Predicting distribution patterns and recent northward range shift of an invasive aquatic plant : Elodea canadensis in Europe

Climate data and distribution data for the Canadian waterweed Elodea canadensis Michx. from North America, whole Europe and Finland were used to investigate the ability of bioclimatic envelope models to predict the distribution range and recent northward range shift of the species in Europe. Four diff erent main types of models were developed using the North American data, including either three ‘baseline’ climate variables (growing degrees days, temperature of the coldest month, water balance) or an extended set of seven climate variables, both averaged either over a 30 year time slice or a longer 90 year time slice. Ten diff erent random selections of pseudo-absences were generated from the North American data, on the basis of which ten separate generalized additive models (GAMs) were developed for each main model type. All the 40 developed GAMs were applied fi rst to North America and then transferred to whole Europe and Finland. All the models showed a statistically highly signifi cant accuracy in the three study areas. Although the diff erences among the four main model types were only minor, the two extended model types showed on average statistically better performance than the two baseline models based on Bayesian information criterion (BIC) values, the amount of deviance explained by the models, resubstitution validation and four-fold cross-validation in North America. Th ey also provided slightly more accurate predictions of climatically suitable area for Elodea canadensis in Finland both in 1961–1984 and 1985–2006. However, the projections from the individual extended models were more variable than projections from the baseline models. Th us model predictions based on a variety of predictor variables but only one selection of pseudoBioRisk 2: 1–32 (2009) doi: 10.3897/biorisk.2.4 www.pensoftonline.net/biorisk Copyright R. K. Heikkinen et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. RESEARCH ARTICLE A peer-reviewed open-access journal Biodiversity & Ecosystem Risk Assessment Heikkinen et al. / BioRisk 2: 1–32 (2009) 2 absences may be subject to biases, and outputs from multiple models should be investigated to better account for uncertainties in modelling. Overall, our results suggest that more attention should be paid to the careful selection of predictor variables and the use of multiple pseudo-absence sets in the ecological niche modelling in order to increase the reliability of the projections of the range shifts of invasive species.


Introduction
Invasive species are recognized as a major environmental problem which can have manifold ecological impacts (Mack et al. 2000, Weidema 2000, Peterson 2003a), cause high economical costs (Forman 2003, Pimentel 2005), change hydrological cycles, fi re regimes and nutrient cycling, and cause signifi cant environmental damage (Forman 2003).When successfully established into a new area, invasive species can displace populations of native species, threaten rare species and ultimately cause local extinctions attributable to predation, grazing and habitat alteration (Forman 2003, Rahel andOlden 2008), and more rarely competition (Davis 2003, Sax andGaines 2008).
Th e spread of invasive species will probably be accelerated by the on-going and projected climate change (Dukes and Mooney 1999, Weber 2001, Hellmann et al. 2008).Th e magnitude of the projected global warming is particularly high in northern latitudes (ACIA 2005), including northern Europe, and thus the likelihood of climate change-induced range shifts of invasive species is pronounced in such areas (Rahel and Olden 2008).In southern and central Europe, warming climate has already boosted the spread of many invasive species, e.g.palms (Walther et al. 2007) and other exotic evergreen broad-leaved plant species (Walther et al. 2001), and thermophilic tropical and Capensis ornamental plants (Vesperinas et al. 2001).Similar evidence is accumulating from northern Europe (Weidema 2000, ACIA 2005), but more systematic analyses of the observed range shifts of invasive species in relation to recent climatic changes are largely lacking.
Identifi cation of areas most at risk of becoming invaded by a given alien species and projections of the further spread of already naturalised species can provide valuable information for management planning (Weber 2001, Mau-Crimmins et al. 2006) and targeting control measures (Kriticos et al. 2003, Richardson andTh uiller 2007).One proactive approach to identify areas at risk is provided by ecological niche modelling (Weber 2001, Roura-Pascual et al. 2004, Ficetola et al. 2007).Th e main steps in ecological niche modelling include: (i) relating the known occurrences of the target species to the ecological characteristics of the study landscape, (ii) producing a model that defi nes the ecological dimensions of the species niche, and (iii) projecting the derived ecological niche model back onto the geographical space to identify regions with environmental conditions inside or outside the species' niche (Peterson and Vieglais 2001).
Ecological niche models can utilize many diff erent environmental predictors such as climate, topography, soil classes and land cover (Peterson et al. 2003, Iguchi et al. 2004, Mau-Crimmins et al. 2006).However, at broad macroecological scales climate variables are often the only predictors available over large areas, and climate also largely determines species distributions (Th uiller et al. 2004, Luoto et al. 2007).Under such circumstances ecological niche modelling becomes materially the same as bioclimatic envelope modelling (Pearson andDawson 2003, Guisan andTh uiller 2005).Indeed, increasing numbers of broad-scale applications of ecological niche models developed for invasive species have been based on climate variables (e.g.Beerling et al. 1995, Baker et al. 2000, Broennimann et al. 2007).Th is study also focuses on broad-scale species -climate models and the 'fi rst-fi lter' identifi cation of the areas potentially at risk of being invaded (Weber 2001, Welk 2004).
However, certain factors may decrease the usefulness of bioclimatic envelope models in modelling invasive species (Pearson and Dawson 2003, Th uiller 2004, Luoto et al. 2005, 2007, Heikkinen et al. 2006a, 2007).In this study we address three potential limitations.First, the selection of climate parameters may signifi cantly aff ect the performance of the species -climate models (Beaumont et al. 2005, 2007, Heikkinen et al. 2006b, Loiselle et al. 2008, Peterson and Nakazawa 2008).Increasing attention should thus be paid to careful selection of climatic variables in order to model and assess potential future species distributions as accurately as possible (Heikkinen et al. 2006b, Beaumont et al. 2007, Peterson and Nakazawa 2008).Second, bioclimatic modelling studies often show a mismatch between the time slice over which the climate data is averaged and the time slice when species records have been collected, but it is insuffi ciently understood whether this aff ects model performance.Such mismatches are common in studies employing plant atlas data bases (such as Atlas Florae Europaeae; Jalas and Suominen 1988; http://www.fmnh.helsinki.fi/english/botany/afe/), which often include agglomerative records from several decades or even centuries (e.g.Beerling et al. 1995, Huntley et al. 1995, Sykes et al. 1996).Th ird, certain modelling methods require both presence and absence data.Many recent studies have adopted a strategy of selecting a set of pseudo-absences from the overall set of assumed absence data points to be used in the model calibration (e.g.McPherson et al. 2004, Guisan et al. 2007).Th e pseudo-absence approach may be a particularly attractive option when the modelling is based on atlases, museum data and databases.Such data sources often do not provide detailed enough information about the recording eff ort in the sites where species has not been detected, and consequently, false absences can be included in the models which decreases the reliability of their predictions (Chefaoui and Lobo 2008).However, models based on only one set of pseudo-absences may be vulnerable to sporadic biases in the selection process (Engler et al. 2004).Developing multiple models based on diff erent sets of pseudoabsences is thus preferable (Th omaes et al. 2008).However, it is poorly known whether increasing the number of predictor variables used in the modelling increases the variability among projections from the models based on diff erent pseudo-absence data sets.
Modelling studies with freshwater invasive species, especially invasive aquatic plant species, are more sparse than studies using terrestrial species (Dominguez-Dominguez et al. 2006; but see Peterson et al. 2003), although invaders can have dramatic eff ects on freshwater communities (Kozhova andIzhboldina 1993, Simon andTownsend 2003).In this study we investigate the potentiality of bioclimatic envelope models to provide useful predictions for an invasive aquatic plant species, the Canadian waterweed Elodea canadensis Michx., in Europe, and to predict recent changes in its distribution range in northern Europe, in Finland, with respect to the climate.We specifi cally investigate the importance of the selection of climatic predictors and the delimitation of time slice over which climate data is averaged for the model performance.Modelling of terrestrial plant species has often focused on similar types of key variables, such as the mean temperature of the coldest month, growing degree day sum above a 5°C threshold, and the ratio of actual to potential evaporation (Huntley et al. 1995, Sykes et al. 1996).We study here how useful these three 'baseline' climate variables are in modelling the distribution of Elodea canadensis in comparison to an 'extended' set of climate variables including four other climate parameters potentially better refl ecting some critical aspects of the biology of Elodea.Th e main questions of this study are: (1) how successful are bioclimatic envelope models in predicting the distribution area and recent northward spread of Elodea canadensis in Europe?; (2) are there diff erences in the performance of models based on medium-term vs. long-term climate data, and models including three baseline climate variables vs. an extended set of climate variables?, (3) which climate variables are the best predictors of the distribution of Elodea canadensis?, and (4) does the model performance vary between the diff erent models based on diff erent sets of pseudo-absences, and is this variation more notable between models with an extended set of climate variables than between models with the three climate variables?

Th e study species
Th e study species, the Canadian waterweed Elodea canadensis Michaux, is a member of the family Hydrocharitaceae (Simpson 1984, Cook andUrmi-König 1985).Elodea canadensis is a submerged aquatic plant which is native only in the New World.Th e species occurs in inland lakes, ponds and slowly moving waters in rivers, streams and canals (Cook and Urmi-König 1985).It prefers cool water temperatures (tolerance ranging between 10-25°C), and calcium-rich eutrophic water (pH 6.5-10).In northern Europe it grows mainly in relatively fi rm, nutrient-rich sediments with a high mineral content (Weidema 2000).Elodea canadensis is able to form dense single-species stands and become a dominant species in water 0.1-1.5 m deep (Cook andUrmi-König 1985, Kozhova andIzhboldina 1993).It tolerates relatively high levels of light, but not frost.Th e species is able to recommence growth as soon as the temperature rises in spring.It fragments easily and disperses eff ectively by vegetative means, as the fragments have a high survival rate (Cook andUrmi-König 1985, Barrat-Segretain et al. 2002).
In optimal growing conditions Elodea canadensis can be a troublesome species.Dense stands of Elodea reduce temperature and oxygen concentrations of water, and decomposing stands cause internal nutrient loading (Cook andUrmi-König 1985, Weidema 2000).In northern Europe, mass occurrences of the species may alter the whole lake ecosystem and turn the water hyper-eutrophic and muddy.In Norway, such mass occurrences have very probably caused disappearances of red listed plant species populations that inhabited certain lakes and ponds before the invasion of Elodea canadensis (Weidema 2000, pp. 98-99).Interestingly, after the establishment of the species in a given waterbody a cyclical trend has often occurred.Within the fi rst 3-4 years, the species attains a pest position during which it can eff ectively exclude other macrophytes.However, after the next 3 to 10 years the populations often decline steadily, and thereafter the species remains as a small relict population, or may disappear for some time (Simpson 1984).
Several diff erent dispersal mechanisms have been suggested for Elodea canadensis, including deliberate translocations in (botanical) gardens, aquarium trade, and fragments carried passively over with timber material or small recreational boats (Simpson 1984, Cook and Urmi-König 1985, Weidema 2000, Pienimäki and Leppäkoski 2004).In addition, the long-lasting fragments of the species disperse eff ectively via watercourses and may also be transported by waterfowl from one lake to another.Remarkably, only female plants of Elodea canadensis occur in northern Europe, meaning that there it is dispersed only by vegetative means, i.e. mainly via fragments that become rooted (Weidema 2000, p. 98).

Distribution data and range shifts
Elodea canadensis is (for most parts) native and widespread in temperate North America, the core distribution area extending in the north to ca. 55°N in Canada and southwards to about 35°N in Alabama, USA.Th e main occurrences of the species concentrate around the Great Lakes and the St. Lawrence Valley (Cook and Urmi-König 1985).Th e distribution of Elodea canadensis in North America was extracted from three sources: (i) the map published by Cook and Urmi-König (1985), (ii) Flora of North America, Vol.22, Hydrocharitaceae (Committee 1993+; accessed via http:// www.fna.org/FNA/), and (iii) the species distribution data base governed by USDA (United States Department of Agriculture; http://plants.usda.gov/).Th e presence records from these three sources were agglomerated and re-sampled into a lattice system using grid cells 0.5° × 0.5° in size, and a geographical window ranging from 20°N, 140°W to 70°N, 52°W.However, as the species occurs predominantly in inland water bodies, only mainland areas in North America and parts of Mexico from this window were included in the actual modelling (Fig 1a), resulting in a set of 9701 grid cells from which 2015 cells had the species.
In Europe, Elodea canadensis was introduced fi rst to Northern Ireland in 1836, then in the 1840s to Scotland and England, and from 1850 onwards it spread rapidly over the British Isles (Simpson 1984, Cook andUrmi-König 1985).In 1850-1860, the species was introduced to Belgium, Germany and the Netherlands, from where it spread rapidly to several other central European countries.In the Nordic Countries, except Norway, the species was fi rst recorded in the late 19 th century.Th e distribution data for Elodea canadensis in Europe were taken from Hultén and Fries (1986), and digitized using a lattice system with cells of 0.5° × 0.5° in size.Th e European window used in this study ranged from 34.5°N, 10.5°W to 71.5°N, 45.0°E.Grid cells occurring in the sea areas were excluded from the data set, and 5083 grid cells were selected in the fi nal European data set, including 1881 cells with known occurrences (Fig. 1b).
In Finland, Elodea canadensis was fi rst planted in the Botanical Garden in Helsinki and other corresponding places but its spreading in Finland became rapid and aggressive only in the 20 th century (Weidema 2000).By 1920, the species was recorded from several locations in southern Finland (Hintikka 1917).Since then, it has continued to expand its distribution range and has recently been recorded from relatively northern water bodies (Fig. 1c).Th e distribution data of Elodea canadensis in Finland was derived from the national atlas data base 'Kastikka' for vascular plants (Lampinen and Lahti 2007; http://www.luomus.fi/kasviatlas).Th e known presence points of the species were recorded using a uni- form grid system with grid cells of 10 × 10 km in size (n = 3544) (Fig. 1c).Th ese records were assigned into two temporally delimited data sets: records made in 1960-1984 and in 1985-2006.Based on the fl oristic resurveys of known occurrences, we made an assumption that all the 10-km grid cells that had occurrences of the species in the earlier surveys still had the species in the later time periods.Th us all the records made in 1960-1984 were also considered as valid positive records in 1985-2006, and records made before 1960 were included both in the 1960-1984 and the 1985-2006 species data.We acknowledge here that this assumption might be unrealistic for many short-lived species.However, for the occurrences of Elodea canadensis it is reasonable.Th is is because the species is able to develop long-lasting populations, regenerate vegetative and spread eff ectively within a particular waterbody (Cook andUrmi-König 1985, Kozhova andIzhboldina 1993).Th e data from the national atlas data base 'Kastikka' for vascular plants, as well as the empirical lake monitoring data collected by one of the authors (HT), suggest that the species is able to persist in the same regions or even the same lakes in Finland for at least 50-60 years.

Climate data
Mean monthly precipitation and temperature values on a grid with 0.5° × 0.5° spatial resolution for North America and Europe matching the species data were extracted from the Climatic Research Unit (CRU) TS 2.0 dataset (New et al. 2002, Mitchell et al. 2003), and averaged over two time periods.Th e two time slices in North America were 1901-1990('long-term' climate data) and 1961-1990('medium-term' climate data), and in Europe 1901-1980and 1951-1980, delimited , delimited to match in both continents with the probably latest recording years in the species data.Climate data for the years 1961-2006 on a 10 × 10 km grid covering the whole Finland was provided by the Finnish Meteorological Institute (Venäläinen et al. 2005) and averaged over two time slices corresponding with to those of the species data, 1961-1984 and 1985-2006 (interpolated values for Finland were not available before 1961).
For each of the three geographical areas and all the diff erent time slices, we calculated two 'competing' sets of climate predictor variables.Th e fi rst data set consisted of three 'baseline' climate variables that are considered to be among the most important broad-scale determinants of the ranges of terrestrial plants: (i) mean temperature of the coldest month (MTCO), growing degree days above 5°C (GDD5) and water balance (WB) (see Beerling et al. 1995, Huntley et al. 1995, Sykes et al. 1996).GDD5 were derived by estimating daily values from monthly mean temperatures using a sine curve interpolation (Brooks 1943).Th e water balance was calculated as the annual sum of the monthly diff erences between precipitation and potential evapotranspiration following Skov and Svenning (2004).Th e formulas applied were the following: (1) where, P i = mean precipitation in month i where, T i = mean temperature in month i In the second case, we complemented the three baseline variables with four additional variables in order to investigate whether the extended set of climate variables would provide more accurate projections of the climatically suitable areas for the species.Th e four additional variables aimed to refl ect some critical stage in the life cycle of Elodea canadensis, including: (i) mean temperature in spring (Temp MAM ; March, April, May), (ii) mean July temperature (Temp J ), (iii) water defi cit in (late) summer ('Defi _sum'; July, August, September), and annual water defi cit ('Defi _ann').Monthly water defi cit values were calculated following Ohlemüller et al. (2006).Th e formula for measuring water defi cit was almost the same as that used to calculate the water balance (Equation 1), the diff erence being that only those values and months are taken into account where PET i exceeds the precipitation (P i ), otherwise P i -PET i is let being 0. Th ese monthly values were summed for July -September and for the whole year.
Th e fi rst reasoning for including these variables was that mean temperatures in spring can be an important determinant for the distribution of Elodea canadensis.Th is is because the species is able to regenerate actively soon after the temperatures increase (Barrat-Segretain et al. 2002).Second, one factor potentially governing the southern range margin of the species is the water temperature during the warmest part of the growing season.In this study we used the July temperature and the water defi cit in late summer as surrogates for direct measurements of the temperature in inland water bodies.Earlier studies have found especially the July air temperature to be a good predictor of maximum surface-water temperatures (Mohseni et al. 2003, Sharma et al. 2007).Water defi cit in late summer summarises the interactions between temperature and precipitation and thus also has the potentiality to indicate landscapes where the water levels in many lakes can become low, and consequently growing conditions can become more readily overly warm for Elodea canadensis.Annual water defi ciency provides an additional indication of the areas which may face an accumulative water defi cit and heating eff ect and thus show high maximum surface-water temperatures.

Statistical analysis
We used generalized additive models (GAMs) in the bioclimatic envelope modelling of Elodea canadensis.Generalized additive models are fl exible data-driven non-parametric extensions of generalized linear models (Hastie and Tibshirani 1990) that allow both linear and complex additive response curves to be fi tted (Wood and Augustin 2002).All the GAM models were developed using the GRASP (Lehmann et al. 2003) user interface in S-Plus (Version 6.1 for Windows, Insightful Corp.).
Th e modelling process included several separate steps.In the very fi rst step, following Beaumont et al. (2009), ten random selections of 2015 pseudo-absence grid cells were taken in North America from the 7686 grid cells with no records of Elodea.Th e 2015 grid cells with known presences were added into each of the ten random draws, and thus all the 10 combined random sets had the recommendable prevalence of 50% (McPherson et al. 2004, Meynard andQuinn 2007).Next, all the random sets were calibrated four times, i.e. using the species data and the four diff erent climate data sets.In total, 40 diff erent GAMs were developed, by applying the 10 random data sets separately into four main types of GAM: (1) medium-term  climate data including 3 baseline variables, (2) long-term  climate data including 3 baseline variables, (3) medium-term climate data including an extended set of 7 variables, and (4) long-term climate data including an extended set of 7 variables.
All the GAMs were built using a stepwise procedure to select relevant explanatory variables and the level of complexity of the response shapes.A starting model including all continuous predictors smoothed with 3 degrees of freedom was fi tted fi rst.Following Bio et al. (2002), the variable dropping or conversion to linear form was tested using Bayesian information criterion (BIC) (Johnston and Omland 2004), which is more selective than the widely used Akaike's information criterion (AIC).All the predictor variables that were selected in the fi nal model were required to make a model contribution (i.e.contribution of a given predictor within the selected models, as measured by GRASP; see Lehmann et al. 2003) of 5% or more.Moreover, from the pairs of highly (>0.90) correlated variables the one with lower model contribution was excluded from the model.Because the response variables represented binary data (presence or absence of the species), a binomial distribution of error via a logistic link function was applied (Lehmann et al. 2003).
Th e performance of the 40 GAMs in predicting the distribution of Elodea canadensis in North America was evaluated by four measures: (i) BIC (smaller values are indicative of a better fi t to the data) (Venables and Ripley 2002), (ii) the amount of deviance explained (D²) (i.e. the ratio of the explained deviance to the total deviance), (iii) the resubstitution method (or 'simple validation', see Lehmann et al. 2003) based on a plot of observed response values against the values predicted by the model, and the subsequent area under the curve (AUC) of a receiver operating characteristic (ROC) plot (Fielding and Bell 1997), and (iv) four-fold cross-validation, carried out with four random subsets of the entire dataset.In the four-fold cross-validation, each randomly selected subset was dropped from the model, the model was recalculated and predictions were made for the omitted data points.Combination of the predictions from the diff erent subsets was then plotted against the observed data (Lehmann et al. 2003), and model performance was measured using the AUC of the ROC plot.Th e following interpretation of AUC-values was used (Swets 1988): AUC>0.9:excellent agreement between observed and predicted distribution; 0.8<AUC<0.9:good model accuracy; 0.7<AUC<0.8:fair; 0.6<AUC<0.7:poor; AUC<0.6:fail.Diff erences between the four main types of GAMs with respect to the four model performance measures were analysed using a paired t-test (Quinn and Keough 2002).
In the fi nal part of analysis of the North American data, probability values were generated for the occurrence of Elodea canadensis in all the 9701 grid cells by fi tting the developed 40 models to this full data set.Th e geographical patterns and variability of the probability values between the four main types of GAMs were visually investigated, both by comparing the mean probability of occurrence values averaged for each grid cell over the 10 random GAMs and their standard deviation, and by investigating the probabilities from the individual random GAMs.
In the second main step of the modelling, the 40 random GAMs calibrated using the North American data were fi tted to the European data sets.Transferring of the models was done between the corresponding pairs of climate data sets, i.e. the 10 random GAMs based on the 1901-1990 climate data set and the three climate variables (MTCO, GDD5, WB) from North America were projected to the European climate data set averaged over 1901-1980 and including the same three variables, and so forth.Th e probability values for the occurrence of Elodea canadensis derived from the transferred models were compared with the distribution records extracted from Hultén and Fries (1986).As some parts of Europe were probably undersampled, we made the assumption that absence data was not available here (cf.Th uiller et al. 2005).
Th e accuracies of the transferred models were tested separately for each of the four main model types in Europe.Using a chi-square test, we compared the number of known presences of Elodea situated in areas predicted to be climatically suitable for the species by <80% (<8 models out of 10; the four main GAM types were tested separately) of the models versus the number of known presences in areas predicted suitable by >80% of the models (cf.Herborg et al. 2007).Prior to the chi-square tests, the probabilities generated by the GAMs were transformed into presence and absence values using a cut-off level defi ned by the prevalence of species in the model calibration data (here 0.50) (see McPherson et al. 2004, Liu et al. 2005).In addition to chi-square tests, the mean probability values in the 1881 grid cells with known occurrences of Elodea canadensis were calculated separately for the four main types of GAMs and their diff erences were compared.Finally, the geographical patterns and variability of the probability values in the full European data set with 5083 grid cells were visually investigated to reveal potential diff erences between the projections from the four main types of GAMs.
In the third main step of modelling, the 40 GAMs calibrated using North American data were fi tted to the Finnish climate sets, both for the time periods of 1961-1984 and 1985-2006 and using the two types of climate predictor sets.Th e performance of the transferred GAMs with the Finnish data was evaluated as described for the whole European data sets.

Models for North America
Th e amount of the explained deviance (D 2 ) in the 40 random GAMs varied between 0.441 and 0.531, being on average highest in the models based on medium-term climate data and the extended set of 7 climate variables (Table 1).With regard to AUC from the resubstitution validation and AUC from the cross-validation, all the 40 GAMs showed an excellent model performance (Table 1).On average, medium-term extended models showed the highest AUC values but the diff erence from the long-term extended models was marginal.In fact, there were no statistically signifi cant diff erences among these two main model types according to any of the four model performance criteria.Th e medi-  standard deviation (and minimum -maximum) in the four accuracy criteria were based on 10 individual random GAMs that were built using diff erent selections of pseudo-absences.Diff erences between the 'medium-term baseline' models vs. 'long-term baseline' models (t 1 ), 'medium-term baseline' models vs. 'medium-term extended' models (t 2 ), 'long-term baseline' models vs. 'long-term extended' models (t 3 ) and 'medium-term extended' models vs. 'long-term extended' models (t 4 ) were tested with paired t-tests.um-term and long-term baseline models diff ered signifi cantly only with regard to their BIC values.However, the medium-term extended models performed signifi cantly better on the basis of all four criteria than the medium-term baseline models, and similarly, the long-term extended models out-competed the long-term baseline models (Table 1).Both in the medium-term baseline and long-term baseline GAMs, the three climate variables (MTCO, GDD5, WB) were selected in all models, and in each model GDD5 showed the highest model contribution.However, the medium-term and longterm extended GAMs were more variable in terms of the selected climate variables (Table 2).GDD5 and Defi _ann were selected in all the 20 extended models, followed closely by WB and Defi _sum (18 extended models).In the extended models, GDD5 and Defi _sum appeared as the two most signifi cant predictors of the distribution of Elodea canadensis, showing the highest model contributions (Table 2).

Main type of GAM
Visual examination of the mean probabilities provided by the four main types of GAMs showed that the projections from the two baseline models diff ered very little, and those from the two extended models were also very similar to each other (Fig. 2).Extended models diff ered slightly from baseline models, for example, in that generally they did not predict suitable areas for the species in Mexico, whereas the baseline models did (Fig 2).Despite their high performance, all the four types of main models failed to predict part of the northernmost known occurrences of the species correctly.However, they agreed in suggesting that Elodea canadensis has not yet spread into all the climatically suitable areas (with mean probability value ≥ 0.50) in North America.
Variability (standard deviation) in the per-grid-cell probability values between the random GAMs indicated that the projections from the extended models vary more than projections from the baseline models.Th e standard deviation of the probability values in the medium-term baseline models ranged from 0.005 to 0.048 (Fig. 3a), in the mediumterm extended models from 0.015 to 0.251 (Fig. 3b), and in the long-term baseline and long-term extended models from 0.006 to 0.048 and from 0.011 to 0.181, respectively.
Table 2. Contributions of climate variables in the 'extended' models for Elodea canadensis in North America.(a) Th e number of times each climate predictor variable was selected in the 20 extended random GAMs based on medium-term  or long-term  time slices and an 'extended' set of seven climate variables, and (b) the number of times a given variable showed the highest model contribution in the models.Th e models were built separately 10 times both for medium-term climate data and long-term climate data.Consequently, the projections between the individual random-set GAMs based on extended climate data diff ered to some extent, particularly in the geographically marginal areas, for example between random-set 2 (Fig. 3c) and random-set 5 (Fig. 3d).

Models for Europe
All the four main types of models developed for Elodea canadensis in North America predicted the known distribution in Europe very well.In the best case, the mediumterm baseline models, only 2.7% of the known occurrences (51 out of 1881 occupied 0.7 -0.9 0.7 -0.9 0.9 -1.0 0.9 -1.0 grid cells; Table 3) were in areas predicted to be climatically suitable by < 80% of the random-set GAMs, whereas 97.3% of the occurrences of the species were in grid cells predicted as suitable by ≥ 80% of the random GAMs (df = 1, chi-square = 1682.5,p<0.001).However, the diff erences between model types were marginal, as the other three main model types also showed a signifi cantly high predictive ability (Table 3).Th e mean probabilities in the European grid cells with known occurrences were highest in the long-term extended GAMs and lowest in the medium-term baseline GAMs (Table 3).Th e two statistically signifi cant diff erences were that medium-term baseline GAMs had signifi cantly lower mean probabilities in the grid cells with occurrences than the medium-term extended GAMs (paired t-test, df = 1880, t = -9.29,p<0.001) and the long-term baseline GAMs (df = 1880, t = -30.80,p<0.001).Th is discrepancy between the results of chi-square tests and mean probabilities in the occupied grid cells was caused by the higher variability in the performance of (separate) extended GAMs (Table 3).For example, the number of grid cells with known occurrences in Europe but predicted not to have the species varied in the separate medium-term extended GAMs from 46 to 85, but in the medium-term baseline GAMs from 49 to 53.
Mean occurrence probabilities for Elodea canadensis in Europe from the 10 medium-term baseline GAMs and 10 long-term baseline GAMs showed a high spatial agreement (Fig. 4a-b).By contrast, long-term extended GAMs provided on average higher probability values than the medium-term extended GAMs (Fig. 4c-d).All the four main types of models identifi ed the favourable northern range margin for the species very well (using the probability of 0.50 as a cut-off level for distinguishing which grid cells are climatically suitable for the species and which are not), and at maximum only 11 records occurred in areas predicted to be climatically unsuitable by the four model types.Th e models also agreed in predicting that the climatically suitable areas for the species extend into much wider areas in the Mediterranean countries and areas next to the Black Sea than indicated by the range map of Hultén and Fries (1986) (Fig. 4).
Th e probabilities generated for all the 5083 grid cells in Europe showed much more variation among the individual extended models than the baseline models.For example, the standard deviation of the per-grid-cell probabilities in the medium-term extended models ranged from 0.005 to 0.351, whereas in the corresponding mediumterm baseline GAMs the range was from 0.002 to 0.057 (Fig. 5a-b).Th e areas where the probabilities varied maximally were geographically and climatically marginal areas in the European study window.Consequently, the projections from solitary GAMs based on extended climate data diff ered occasionally considerably in these areas (Fig. 5c-d).

Models for Finland
All the four main types of models showed a high predictive ability (chi-square = 264.13-272.14, p<0.001:Table 4) for the climatically suitable areas for Elodea canadensis in Finland on the basis of the climate and species data from 1961-1984.In the two extended models, 99.6% (275 out of 276) of the grid cells with occurrences of Elodea canadensis were predicted to have the species by ≥ 80% of the random GAMs, and the two baseline models performed almost equally well (Table 4).Th e mean probabilities derived from the two baseline types of models were very similar to each other (Fig. 6ab), but the projections derived from the extended models diff ered slightly in some areas (Fig. 6c-d).Th e area predicted as climatically suitable by the extended models extended ca.100-200 km further north than in the baseline models.However, there was more variation in the probability values derived from extended models than in those from the baseline models.Moreover, projections from the individual extended GAMs diff ered occasionally considerably (Fig. 6e-h), as also did the number of grid cells with known occurrences but predicted not to have the species by the individual models (Table 4).
Transferring the models into the climate and species data from 1984-2006 indicated that the four types of models also have a high predictive ability in predicting the most recent distribution of Elodea canadensis in Finland p<0.001: Table 5).Th e majority of the new records for Elodea canadensis in Finland discovered in  were located in the areas projected as climatically suitable, but 6 or 7 new records occurred in the 10-km grid cells situated northwards from the area predicted as climatically Mean probability 0.0 -0.1 0.1 -0.3 0.3 -0.5 0.5 -0.7 0.7 -0.9 0.9 -1.0 suitable (Fig. 7).Similarly as with the 1961-1984 data, the area predicted as climatically suitable extended further north in the extended models than in the baseline models, the extended models showed higher variation in their probability values, and projections from the solitary extended models diff ered occasionally considerably (Fig. 7, Table 5).0.7 -0.9 0.7 -0.9 0.9 -1.0 0.9 -1.0

Discussion
According to Rahel and Olden (2008) there are few examples of geographic range shifts consistent with recent changes in climate in freshwater organisms, in contrast to several examples in terrestrial and marine species.Sporadic data includes observations of the recent invasion of Ranunculus trichophyllus in high-elevation lakes in the Himalayas, considered as a signal of a warming climate (Lacoul and Freedman 2006), poleward range shifts in four freshwater taxa in UK during the recent period of climate warming (Hickling et al. 2006), and some solitary observations of new occurrences at high latitudes (for a review see Heino et al. 2009).Th is study contributes to this accumulating evidence and shows that Elodea canadensis, an introduced freshwater plant species, has recently spread northwards in northernmost Europe, in Finland, in concert with the recent climatic changes and in agreement with the predictions from bioclimatic envelope models.
A number of earlier studies have reported the ability of ecological niche models and bioclimatic envelope models to predict the geographic occurrences of invasive freshwater species in their native and introduced range, mainly for fi sh species (Iguchi et al. 2004, Chen et al. 2007) and more rarely for aquatic plants (Peterson 2003a, Peterson et al. 2003).However, some recent studies have reported notable mismatches between the model projections developed for the invaded areas and the observed occurrences therein (Broennimann et al. 2007, Fitzpatrick et al. 2007).Such discrepancies may refl ect the potentiality of invasive species to occupy climatically distinct niche spaces in the invaded areas (Broennimann et al. 2007), a phenomenon which would decrease the usefulness of niche -based models to assess the potential spread of introduced species.However, such mismatches did not occur in our results.Th us bioclimatic envelope models appear to have the potentiality to produce useful fi rst-fi lter predictions for the distribution of Elodea canadensis, and to identify the broad-scale geographical limits to the species' spread and areas most vulnerable to invasions (cf.Peterson 2003a, Peterson et al. 2003, Herborg et al. 2007).
All the four main types of models applied in this study provided accurate and statistically highly signifi cant predictions of the occurrences of Elodea canadensis both in the native and invaded range.In Europe, the most notable mismatches between the model projections and the distribution map of Elodea canadensis by Hultén and Fries (1986) occurred in the Alps and in southernmost areas in Europe and adjacent areas around the Black Sea.All the four main model types predicted that there are no climatically suitable areas for the species in the Alps, whereas Hultén and Fries (1986) reported that the species occurs throughout this area.Th is discrepancy may be based on possible errors in the expert-drawn delineation of historical range of Elodea canadensis in areas with few known occurrence points (Habib et al. 2003, Graham et al. 2008), in other words, exaggerating the extent of occurrences in the Alps.Alternatively, the Table 5. Performance of the four main types of models in Finland with data from 1985 -2007.Th e number of the grid cells with known occurrences of Elodea canadensis (a) predicted to have the species by < 80% of the random GAMs, (b) predicted to have the species by ≥ 80% of the random GAMs, (c) range (min -max) in (a) among the 10 individual random GAMs, (d) statistics from the chi-square test for (a) vs. (b), and (e) mean probability of occurrences averaged across the 375 grid cells with known occurrences.species may have been recorded to occur in the Alps in lakes situated in microclimatically sheltered valleys and at the base of the mountains, at altitudes over 750 meters a.s.l.(Unni 1977, Dubois et al. 1988).Bioclimatic envelope models generally use the mean values of climate variables averaged over the whole grid cell, and thus in topographically heterogenous landscapes they may fail to detect the existence of sheltered, climatically suitable sites for the appearance of lowland species (cf.Peterson 2003b, Luoto andHeikkinen 2008).

Main model type
Our models suggested that the climatically suitable area for Elodea canadensis covers much larger areas in southern Europe than those where the species was mapped by Hultén and Fries (1986).Th is disagreement may be a result of the poor ability of our models to detect the southern range limit of the species, leading to consequent overpredictions in the model projections.However, more probably the species had not yet spread to these climatically suitable areas before the map of Hultén and Fries was published, as indicated by the recent observations of the species from Turkey (Akbulut et al. 2001) and northern Africa (Vilá et al. 1999).Th us although Elodea canadensis was introduced in Europe in the 1830s and has spread eff ectively since then, it apparently still had not reached all climatically suitable areas in Europe and adjacent areas by the 1980s.Th is suggests that the delimitation of the full climatic limits for the species can be subject to biases if made only on the basis of the invaded range.In a similar vein, Welk (2004) argued that a reliable prediction of the invaded range of Lythrym salicaria in North America was only possible using a large cumulative data set compiled during ca.150 years of monitoring of the species range changes in North America.Th is calls for special caution in ecological niche modelling of recently introduced species based on invaded range only.
Interestingly, in Finland about half a dozen new observations of Elodea canadensis discovered in 1985-2006 occurred up to a maximum of 300 km north from the areas predicted as climatically suitable.Th ese new records suggest that either the species has been able to accelerate its spread towards northernmost Europe during recent years more than simulated by the bioclimatic models, or that a series of unusually warm years during the last ca.15 years in Finland (Tuomenvirta 2004, Pöyry et al. 2009) and elsewhere in Europe (Della-Marta et al. 2007) has enabled Elodea canadensis to make major dispersal jumps.Indeed, the northernmost records have been made quite recently, one in 1994 and the other in 2001, and thus these observations probably refl ect the accumulating eff ect of the recent warm years.
Th ree factors potentially aff ecting the performance of the bioclimatic envelope models were examined here: temporal delimitation of the climate data, selection of climate variables, and interactions between multiple sets of pseudo-absences and increasing the number of predictor variables.Several studies have used climate data averaged over a 30 year period (e.g.Huntley et al. 1995, Sykes et al. 1996, Hartley et al. 2006), although the species data might have been collected over a much longer time slice.We used climate predictor variables that were averaged both over a 30 year period and over a 80-(Europe) or 90-(North America) year period.However, the use of longer-term climate data (which better covered the time slice when the species occurrence records were made) did not signifi cantly improve the model accuracy or aff ect the geographical predictions of suitable areas.Th us climate data averaged over a 30 year time slice also appear to off er in our case useful predictors for species data collected over a longer time slice.However, it is not possible to assess the generality of this fi nding, i.e. whether it is a special case or could be applied to other corresponding bioclimatic modelling studies as well.Similar results are likely to emerge in studies where the climate data averaged over a shorter time period do not deviate much from the data averaged over a longer time period.If the two climate data sets deviate notably, diff erences in the model outputs may occur especially when the models are fi tted to the climate scenario data to assess potential future species distributions.
Additional factors which might critically aff ect the model performance are the time slice and the climate conditions under which the species data in the invaded range have been collected.In particular, if several occurrences have been made in climatically extreme years that have enabled notable dispersal jumps for the species, models based on climate data sets averaged over several decades can fail to predict correctly such abrupt changes in distribution range (Baker et al. 2000, Heikkinen et al. 2006b).Th us in projecting the models to the invaded range, it should be noted that changes in the range margins may be related to climatically highly optimal short-term time periods and associated dispersal jumps of the species (cf.Mitikka et al. 2008), as also suggested by our results.
Insuffi cient attention has been paid to the potential impacts of selection of climatic variables (Beaumont et al. 2005, Heikkinen et al. 2006b, Beaumont et al. 2007), although the observed discrepancies between model predictions and invaded ranges may be caused by the choice of climatic predictors or climate data sets used in the modelling (Peterson and Nakazawa 2008).Here, the extended models including seven climate variables showed signifi cantly better model performance in North America (and in Finland) than the baseline models with three climate variables.Th e diff erences in spatial projections of the climatically suitable areas between the baseline and extended models were slight in North America, but showed a tendency to become more noticeable when the models were transferred to Europe, particularly to Finland (cf.Th uiller 2003).In general, the success of the attempts to transfer species distribution models from one continent or region to another has varied between the studies.Some studies have reported a high success for the projections of the transferred models (e.g.Peterson 2003a, Iguchi et al. 2004, Chen et al. 2007), while some other studies have shown notable diff erences between the model predictions and observed species distributions (e.g.Fitzpatrick et al. 2007, Broennimann et al. 2007, Beaumont et al. 2009).Recent studies suggest that habitat models based on essential functional resources for the studied species could be transferred better in space than models that use indirect environmental variables, such as biotope types (Vanreusel et al. 2007), and that the transferability may be reduced due to the peculiarities of the study areas, such as diff erences in the ranges of environmental factors and the varied impact of land-use history between the model calibration and model evaluation areas (Randin et al. 2006).
With regard to individual climate variables, GDD5 was among the two most important predictors of the distribution of Elodea canadensis in all models.GDD5 has been successfully employed in broad-scale modelling of the distribution of terrestrial plant species (Beerling et al. 1995, Huntley et al. 1995, Sykes et al. 1996), and it also appears to provide a useful predictor of the range limits and climatically suitable areas for invasive aquatic plants as well.In North America, Welk (2004) concluded that Lythrum salicaria, an invasive wetland species, is sensitive especially to variation in length of the growing season.Growing degree days, which is an indicator for the length and thermal intensity of the growing season, can thus be a highly useful predictor in delimiting the northern range boundaries for a wide range of plant species from diff erent habitats.By contrast, mean temperature of the coldest month (MTCO) was in most cases replaced in the extended models by one or more of the four additional variables.Th e lower explanatory power of MTCO for aquatic plants in comparison to terrestrial species is probably related to the fact that water bodies tend to mitigate the eff ects of extreme minimum temperatures, and moreover, ice cover isolates the overwintering submerged aquatic plants from the eff ects of extreme cold periods.Annual water balance (WB) was selected almost equally as often as the two water defi cit variables into the extended models, but made a lower model contribution than the two water defi cit variables.
Contrary to our expectations, July temperature did not appear as a signifi cant predictor for Elodea canadensis.It is possible that the two water defi cient variables that combine the impacts of temperature and precipitation better refl ect the areas where water temperatures in inland watercourses are exposed to critical levels of warming, whereas the northern range limit for the species is more accurately determined by GDD5 than by July temperature.
Overall, the improvements in model performance observed here between the baseline models and the extended models support the conclusions reached by Beaumont et al. (2005): more consideration should be paid to the selection of variables in order to identify those that have the greatest predictive power, and knowledge on the biology of the modelled species should be used as much as possible during the variable selection.In particular, the use of one baseline set of environmental variables which is readily at hand in multispecies modelling studies (instead of careful species-specifi c selection of variables) may result in suboptimal models being generated for some, or even many, of the species (Heikkinen et al. 2006b).
However, inclusion of more predictor variables in ecological niche models can also cause drawbacks.Most importantly, excessive inclusion of predictors may complicate the interpretation of the importance and eff ect of individual predictor variables (Heikkinen et al. 2004, Hartley et al. 2006), and result in over-fi tting and overly complex models (Hartley et al. 2006).In addition, our results show that increasing the number of candidate predictors increases the uncertainty in model predictions in a hitherto rarely acknowledged way, i.e. via its interaction with the use of pseudo-absences.Th ere are several approaches for generating pseudo-absence points (Pearce and Boyce 2006), including selecting points randomly (McPherson et al. 2004), randomly with caseweighting to reduce the eff ective sample size of pseudo-absences (Guisan et al. 2007), or via environmentally weighted random sampling (Zaniewski et al. 2002).Th is selection of approach can aff ect the outcomes of the models (Engler et al. 2004), but the pros and cons of diff erent approaches remain open to debate (Chefaoui and Lobo 2008).Here, following McPherson et al. (2004), the pseudo-absences were selected randomly.Our results show that increasing the number of predictors may notably increase the variability of the model projections based on diff erent random sets of pseudo-absences, due to the varying combinations of climate variables that were selected in the diff erent extended GAMs.Th is variability between the individual extended models caused increased variation in the per-grid-cell probability values and in the spatial predictions of the suitable areas between the individual models (Fig. 3, 5, 7 and 9).
Th is suggests that in order to lower the risk of choosing an inappropriate set of pseudoabsence points and generating suboptimal models, multiple sets of pseudo-absences should be generated instead of using only one selection (Engler et al. 2004), as well as averages calculated across multiple models to provide consensus predictions (Hartley et al. 2006).Projections from multiple models allow quantifi cation of the uncertainty in model predictions, which in turn assists the making of management decisions with greater certainty (Hartley et al. 2006).In our case, mapping the standard deviation of the per-grid-cell probability values provided a simple way to visualise where the predictions from the individual extended GAMs diff ered most and where they agreed most.
It is obvious that identifi cation of the detailed locations most at risk to the invasions by Elodea canadensis would benefi t from including information on other factors in addition to climate (cf.Rahel and Olden 2008).Potentially useful additional predictors include factors describing the degree of human infl uence (population density, land transformation, presence of infrastructures etc.) (Ficetola et al. 2007), and physical and chemical characteristics of water bodies (cf.Buchan and Padilla 2000).In the case of Elodea canadensis particularly water chemistry might matter.Although the species has a relatively wide tolerance for water pH, it favours calcium-and nutrient-rich eutrophic waters (Weidema 2000).
It is very likely that Elodea canadensis will continue to spread further north in Finland and elsewhere in northernmost Europe.Th is is because the magnitude of the projected climate change is particularly high in northern latitudes (ACIA 2005).Warming climate can reduce the extent of ice cover and cause warmer water temperatures in high latitude water bodies, and thus allow the further expansion of invasive aquatic species such as Elodea (Rahel and Olden 2008).In general, freshwater organisms are less capable of tracking the geographic shifts in climatic optima than terrestrial organisms (Rahel and Olden 2008).However, Elodea canadensis is probably better equipped to pass the four main barriers in the process of species invasion into new areas (see Hellmann et al. 2008) than aquatic species in general: i.e. eff ective passing of (1) Geography-barrier (many dispersal vectors, long-lasting fragments), (2) Abiotic conditions -barrier (survives in invaded areas due to relatively wide tolerance capability), (3) Biotic interactions -barrier (able to compete eff ectively with native macrophytes and become dominant), and (4) Landscape factors -barrier (vegetative fragments spreading via watercourses and passive transportation by human activities and waterfowl) (Goodwin et al. 1999, Barrat-Segretain et al. 2002, Richardson et al. 2007).

Conclusions
Our results suggest that bioclimatic envelope models can provide a useful fi rst-step tool for the identifi cation of areas most at risk to colonization by Elodea canadensis, and possibly also for other similar aquatic invasive species.Such models may help in targeting early preventive or ameliorative measures in a timely manner (Kriticos et al. 2003), planning and prioritizing of control measures (Weber 2001, Roura-Pascual et al. 2004), and inform us as to the potential further spread of the species across the new landscape (Chen et al. 2007).However, increasing attention should be targeted to careful consideration and selection of environmental variables included in the models, generating consensus predictions based on multiple models (especially when employing pseudo-absences), and investigating and quantifying the geographic patterns of the uncertainties in the model predictions.Th ese actions would help in improving the usefulness of bioclimatic envelope models, and ecological niche models in general, in predicting the distributions and range shifts of invasive aquatic species.

Figure 1 .
Figure 1.Distribution of Elodea canadensis in the three study areas.(a) Grid cells in North America with known occurrences (n = 2015, in dark grey) and cells in which the species has not been recorded (n = 7686, in light grey), (b) grid cells in Europe with known occurrences (n = 1881) and cells with no known occurrences (n = 3202), and (c) grid cells in Finland in 1961-1984 (in dark grey) and 1985-2006 (in black) with known occurrences (n = 276 and 375) and cells with no known occurrences (in light grey).For all the 10 data sets used in calibrating the models in North America, 2015 random pseudo-absence points were selected from the 7686 (presumed) absence grid cells.
, (b) the amount of deviance explained (D²), (c) AUC from resubstitution validation, and (d) AUC from four-fold cross-validation.Th e mean values and their

Figure 2 .Figure 3 .
Figure 2. Projected distribution of Elodea canadensis in North America based on four diff erent modelling approaches.Th e maps show the mean probability of occurrence derived from 10 random GAMs based on (a) medium-term climate data including 3 baseline variables, (b) long-term climate data including 3 baseline variables, (c) medium-term climate data including an extended set of 7 variables, and (d) longterm climate data including an extended set of 7 variables.Known occurrence points for Elodea canadensis are shown in (a) with green dots.Th e maps are in the same scale.Probabilities ≥ 0.5 indicate areas were the species is projected to occur.

Figure 4 .
Figure 4. Projected distribution of Elodea canadensis in Europe based on four diff erent modelling approaches.Th e maps show the mean probability of occurrence derived from 10 random GAMs calibrated with species and climate data from North America and transferred into Europe: (a) medium-term baseline models, (b) long-term baseline models, (c) medium-term extended models, and (d) long-term extended models.Known occurrence points are shown in (a) with green dots.Th e maps are in the same scale.

Table 4 .Figure 5 .
Figure 5. Variation in probability values and probabilities of occurrence from two individual models in Europe.Th e per-grid-cell variation shows the standard deviation of probability values for the occurrence of Elodea canadensis derived from the 10 random GAMs based on (a) medium-term baseline climate data, (b) medium-term extended climate data.Probabilities of occurrence based on two individual mediumterm extended models were derived from (c) a model based on pseudo-absence set 2, and (d) a model based on pseudo-absence set 5. Known occurrences are shown in (a) and (b) with green dots.

Figure 6 .
Figure 6.Projected distributions, variation in probability values and probabilities of occurrence from two individual models in Finland.Projected distributions show mean probability of occurrence for Elodea canadensis in Finland, based on 10 random GAMs fi tted to climate data from 1961-1984: (a) medium-term baseline models, (b) long-term baseline models, (c) medium-term extended models, and (d) long-term extended models.Th e standard deviation of per-grid-cell probabilities derived from 10 random GAMs is shown for (e) the medium-term baseline models, and (f) the medium-term extended models.Probabilities of occurrence based on two individual medium-term extended models were derived from (g) a model based on pseudo-absence set 2, and (h) a model based on pseudo-absence set 5. Known occurrence points from < 1985 are shown with green dots.Th e maps are in the same scale in (a) -(d), in (e) and (f ), and in (g) and (h).

Figure 7 .
Figure 7. Projected distributions, variation in probability values and probabilities of occurrence from two individual models in Finland.Projected distributions show mean probability of occurrence for Elodea canadensis in Finland, based on 10 random GAMs fi tted to climate data from 1985-2006: (a) mediumterm baseline models, (b) long-term baseline models, (c) medium-term extended models, and (d) longterm extended models.Th e standard deviation of per-grid-cell probabilities derived from 10 random GAMs is shown for (e) the medium-term baseline models, and (f) the medium-term extended models.Probabilities of occurrence based on two individual medium-term extended models were derived from (g) a model based on pseudo-absence set 2, and (h) a model based on pseudo-absence set 5. Known occurrence points from < 1985 are shown with green dots, and from 1985-2006 with blue dots.

Table 1 .
Modelling accuracy of the four main types of GAMs for Elodea canadensis in North America.Accuracy was measured by

Table 3 .
Performance of the four main types of models for Elodea canadensis in Europe.Th e number of the grid cells with known occurrences of the species (a) predicted to have the species by < 80% of the random GAMs, (b) predicted to have the species by ≥ 80% of the random GAMs, (c) range (min -max) in (a) among the 10 individual random GAMs, (d) statistics from the chi-square test for (a) vs. (b), and (e) mean probability of occurrences averaged across the 1881 grid cells with known occurrences.