Forecasting the expansion of the invasive golden mussel Limnoperna fortunei in Brazilian and North American rivers based on its occurrence in the Paraguay River and Pantanal wetland of Brazil

The bivalve Limnoperna fortunei (Dunker, 1857), also called golden mussel, is native to Asia but becoming dispersed around the world. The golden mussel resembles the invasive dreissenid bivalves in many respects, and although much less studied it evidently has broader environmental tolerances. The golden mussel was introduced into the La Plata River estuary (South America) and quickly expanded upstream to the north, into the tropical Paraguay River reaching a large floodplain area in Brazil known as the Pantanal wetland. The golden mussel tolerates environmental conditions in the Pantanal that would be inhospitable for most bivalves, but mussel mortality has been observed during the most extreme oxygen depletion events. Based on knowledge about the limiting factors for the golden mussel in the Pantanal wetland, its potential distribution was predicted for the remainder of the Paraguay River basin where the species is not present, as well as in other river systems throughout Brazil. Forecasts of potential distribution in Brazilian river systems were based on physicochemical limitations for shell calcification, and specifically on lower thresholds of dissolved calcium concentrations and the calcium carbonate (calcite) index of saturation, which may be a better indicator of calcification potential in low-calcium waters than calcium concentration alone. In addition to examining spatial patterns in calcium and calcification potential, these and other limnological and climate variables were used in ecological niche modeling using GARP and Maxent algorithms. Forecasts of potential distributions in three major North American river systems (Mississippi, Colorado, and Rio Grande) were based mainly on water temperature because calcium availability and calcification evidently would not be limiting to golden mussel establishment in those waters. Due to the greater tolerance of the golden mussel to conditions known to limit other bivalves, as well as its greater ability for shell calcification in low-calcium water, the golden mussel could potentially become broadly distributed throughout Brazil. According to its thermal tolerance L. fortunei could become established in the Mississippi, Colorado and Rio Grande drainage systems, although the northern Mississippi River system including the Missouri River may be too cool in the winter to support the golden mussel.


Introduction
Three invasive freshwater mollusks, apparently dispersed via transoceanic shipping, have become well established in the Western Hemisphere, causing numerous environmental problems, as well as economic costs.The zebra mussel Dreissena polymorpha (Pallas 1771), family Dreissenidae, has spread widely across North American fresh waters since its introduction into the Laurentian Great Lakes in the 1980's, resulting in costly impacts due to biofouling and inducing ecological changes throughout aquatic food webs (Schloesser and Nalepa 1994;Caraco et al. 1997;O'Neill 1997;Strayer et al. 1999;Bykova et al. 2006).The spread of D. polymorpha has been followed to some extent by the closely related quagga mussel D. rostriformis bugensis.The golden mussel Limnoperna fortunei (Dunker 1857), family Mytilidae, became established in southern South America in 1990 and is producing similar economic and ecological impacts (Darrigran and Escurra de Drago 2000;Darrigran 2002;Boltovskoy et al. 2006;Oliveira et al. 2006).
In order to estimate the potential dispersion and eventual geographic distribution of invasive species, many studies have considered their means of transport to a new location, as well as establishment and integration of the invader into the new environment (Moyle and Light 1996;Shea and Cheson 2002).The rapid expansion of the zebra mussel in North America has resulted from propagule spread via water craft (Bossenbroek et al. 2007;Colautti et al. 2006) and generally favorable physical and chemical characteristics that facilitate growth and reproduction (Ramcharan et al. 1992).In the cases mentioned above other distinctive characteristics not found in native species, including byssal threads for attachment and a planktonic larval phase (veliger) for dispersal, have contributed to success in colonization of new environments (Johnson and Carlton 1996;Johnson and Padilla 1996;Bobeldyk et al. 2005).
Considering that the means of introduction are present in most environments, the expansion of these invasive species can be forecasted on the basis of characteristics of the receptor environment in relation to their ecological niches (Peterson and Vieglais 2001).Two examples where ecological niche modeling has been applied are the prediction of potential distribution of D. polymorpha in North America (Drake and Bossenbroek 2004;Bossenbroek et al. 2007) and the expansion of L. fortunei globally (Kluza and McNyset 2005).These models have shown good results over large spatial scales using climatological, geological and topographic spatial data.
Global-scale analyses have shown that L. fortunei could likely colonize most waters of South America, including the Amazon, Orinoco and Magdalena river systems, where this species has not yet been recorded (Boltovskoy et al. 2006).It has been proposed that L. fortunei may also be able to colonize warmer waters in the southern United States where D. polymorpha does not occur, on the basis of both species' thermal tolerances and the chemical characteristics of southern US waters (Ricciardi 1998;Kluza and McNyset 2005;Boltovskoy et al. 2006;Karatayev et al. 2007).These studies, however, only provide information at very coarse geographic scales and do not account for limnological variation within broad climatic regions.
For finer-scale forecasts of distributions in specific water bodies, limnological variables such as calcium concentration and pH have been used to predict the distribution and density of the invasive mussel D. polymorpha in North America (Ramcharan et al. 1992;Neary and Leach 1992;Mellina and Rasmussen 1994).Low concentrations of calcium and low pH are suspected to reduce population density or restrict the establishment of bivalves since in most mollusks shell formation (calcification) requires a threshold level of available calcium and a pH range that does not inhibit calcification (Mackie and Flippance 1983;Ramcharan et al. 1992;Checa et al. 2007).Temperature can be important as well because L. fortunei has a relatively high tolerance to warmer water temperatures compared to D. polymorpha (Morton 1982;Ricciardi 1998;Boltovskoy et al. 2006;Karatayev et al. 2007).
The aim of this study was to forecast the geographic expansion (i.e., risk of establishment) of L. fortunei in Brazilian and North American river systems based on their physical and chemical variables.These variables are not commonly used in regional-scale models.The advantage of modeling the potential distribution is that the possibility of an invasion can be assessed before the actual introduction of a species occurs (Peterson and Vieglais 2001).Results from this study can be used to establish priority areas for monitoring, management, and biodiversity conservation as L. fortunei expands its range in the Americas.

Data compilation and modeling
The potential distribution of L. fortunei in the Brazilian river systems was predicted through an exploratory analysis based on limnological data integrated into two niche models that have previously been used to predict alien species invasions: GARP (Genetic Algorithm for Ruleset Production), http://openmodeller.sf.net and Maxent (Maximum Entropy Method), http://www.cs.princeton.edu/~chapire/maxent,version 3.0.4beta.Detailed descriptions of the GARP algorithm are presented by Stockwell and Noble (1992), Peterson and Cohoon (1999), Stockwell and Peters (1999), and Anderson et al. (2003).Maxent modeling is described by Philips et al. (2004 and2006).Both GARP and Maxent models are based on presence records.Brazilian river systems modeling followed procedures outlined in Oliveira (2009).To test the accuracy of the GARP and Maxent models we used the receiver operating characteristic (ROC) analysis, which characterizes the performance of a model at all possible thresholds by a single number, the area under the curve (AUC) (Phillips et al. 2004 and2006).The AUC can be interpreted as the probability that a model set correctly predicts presence in a randomly selected grid cell.The higher the AUC, the more sensitive and specific the model set, ranging from 0.5 (random accuracy) to a maximum value of 1.0 (perfect discrimination).Only models that presented an AUC above 0.75 were considered in this study.To assess the soundness of the predictions we also used a threshold value in Maxent (Phillips et al. 2006).Values below these thresholds were considered to have conditions of low suitability for L. fortunei occurrence.
Limnological variables used in the modeling included water temperature, dissolved oxygen, conductance, pH, calcium concentration, and the calcite saturation index (SI calcite ).SI calcite reflects the thermodynamic propensity for calcification, calculated from water temperature, pH, conductance, total alkalinity (Gran 1952), anddissolved calcium, following APHA (2005).The SI calcite is usually interpreted on a log 10 scale where zero indicates thermodynamic equilibrium with respect to CaCO 3 , a positive index indicates supersaturation, and a negative index indicates undersaturation.We did not use total suspended solids (TSS) and sestonic chlorophyll a in the models, but we used these variables to compare quantity and quality of food among different aquatic systems.
The tolerances of L. fortunei are not known for all of these variables.We considered the minimum pH, calcium and SI calcite requirements for L. fortunei development to be 6.0, 1.0 mg l -1 and -4.0, respectively, based on field observations previously made in the Paraguay River basin (Oliveira 2009).Above these limits, we considered that waters could potentially support L. fortunei invasion, and below these limits that the risk of invasion was low.
At low dissolved Ca concentrations, the SI calcite is likely to provide a better indicator of the suitability of a particular water body for shell calcification.The relationship between calcium concentration and SI calcite is specific to a particular water body, reflecting its hydrogeochemical composition and aquatic ecosystem metabolism (a control on dissolved CO 2 concentrations).Typically there is a curvilinear relationship between dissolved Ca concentrations and SI calcite in natural waters, but at low concentrations of dissolved Ca (i.e., <5 mg/L), the relationship is not strong and SI calcite can vary over more than 2 orders of magnitude for a given Ca concentration, as shown in an example from the Amazon River (Figure 1).Limnological data for the Brazilian river systems are from the 'Brasil das Águas' project (http://www.brasildasaguas.com.br)except for the Paraguay River basin, where data are from Embrapa Pantanal.We used 786 sampling sites located along six systems: Amazon, Paraná/ Paraguay, São Francisco, Tocantins-Araguaia, North Atlantic coastal drainages, and South Atlantic coastal drainages.Except for the Paraguay system, each site was represented by a one-time synoptic survey conducted between 2003 and 2004 for the aforementioned program.We only considered environments with salinity below 12.0 PSU, thereby remaining within the tolerance of L. fortunei (Ricciardi 1998).We used 24 records of occurrence in the Paraguay basin for the Brazilian river system models, plus six sites in the Paraná River.
To forecast the expansion of L. fortunei in North America we considered three major river systems: the Mississippi (with its Missouri and Ohio River tributaries), the Rio Grande, and the Colorado.Limnological data were taken from the US Geological Survey's NASQAN program (description available at http://pubs.usgs.gov/wri/wri014255/).We analyzed data for 23 sites consisting of means from monthly sampling between 1995 and 2000.We considered the same set of limnological variables used for the Brazilian rivers, including water temperature, dissolved oxygen, conductance, pH, dissolved calcium concentration, total suspended solids (TSS), and the calcite saturation index (SI calcite ), calculated as described above.
The North American rivers had dissolved Ca concentrations, pH, SI calcite , and dissolved oxygen concentrations that were well above the estimated minimum requirements for L. fortunei establishment based on our field observations in the Paraguay River and Pantanal wetland, and thus the limnological data were not used to model the potential distribution of L. fortunei in North American rivers.Given their favorable water quality but seasonally low temperatures, we focused on the mean minimum water temperature (from December to February, 1995February, to 2000) ) as the main physicochemical limitation to L. fortunei establishment in these North American rivers.

Experimental determination of thermal tolerance
Previous estimates of the low-temperature tolerance of L. fortunei have been based on observations on the occurrence of L. fortunei in waters subject to seasonally cool temperatures.In the Paraguay River basin, occasional cold fronts can bring sudden temperature drops during the winter, but protracted periods with water temperatures below ~20°C are uncommon.Therefore we performed laboratory tests where adult L. fortunei from the Paraguay River were acclimated at 26°C (the temperature of Paraguay River water when mussels were collected) and then gradually exposed to lowering temperatures, eventually reaching 0, 5, and 10°C±0.5°C.A treatment at 26°C was maintained during the experiment period as a control.There were 9 replicates for 0°C and 5 replicates for each other tested temperature.Each replicate consisted of 20 mussels with shell length between 8-13 mm in a 600-mL beaker.The treatments were maintained in a thermostatically controlled incubator.Additionally, we used an external digital thermometer to check the water temperature inside the beaker.
The period of acclimation for 26°C was around 20 days, followed by daily decreases of 1°C until attaining the target temperatures.The experiment was monitored during 30 days after the water reached the target temperature.No additional food or aeration was provided; rather, the water in the beakers was replaced with water from the Paraguay River every day for the control and every week for treatments with temperatures ≤ 10°C, in which the mussels were relatively inactive.The characteristics of the Paraguay River water collected periodically for the experiment were: temperature 26-27°C, dissolved oxygen above 6.0 mg.l -1 , pH between 6.0 and 7.0, and conductance between 70 and 90 µS cm -1 .Dissolved oxygen and pH were monitored once a day and temperature was monitored every 3 hours.During the incubation dissolved oxygen was ≥ 1.0 mg l -1 , and the pH and conductance were in the same range as in the Paraguay River.Mussels were checked for survival daily by examining open shells and looking for movement.Mussels that were considered dead were transferred to fresh water at 26°C and checked for movement for about 12 hours.The results were expressed in survival rate per day.

Limnological characterization of Brazilian river systems
Conductance among Brazilian aquatic systems ranged widely from 0.0 to more than 7,000 µS cm -1 (Figure 2A).The waters of highest ionic strength were in the Atlantic coastal drainages (North and South), although some streams in these regions can have waters with very low conductance.The Amazon River system also had a large variation in conductance, and included the most ionically dilute and acidic waters.The Paraguay, Paraná, Tocantins-Araguaia, and São Francisco systems had conductances around 100-200 µS cm -1 .Conductance was around 400 µS cm -1 in the Uruguay River system.Values of pH between 7.0 and 8.0 were most common, but the pH was sometimes lower than 6.0 in the Amazon and Paraguay systems (Figure 2B).
Mean water temperature in the Brazilian rivers was between 25 and 29°C.Mean dissolved oxygen was higher, ranging from 3.1 and 8.0 mg l -1 .Chlorophyll a means ranged from 0.0 to 10.0 µg l -1 in the Paraguay and São Francisco systems, 10 to 100 µg l -1 in the Amazon, Tocantins-Araguaia and North Atlantic systems, and higher than 100 µg l -1 in the Paraná and South Atlantic systems.
Calcium concentrations ranged from as low as 0.0 up to 20 mg l -1 in most rivers, and exceeded 100 mg l -1 in some Atlantic coastal rivers (Figure 2C).Waters from the Amazon, Tocantins-Araguaia, and Paraguay rivers can have Ca concentrations less than 1.0 mg l -1 .Most of the Brazilian river systems had less extreme undersaturation with respect to CaCO 3 than the Paraguay River, except for some sites in the Amazon system, and most were above the minimum estimated SI calcite required for the establishment of L. fortunei based on our field observations in the Paraguay River (SI calcite threshold ~ -4.0) (Figure 2D).

Forecasting the expansion of L. fortunei in Brazilian river systems
The same procedures used to forecast the potential distribution of L. fortunei in the upper Paraguay basin (Oliveira 2009) were employed to forecast the occurrence of L. fortunei in other major Brazilian river systems.The main physicochemical controls of the potential distribution of L. fortunei appear to be the dissolved calcium concentration and SI calcite These variables indicated that most waters in Brazil have medium to high risk of establishment (Figures 3A and 3B).Included in the regions with high risk are the estuaries of the Amazon and Tocantins rivers, some coastal drainages to the Atlantic (North and South) such as the Mearim River estuary (State of Maranhão) and the Jequitinhonha, Mucuri, Doce, and Paraiba do Sul rivers.Medium to low probabilities were found for some tributaries of the Amazon River, such as the Negro, and portions of the Tapajós and Xingu rivers, as well as the Araguaia River.
Results from both the GARP and Maxent models using SI calcite (Figures 4A and 5A) showed fewer regions with high risk of L. fortunei establishment in the Brazilian rivers than did empirical forecasting using calcium concentration and SI calcite , although most environments presented medium to high risk of L. fortunei establishment.The Maxent combined variables model indicated far fewer sites with favorable conditions for L. fortunei establishment than the GARP model.GARP and Maxent models using SI calcite predicted medium risk of L. fortunei establishment in the Uruguay River and Guaiba Lake where the species is already present.and SIcalcite (B).We considered low risk of L. fortunei occurrence in rivers where the mean calcium concentration was between 0.0 and 1.0 mg l -1 and SIcalcite was < -4.0, medium risk between calcium concentrations of 1.0 and 3.0 mg l -1 and SIcalcite between -4.0 and -3.0, and high risk where calcium concentration was >3.0 mg l -1 and SI calcite was > -3.0.We considered the probability of establishment of L. fortunei as low (pale gray) when less than 5% of the models predicted the occurrence, medium (dark gray) when 5-50% of models predicted the occurrence and high (black) probability when more than 50% of models predicted the occurrence.

Limnological characterization of major North American river systems
Limnological characteristics of the North American rivers are depicted in Figure 6.Compared to the Paraguay River system (Figure 2), the North American rivers carry waters with higher conductance and dissolved calcium concentrations.Calcium in the North American rivers always exceeded 10 mg l -1 and pH was above 7.0.SI calcite was usually in the range of -2 to 0, except for the Ohio River where SI calcite was sometimes as low as -3.Dissolved oxygen was above 1.0 mg l -1 and concentrations of total suspended sediments often were higher than in Brazilian waters.

Water temperature as a limiting factor in North American rivers
In contrast to Ca concentrations and the SI calcite , which do not appear limiting to the establishment of L. fortunei in the major North American rivers, seasonally low water temperatures may present a limitation in northern regions.Winter water temperatures in the North American rivers range between 0 and 5°C in the upper Mississippi and its tributary the Missouri River (Figure 7).This low temperature can last for about 3 months in those rivers.In the Ohio River, the main eastern tributary of the Mississippi, minimum water temperatures are slightly higher than 5°C (Figure 8).The Colorado and Rio Grande rivers showed higher mean minimum temperatures, above 8°C during the winter season.
Our thermal tolerance assays using specimens of L. fortunei from the tropical Paraguay River provide an indication of how this species responds to low temperatures.Adult mussels survived up to 15 days at water temperatures of 0-1°C, although they were inactive during that time (Figure 9).Survival at 5-7°C was <50% during the first 20 days, with a maximum survival of about 38 days.At temperatures above 10°C mussels were active, and about 80% of them survived for the entire 30 days of the experiment.These data lend support to a threshold of ~5°C for protracted exposure of L. fortunei to low winter temperatures (i.e., weeks to months).

Forecasting the expansion of L. fortunei in Brazilian river systems
In most places where L. fortunei occurs naturally (Morton 1975, Wang et al. 2007;Cai et al. 2008), or as an invader in the case of Brazilian river systems, the pH is above 6.4 and calcium concentrations are higher than 2.4 mg l -1 (Morton 1975(Morton , 1977;;Magara 2001;Cataldo andBoltovskoy 1999 and2000).Nevertheless, in the Pantanal L. fortunei can occur in water where pH is around 6.0 and with low calcium concentrations (e.g., 1.0 to 6.0 mg l -1 in the Paraguay River) (Oliveira et al. 2006;Oliveira 2009).Considering the thresholds of tolerance of L. fortunei to diluted water as demonstrated by Deaton et al. 1989, we suggest that waters with less than 1.0 mg l -1 of calcium concentration have low risk of L. fortunei establishment.Thus, most Brazilian river systems have medium to high probability of invasion based on calcium availability, with some exceptions located mainly in the Paraguay and Amazon River systems.
Both dissolved calcium concentrations and SI calcite showed the potential for colonization of most Brazilian rivers.Neary and Leach (1992) predicted the expansion of the zebra mussel in Ontario (Canada) using calcium and pH, and the current distribution of zebra mussels after about 16 years (Zoltak 2008) matches the high risk areas indicated in that prediction.Models that simultaneously consider Ca and pH are effectively similar to the SI calcite since those are the most important controls on SI calcite .
The minimum SI calcite value observed in the Paraguay River system where L. fortunei is present was -4.0, in water with less than 1.0 mg l -1 of calcium.Most other Brazilian river systems had higher values of SI calcite than the Paraguay River system, thus, it is likely that L. fortunei would have better conditions for calcification and therefore growth in most other Brazilian river systems compared to the Paraguay River system.Field observations are lacking for whether L. fortunei can become established in waters more undersaturated with respect to calcite than the Paraguay River value (i.e., SI calcite below -4).During oxygen depletion events, when SI calcite values were around -5.5, high mortalities were observed, although dissolved oxygen depletion occurred simultaneously and both low O 2 and low SI calcite may have been stress factors (Oliveira 2009).Whereas both calcium and SI calcite are good predictors for L. fortunei expansion in Brazil, they may not be good predictors for the major North American rivers, where calcium availability and calcification appear unlikely to be limiting factors.
Our study has focused on limiting factors for the occurrence of L. fortunei but conditions may act to limit the abundance of L. fortunei rather than preclude its establishment.Although there is no information about the effects of suspended sediments on L. fortunei, we have suggested that the combination of high concentrations of suspended sediments, low food availability, and high water velocity may be limiting factors for larval survival, settlement and growth in the Miranda River (upper Paraguay River basin) (Oliveira 2009).In rivers of the Pantanal, total suspended solids varied from 10 to 120 mg l -1 and chlorophyll a concentrations averaged less than 1.0 µg l -1 .High suspended sediment concentrations were observed mainly during the reproductive period of L. fortunei and may explain the low larval survival, perhaps together with water velocities exceeding 0.9 m s -1 .
L. fortunei can survive in turbid river waters with low food availability, and evidently it can use detrital organic carbon sources in addition to algae (Calheiros 2003;Sylvester et al. 2005).River-connected lakes in the Pantanal floodplain showed higher L. fortunei densities than the Paraguay River (Oliveira, unpublished).When positioned along river systems, these lentic water bodies may present improved conditions for  populations of L. fortunei and act as a source of larvae for downstream river reaches.Higher densities in lakes and a downstream decline in abundance of larval and settled mussels were also observed in small rivers in Ireland (Lucy et al. 2008).
GARP and Maxent models showed fewer regions where L. fortunei could become established compared to our conclusions based on the lower thresholds for dissolved Ca and SI calcite .In the Brazilian river systems the ranges of conductance and calcium concentration were very broad compared to the area of occurrence of L. fortunei in the Pantanal, and some of these regions were predicted to be of low invasion risk by GARP and Maxent but had medium to high risk based only on thresholds of calcium and SI calcite .Additionally, both GARP and Maxent models failed to predict L. fortunei expansion in several relatively large-scale Brazilian river systems where calcium concentrations and SI calcite values are favorable for its establishment.This suggests that these models might not be accurate when the calibration data used by the model to build the ecological niche do not span ranges similar to the data where predictions are made.
The GARP and Maxent models consistently predicted medium to high probability of L. fortunei occurrence in the Paraguay River, and most models predicted occurrence in the Paraná River, in both cases for sites where the species was already present.Furthermore, our predictions for the establishment of L. fortunei in Brazilian rivers were generally in agreement with analyses conducted by Kluza and McNyset (2005) over large spatial scales using mainly climatological data.According to our predictions sites located in the Amazon estuary as well as waters in the upper section of southern Amazon tributaries, which extend close to the Paraguay River system, such as the Tapajós, Teles Pires, and Araguaia rivers, have limnological conditions suitable for the occurrence of L. fortunei.However, they were predicted as low-risk areas by the Kluza and McNyset (2005) model.Low risk was also predicted for the São Francisco system and parts of the Paraná system, such as the Paranaíba River, in that model, contrasting with our prediction that these regions have medium to high potential of L. fortunei invasion.
Environmental variables that were input to the model and spatial scales of analysis are likely responsible for the differences between the Kluza and McNyset (2005) model results and our results.The Kluza and McNyset (2005) model was built using East Asian occurrence data and climatological and topographic variables for that region.The advantage of our method based on limnological variables is that it provides more detailed and waterbody-specific information; we can thus analyze each river system separately, and at finer spatial scales if desired, as we have done for the upper Paraguay River basin.
Considering the high potential risk in the vast majority of Brazilian river systems for the establishment of L. fortunei, management systems for invasions should focus on potential points of entry.The major South American hydrographic basins including the Amazon, Orinoco, and Magdalena are readily accessible through their estuaries by ocean-going vessels, which make them highly vulnerable to invasions via ballast water releases (Boltovskoy et al. 2006).In central Brazil transport of mussels by recreational boaters and other human activities will also contribute to the range expansion of L. fortunei.Regions with high potential for invasion in the Paraguay and Paraná systems are close to those regions with high potential in the Amazon and São Francisco basins, and hence the risk of interbasin movement is great.

Predicting invasion potential of L. fortunei in North American rivers
If given the opportunity, L. fortunei probably will colonize North American waters, especially warmer waters in the southeast, potentially being introduced through ports along the Gulf of Mexico (Ricciardi 1998;Kluza and NcNyset 2005;Karatayev et al. 2007).We can apply the knowledge of environmental tolerances of L. fortunei in the Pantanal, a region with relatively extreme environmental conditions, and elsewhere to project its potential distribution in representative major North American rivers.Low calcium availability and pH are unlikely to be limiting in these North American rivers because they are much higher compared to the native environments and Pantanal waters where L. fortunei is present.
In addition to the relatively low calcium and pH in some rivers of the Pantanal where L. fortunei has colonized, oxygen depletion events are common every year, particularly during the rising water phase of the annual inundation season, when river water first contacts the floodplains after the dry season (Calheiros and Hamilton 1998;Hamilton et al. 1997).The major North American rivers examined do not experience oxygen depletion events akin to those in Pantanal waters that can control the density of L. fortunei, although hypoxia is common during the summer in the Mississippi River estuary, and when combined with high temperature can provoke mortality of Dreissena polymorpha (Mihuc et al. 1999), even when dissolved oxygen concentrations are higher than 1.0 mg l -1 .Above its delta, oxygen concentrations in the Mississippi River are normally higher than 1.0 mg l -1 .The Rio Grande experiences some hypoxia also, but concentrations of oxygen remain above 1.0 mg l -1 .High turbidity has been considered an important limiting factor for zebra mussel populations in large rivers like the Mississippi River, particularly in combination with high temperature (Alexander et al. 1994;Allen et al. 1999).Suspended sediments in the three major North American rivers considered here were usually higher compared to the rivers of the Pantanal.In the Mississippi River, where mean winter water temperatures are above 5°C, concentrations of total suspended solids ranged between 51 and 1,360 mg l -1 , and DOC concentrations were low compared to the Paraguay River.This combination of high suspended sediments and low food availability could limit the abundance of L. fortunei where the temperature is not a limiting factor.
L. fortunei lives in tropical waters in the Pantanal, where water temperatures of around 30°C last about 7 months of the year, and minimum temperatures are usually above 17°C (Oliveira et al. 2006;Oliveira 2009).L. fortunei is able to survive and undergo larval development in temperatures up to 33°C in the Pantanal wetland (Oliveira 2009).Whereas high water temperature limits dreissenid mussels in North America, low water temperature may be more likely to be the key environmental variable determining distribution patterns of L. fortunei in North American rivers (Ricciardi 1998), although Karatayev et al. (2007) suggested that the lower thermal limits of L. fortunei may resemble those of the invasive dreissenids that flourish in the temperate climate of the Laurentian Great Lakes region (US and Canada).Thermal tolerance depends on duration of exposure as well as maximum or minimum temperatures.Observations in the literature indicate that L. fortunei can exist at high densities in waters that fall as low as 5-8°C (Japan: Magara et al. 2001;Goto 2002), although in both of these cases the season of low water temperatures was short, lasting about 2 months; or near 0°C (South Korea: Choi and Kim 1985;Choi andShin 1985, reviewed in Karatayev et al. 2007).
Based on our water temperature tolerance assays, the probability of L. fortunei establishment would be low in water bodies with temperatures below 5°C for protracted periods.In the Upper Mississippi the minimum winter temperature is about 0°C, with around 3 to 4 months of temperatures lower than 5°C.It is possible that this protracted cool period is too long for adult L. fortunei survival.The probabi-lity of establishment and survival is greater in the Mississippi River below its confluence with Ohio River (Mississippi River at Thebes, IL), as well as in the Colorado River and Rio Grande, where the minimum winter water temperature is above 5°C.
The potential distribution of L. fortunei overlaps the current distribution of the corbiculid and dreissenid mussels in North America and moreover further extends into waters that are warmer, lower in calcium, and subject to oxygen depletion events.Hence the ecological and economic impacts of the spread of L. fortunei are potentially more far-reaching than those of the dreissenids, and efforts to prevent its introduction and contain its spread are well justified.

Figure 1 .
Figure 1.Relationship between the calcite saturation index (SIcalcite) and dissolved Ca concentrations in rivers throughout the Amazon River basin (based on a nationwide synoptic survey; data downloaded from http://www.brasildasaguas.com.br and SIcalcite calculated as described in the text.

Figure 2 .
Figure 2. Ranges of conductance (A), pH (B), calcium concentration (C), and SIcalcite (D) in the Brazilian river systems.Limnological data from synoptic surveys were provided by "Brasil das Águas Project" except data for the Paraguay River system, which came from Embrapa Pantanal (see text for details).The dashed lines depict approximate lower thresholds for L. fortunei establishment based on field observations in the Paraguay River basin (Oliveira 2009).

Figure 3 .
Figure 3. Potential distribution of L. fortunei in the Brazilian river systems based on lower thresholds of calcium concentration (A)and SIcalcite (B).We considered low risk of L. fortunei occurrence in rivers where the mean calcium concentration was between 0.0 and 1.0 mg l -1 and SIcalcite was < -4.0, medium risk between calcium concentrations of 1.0 and 3.0 mg l -1 and SIcalcite between -4.0 and -3.0, and high risk where calcium concentration was >3.0 mg l -1 and SI calcite was > -3.0.

Figure 4 .
Figure 4. Predicted potential distribution of L. fortunei in the Brazilian river systems based on the GARP model calibrated to observed distributions within the Pantanal: (A) variable: SIcalcite, AUC= 0.82, Accuracy= 94%, Omission error= 5.8% (B) variables: calcium concentration, conductance, pH, water temperature, dissolved oxygen, AUC= 0.92, accuracy= 97%, Omission error= 2.9%.We considered the probability of establishment of L. fortunei as low (pale gray) when less than 5% of the models predicted the occurrence, medium (dark gray) when 5-50% of models predicted the occurrence and high (black) probability when more than 50% of models predicted the occurrence.

Figure 5 .
Figure 5. Predicted potential geographic distribution of the L. fortunei in the Brazilian river systems based on the Maxent model calibrated to observed distributions within the Pantanal: (A) variable: SIcalcite, AUC= 0.82, threshold value= 3.0 (B) variables: calcium concentration, conductance, pH, water temperature and dissolved oxygen, AUC= 0.96, threshold value= 5.5.Three shades are used to indicate the strength of the prediction.Maxent produces a continuous prediction with values ranging from 0 to 100, high in regions with better predicted conditions.The values are depicted here using light gray (between 0.0 and threshold value, low risk); dark gray (between threshold value and 50, medium risk); black (50-100, high risk).

Figure 7 .
Figure 7. Spatial variation of water temperature (°C) in the Mississippi River system, including the Ohio and Missouri rivers, and in the Rio Grande and Colorado rivers.Data were taken from US Geological Survey's NASQAN program (description available at http://pubs.usgs.gov/wri/wri014255/)and represent mean of minimum water temperatures at 23 sites, from December to February, 1995 to 2000.

Figure 8 .
Figure 8. Mean seasonal patterns of water temperature (°C) in North American river systems.Data were taken from US Geological Survey's NASQAN program (description available at http://pubs.usgs.gov/wri/wri014255/)from1996 to 2000.