at each site in July 2014 and late May of 2015 (high water in May and June 2014 prevented field work at some sites until July).The blocks were laid with one lengthwise surface on the stream bed, across-stream so that flow passed through the holes.Blocks were checked monthly and cleared of entangled vegetation.They were retrieved in autumn, and all juvenile and adult mussels were removed and counted.Recruitment was expressed as number of juveniles per m 2 surface.Since recruitment was 0 at most downstream sites (Table S2), data were analyzed to examine variation in recruitment among streams and between stream positions [upstream-most ("outlet") sites vs. all other ("downstream") sites].Variance in recruitment was judged for equality between stream positions and among streams using Levene's test and found to be unequal, so differences in recruitment were analyzed by Wilcoxon's test (between sites) and Welch's ANOVA (among streams).We used JMP 12.0.1 and SAS 9.4 (SAS Corporation, Research Triangle Park, NC) for all statistical analyses.

Lake connections
We evaluated 91 MN lakes that were infested with zebra mussels by the end of 2015.Using the 30-km proximity cutoff, 5,682 lakes were identified and we evaluated over 15,500 comparisons involving these lakes for infestation status, hydrologic connectivity and flow direction.We found that for lakes connected to other infested lakes, the percent infested was 8.7 times higher than for lakes that were not connected (Table 1).Frequency of infestation was highly dependent upon presence of connections between lakes (G adj = 1199.4,P < 0.001).Out of the connected lakes, the percentage of lakes infested that were downstream of infested focal lakes was 3.1 times higher than for upstream lakes and the frequency of infestation was significantly higher downstream (Table 2; G adj = 187.06,P < 0.001).Together, upstream connections increased the frequency of lake invasion (relative to unconnected lakes) 27-fold.
We also found some evidence that distance effects frequency of infestation.Only 50 downstream connected lakes were not infested, and 150 were infested.Of the 36 that are connected and are  1 rkm downstream of other infested lakes, 32 were infested by 2015 (Figure 5).The median distance downstream for infested lakes was 6.2 rkm, compared to 11.5 rkm for non-infested lakes, a marginally significant difference (Z = 1.907,P = 0.056).

Larval supply and downstream dispersal
Veliger concentrations varied substantially across the 4 systems, both in source lakes (not shown) and at stream outlets (Table 3).Exploratory analyses, while the sample size was small (8 total data points), revealed that monthly veliger counts at stream outlets were not correlated with counts at the nearest lake sampling site [Kendall's  = 0.214, P = 0.536 (2-tailed)], but they showed marginally significant correlation with the mean veliger count for that month across all stations within the lake ( = 0.571, P = 0.063), suggesting some correspondence with veliger supply from the lake.The analysis could not include Minnehaha Creek because veliger data from Lake Minnetonka were taken in 2014 and not 2015 when the creek was sampled.
Veliger concentrations (and flux estimates) declined sharply with distance downstream on each river and in most months of the study (Tables 3, 4; Figures 6-9).Ten out of 11 curves of decline showed strong fit to linear and non-linear functions.In 7 cases, a 2parameter negative exponential function fit the data closely (r 2 > 0.85) and far better than a linear function [based on adjusted Akaike Information Criterion (AICc) values and weights: Table 4].In the other four cases, the data fit descending functions but linear and non-linear fits were indistinguishable (based on the AICc).
Month to month variation occurred on all streams.On the Pine, Gull, and Pelican Rivers, veliger flux at the upstream outlet was highest in early season, then declined through the summer.On the Pelican River, this seasonal decline was the most dramatic, with veliger counts falling > 175-fold from June through August (Figure 6, Table 4).Only Minnehaha Creek showed the opposite seasonal pattern, with veliger flux at the outlet from Lake Minnetonka increasing from June to July to August.Decline in observed veliger flux downstream along the length of the river to the inlet was > 90% in 8 out of 11 cases (Table 4).The point at which estimated flux fell below 0.1 veliger per second was upstream of the inlet to the downstream water body in July on the Gull, in June, July and August on Minnehaha Creek, in August on the Pine, and in July on the Pelican River.On Minnehaha Creek, veliger flux was below this threshold throughout the entire reproductive season.

Recruitment
Recruitment was confined to the site immediately downstream of the outlet to the Pelican and Gull Rivers in 2014, and to the Pelican Brook and Pine River in 2015 (Table S2).At all sites farther downstream, no recruitment occurred despite large numbers of larvae flowing past (observed in our veliger sampling).These same patterns held on the Pelican River in 2015.Immediately downstream of each of the 3 source lakes there were moderate levels of recruitment.Below Pelican Rapids and farther downstream, in contrast, from 0 to 1 juvenile settled per block for the entire 2015 season.Minnehaha Creek showed the least localized recruitment of all systems.Recruitment extended as far as 4 rkm downstream of the outlet, showing a sharp decline over this distance.Recruitment was then 0 at all sites farther downstream.Due to the dominance of zero values downstream, variance in recruitment was much lower at downstream sites than at outlet sites (Levene's test: F [1,63] = 19.583,P < 0.001).A Wilcoxon test confirmed highly significant differences in recruitment between outlet and downstream sites (S = 1218, Z = 6.748,P < 0.001)., where Y = flux (veligers/sec), x = distance (km downstream), a = scale parameter and b = the decay rate (negative in all cases).2AICc is the Akaike Information Criterion value for goodness of fit of the model, adjusted for small sample sizes.The model with the lower value of AICc shows better fit.The AICc weight is the normalized AICc value.
At outlet sites, recruitment also varied among lake/stream systems (Table S2; Figure 10).There was significant heterogeneity in variances among streams (Levene's test: F [5,17] = 20.465,P < 0.001), so we used Welch's ANOVA, which detected significant differences in recruitment (F [5,6.44]= 6.692,P = 0.016).We also examined associations between recruitment and larval supply in the water column at the outlet sites and found none (Kendall's  = −0.400,N = 8, P = 0.462).Veliger flux (averaged over the entire summer season) at the outlets below Pelican and Prairie Lakes were the highest across all surveyed, but recruitment at these sites were the 2 lowest.Conversely, the outlet to Pelican Brook showed the highest recruitment of any site we studied, yet larval supply at this outlet was the second lowest (Figure 10). .Decline in veliger flux with distance downstream of source lakes in the Pelican River system.On the X-axis, Km downstream is in reference to the Prairie Lake outlet (negative values are upstream).In June and July, flux rises as the stream flows from Pelican through Lizzie and through Prairie Lakes.Downstream of Prairie, a steep decline is observed, and the fitted lines represent the 2parameter negative exponential fit.In August, veliger counts were much lower, and distance downstream had no significant effect on veliger flux.

Discussion
Minnesota contains > 13,000 inland lakes, and multiple regions where clusters of lakes are highly interlinked by waterway connections.Our results indicate that hydrologic connectivity is a strong determinant of spread throughout the state, and that stream dispersal is clearly a high-risk pathway.

Analysis of lake connections
In Minnesota, connected downstream lakes were about 27 times more frequently infested than unconnected lakes.Bobeldyk et al. (2005) surveyed all US states from 1988 (when the species first arrived in North America) until 2003, and found about 10 times as many downstream connected lakes were infested than unconnected lakes.They tallied lakes < 1 km from focal infested lakes, so most were pairs of adjacent lakes, connected or not.The present study surveyed a 30-km radius around focal infested lakes, so it contrasted invasion frequencies in wider geographic windows, and examined far more comparisons between each focal lake and other lakes."Connected and downstream" in the present study also spanned much greater stream distances between lakes, but still, 65.9% of these lakes were infested, compared to 79% of adjacent lakes in Bobeldyk et al. (2005).This may indicate that stream connections continue to increase the likelihood of invasion over  extended distances downstream, even if the significance of the distance effect was marginal in our study.Over short distances (in this case, < 1 rkm), lakes were more likely to be infested than not, but the signal was weak and it disappeared over longer distances.The fact that 3 times as many downstream connected lakes were infested than not may weaken the power of this analysis.On the other hand, the substantial number of veligers found, at times, far downstream of the source lake also supports the idea that any connection represents a higher risk of infestation than no connection at all.Stream connections also may allow propagules to be carried between lakes by boats.That recreational boats act as an overland transport vector and that commercial barge traffic transports propagules in large rivers has been directly documented several times (e.g.Allen and Ramcharan 2001;De Ventura et al. 2016;Johnson et al. 2001;Karatayev et al. 2013;Keevin et al. 1992;Montz and Hirsch 2016).However, the hypothesis that boats navigating waterway connections between inland lakes also carry AIS propagules has been directly tested to our knowledge only once: water in boats traveling through the Trent-Severn waterway that connects neighboring lakes to Lake Simcoe (Ontario, CA) carried a few zebra mussel veligers in addition to several native zooplankters (Kelly et al. 2013).We found that lakes downstream were 3 times more likely to become infested than lakes upstream of infested lakes.While boating traffic navigating between lakes would not be expected to produce this bias, we cannot discount that boaters also play a role in connected lake invasions.

Larval supply and downstream drift
Veliger concentrations and flux in source lakes and lake outlets were highly variable-among sampling dates, lakes, sites within lakes and lake/stream systems.The causes of variation remain obscure.However, veliger concentrations are clearly not a simple function of, for example, adult biomass.The largest source lake in our study, Minnetonka (5,749 hectares), exhibits very large biomass of adult mussels, yet veliger concentrations were on average lower lake-wide than Pelican Lake (3,963 acres).Larval supply at lake outlets showed marginally significant correlations with means of veliger density across multiple stations in the source lakes, but not to values at the stations nearest the outlet.Similarly, in southwest Michigan veliger concentrations at lake outlets were quite different from concentrations within the source lakes themselves (Horvath and Lamberti 1999b).Winddriven currents and local circulation patterns are likely to drive spatial variation in veliger density, as shown for the Asiatic clam (Hoyer et al. 2015), which may influence export of larvae by outlet streamflow.One of the strongest patterns common to all systems was the sharp decline in veliger flux with distance downstream of the source lake; in most cases, flux dropped ≥ 90% from the source lake outlet to the downstream inlet.This decline represents actual loss of larvae from the water column, not mortality per se, as we did not score whether the larvae recovered were alive or dead (i.e. they were all fixed at the time of collection).
Past studies have focused on potential causes of loss of zebra mussel larvae during transport down streams and rivers.Horvath and Lamberti (1999a) were the first to invoke mechanical sheer stress in turbulent, flowing water-they reported a 3-fold decline in survival of larvae during transport 18 rkm down a small stream in southwest Michigan.That zebra mussel larvae die from exposure to hydrodynamic forces has also been demonstrated in laboratory studies of turbulence created by bubble plumes (Rehmann et al. 2003) and in laboratory studies in which mortality was induced by spinning larval suspensions in flasks on an orbital shaker for extended durations (Horvath and Crane 2010).Vegetation density within the streams is another feature of the physical environment that may account for loss of larvae downstream.Indeed, streams that flow through vegetated wetlands have been shown to exhibit sharp drops in veliger concentrations (Bodamer and Bossenbroek 2008;Miller and Haynes 1997), and in juvenile recruitment and adult density in the stretches downstream (relative to upstream) of the vegetated wetland (Bodamer and Bossenbroek 2008).A combination of slowed water velocity, particle retention by wetland vegetation, and settlement onto poor quality habitat was hypothesized as leading mechanisms for explaining the "wetland filtration" effect (Bodamer and Bossenbroek 2008).Each of the rivers and streams that we studied flow through extensive wetlands that vary greatly in the density of vegetation and the aquatic plant species present.Loss due to particle retention and fatal settlement into poor habitat in vegetated areas are thus viable explanations for downstream decline in our study.One caveat is that rhizomes of cattails (Typha latifolia, T. angustifolia and their hybrids T. × glauca), can provide excellent substrate for settlement of zebra mussels as seen in the wetland below Lake Lizzie on the Pelican River (personal observation).
Notwithstanding the steep decline with distance, veliger counts were above the low-risk threshold at the inlet to the downstream water body, at least for a portion of the summer, on 3 out of 4 of the systems studied.Only at the downstream inlet from Minnehaha Creek did veliger flux remain below threshold for the entire reproductive season.On the Pelican River in June, for example, larval flux was estimated to be above threshold as far as 78 rkm downstream, below the confluence with the Otter Tail River.This was true despite a steep exponential decline from very high veliger counts at the Prairie Lake outlet.In June, Prairie Lake was releasing over 300,000 veligers per second into the Pelican River, so even with 96% decline at the sampling station farthest downstream (64 rkm), veliger counts were high enough to create appreciable risk to the Otter Tail River.The latter then flows into Dayton Hollow Reservoir (5.4 rkm downstream), which finally flows into Orwell Reservoir (3.4 rkm downstream); both reservoirs were infested in 2012.Therefore, our results indicate that downstream drift must be considered an alternative route to overland spread for invasion of these reservoirs.

Recruitment
In each lake/stream system, we found recruitment of juveniles to be localized to stream bed a short distance downstream of source lakes.Decline to 0 recruitment occurred over < 1 rkm in 3 out of 4 streams, with recruitment extending farther only down Minnehaha Creek.This is similar to results from recruitment samplers in Christiana Creek in southwest Michigan, where recruitment fell to 0 at distances > 1 rkm downstream in each of 2 years (Horvath et al. 1996).It is also similar to results from counts of natural recruitment on stream beds in the same watershed in Michigan and Indiana (Bobeldyk et al. 2005).These showed decline to 0 recruitment within 1 rkm down 6 streams in both years; in at least 1 of the 2 or 3 years of study, recruitment dropped less steeply-to 0 between 5 and 10 rkm down 6 other streams.Localized recruitment no doubt helps account for the reported absence of zebra mussels from small streams.All 161 surveyed European streams < 10 m wide lack zebra mussel populations (Strayer 1991).On the other hand, larger streams can harbor selfsustaining metapopulations, where riverine pools or lakes can maintain large adult populations that serve as larval sources for recruitment to downriver sites (Stoeckel et al. 2004;Stoeckel et al. 1997).
In smaller streams, the causes for the sharp drop in recruitment with distance downstream are not obvious.Horvath and Lamberti (1999b) considered a range of pre-settlement factors (acting on veligers) and post-settlement factors (acting at settlement or on juvenile recruits).They concluded that veliger loss during drift downstream was less steep than the decline in recruitment.In the present study, high veliger concentrations in the water column extended downstream well past where recruitment stopped.Given that veliger loss cannot easily explain the abrupt decline in recruitment, decline in settlement cues and/or in post-settlement survival or growth are likely alternatives.Motivated by the observation that population densities of native benthic filter feeders decline sharply with distance from stream outlets (Richardson and Mackay 1991), Horvath and Lamberti (1999b) tested the hypothesis that downstream decline in food quantity led to decreased growth.While they showed that concentrations of chlorophyll a declined rapidly with distance, bagged adult mussels displayed no decline in growth (Horvath and Lamberti 1999b).This all means that both preand post-settlement processes acting on stream dwelling zebra mussel populations deserve further study (particularly at settlement and in newly settled young).Meanwhile, localized zebra mussel recruitment may limit impact on native unionid mussel populations in small streams.This is some measure of good news, given that zebra mussels caused sharp declines in freshwater mussels in the Great Lakes (Nalepa et al. 1996;Schloesser and Nalepa 1994) and North American rivers (Ricciardi et al. 1996;Strayer and Smith 1996).

Concluding remarks and management implications
The most recent list shows that by the end of 2016, 114 inland lakes were infested in MN, and (by our count) 47% of these are connected to upstream infested lakes.This study estimates that the magnitude of increased risk for invasion for sites downstream of a newly infested lake is substantial, and it provides more information on the likely mechanisms.Veliger supply on a daily basis can be so massive that infestation of the most proximal lakes seems a virtual certainty.And while this risk drops steeply with distance, in a majority of systems, lakes can feed larvae several tens of kilometers downstream at peak times.The question remains, what can managers do about any of this?For one, in smaller streams, the "downstream march" model (Bobeldyk et al. 2005) fails to fit and the "source-sink" model still applies (Bobeldyk et al. 2005;Horvath et al. 1996).Streams provide conduits for delivery of larvae, but they are poor habitats for colonization (lakes along the way and large rivers are a different matter).This means that attention is better focused away from managing infestations in connecting streams themselves, and towards preventing invasion of upstream lakes.While a challenging goal, watersheds at risk of new invasion by zebra mussels should focus on prevention; for example, by rigorous watercraft inspection and decontamination programs.And if these fail, population suppression or other intervention efforts (e.g.restoration of downstream wetlands) should be considered for lakes with high potential as sources for downstream spread.

Figure 1 .
Figure 1.Map of the four Minnesota lake/river systems studied.The red shaded tracing shows reaches of the Mississippi River that we consider to be at increased risk of infestation from upstream sources in the Pine and Gull River systems.While the Mississippi river downstream of the Twin Cities is highly infested, these middle reaches from the Twin Cities upstream to Brainerd show only patchy populations [Cope et al. 1997; M Davis, MN DNR, pers.comm.; McCartney, pers.obs.].

Figure 2 .
Figure 2. Expanded map of the Pine and Gull River systems.Red shaded tracings show portions of the Pine and Gull Rivers and PelicanBrook that, along with the red shaded portion of the Mississippi River, we consider to be at increased risk of infestation from downstream drift.The green shaded portion of the Mississippi is upstream of and not at risk from veligers from the Pine River.Sampling sites for veligers and recruitment in the Pine and Gull (e.g.GR-1) are marked with green dots.Lakes labeled in red text were infested with zebra mussels as of December 2015.

Figure 3 .
Figure 3. Expanded map of the Minnehaha Creek system.For labeling of map elements, see Figure 2 legend.In this system, downstream waters under risk of infestation (red shaded) include Minnehaha Creek, Lakes Nokomis and Hiawatha (the latter, already infested) in the Minneapolis Parks, and downstream portions of the Mississippi River.

Figure 5 .
Figure5.Influence of stream distance on invasion frequency of lakes connected downstream of infested source lakes.Each plot is a frequency distribution of stream distances to lakes that are connected and downstream of infested lakes; filled bars = infested and empty bars = un-infested downstream lakes.To adjust for the fact that many more downstream connections lead to infested (160) than to uninfested lakes (50), the lower panel shows these data as proportions of the total number of connections.

Figure 6
Figure6.Decline in veliger flux with distance downstream of source lakes in the Pelican River system.On the X-axis, Km downstream is in reference to the Prairie Lake outlet (negative values are upstream).In June and July, flux rises as the stream flows from Pelican through Lizzie and through Prairie Lakes.Downstream of Prairie, a steep decline is observed, and the fitted lines represent the 2parameter negative exponential fit.In August, veliger counts were much lower, and distance downstream had no significant effect on veliger flux.

Figure 7 .
Figure 7. Decline in veliger flux with distance downstream of the source (Cross Lake) in the Pine River system.Flux (number of veligers/sec) on the Y-axis is plotted against rkm downstream on the X-axis at each of 4 sites in June, July and August of 2015.The fitted lines represent the 2-parameter negative exponential fit to these data.Note the broken Y-axis to allow detail to be seen in the July and August data.

Figure 8 .
Figure 8. Decline in veliger flux with distance downstream of the source (Gull Lake) in the Gull River system.Flux (number of veligers/sec) on the Y-axis is plotted against rkm downstream on the X-axis at each of 4 sites in July and August of 2014.The fitted lines represent the 2-parameter negative exponential fit to these data.

Figure 9 .
Figure 9. Decline in veliger flux with distance downstream of the source (Lake Minnetonka) in the Minnehaha Creek system.Flux (number of veligers/sec) on the Y-axis is plotted against rkm downstream on the X-axis at each of 7 sites in June, July and August of 2015.The fitted lines represent the 2-parameter negative exponential fit to these data.

Figure 10 .
Figure 10.Graphical analysis of the relationship between veliger supply and recruitment at stream outlets from lakes.The absence of a clear relationship indicates that other unidentified factors influence recruitment at stream outlets.Error bars represent one standard error.

Table 1 .
Lake connectivity and zebra mussel infestations in MN.Values in cells are numbers of comparisons between focal infested lakes and all other lakes  30 km from the focal lakes (see text for details).

Table 2 .
Position up or downstream influences the likelihood of infestation for connected lakes.Values in cells are numbers of comparisons between focal infested lakes and other connected lakes  30 km from the focal lakes (see text for details).

Table 3 .
Veliger flux at upstream outlets and downstream inlets (observed and predicted).

Table 4 .
Decline in veliger supply with distance downstream: linear and non-linear regression analysis.