Modeling the role of the close-range effect and environmental variables in the occurrence and spread of Phragmites australis in four sites on the Finnish coast of the Gulf of Finland and the Archipelago Sea

Phragmites australis, a native helophyte in coastal areas of the Baltic Sea, has significantly spread on the Finnish coast in the last decades raising ecological questions and social interest and concern due to the important role it plays in the ecosystem dynamics of shallow coastal areas. Despite its important implications on the planning and management of the area, predictive modeling of Phragmites distribution is not well studied. We examined the prevalence and progression of Phragmites in four sites along the Southern Finnish coast in multiple time frames in relation to a number of predictors. We also analyzed patterns of neighborhood effect on the expansion and disappearance of Phragmites in a cellular data model. We developed boosted regression trees models to predict Phragmites occurrences and produce maps of habitat suitability. Various Phragmites spread figures were observed in different areas and time periods, with a minimum annual expansion rate of 1% and a maximum of 8%. The water depth, shore openness, and proximity to river mouths were found influential in Phragmites distribution. The neighborhood configuration partially explained the dynamics of Phragmites colonies. The boosted regression trees method was successfully used to interpolate and extrapolate Phragmites distributions in the study sites highlighting its potential for assessing habitat suitability for Phragmites along the Finnish coast. Our findings are useful for a number of applications. With variables easily available, delineation of areas susceptible for Phragmites colonization allows early management plans to be made. Given the influence of reed beds on the littoral species and ecosystem, these results can be useful for the ecological studies of coastal areas. We provide estimates of habitat suitability and quantification of Phragmites expansion in a form suitable for dynamic modeling, which would be useful for predicting future Phragmites distribution under different scenarios of land cover change and Phragmites spatial configuration.


Introduction
The common reed Phragmites australis is a perennial vascular plant found in wetlands with a nearly worldwide distribution (Haslam 1972;Lambertini et al. 2008). In North America, the common reed is considered a highly problematic cryptic invader because the Eurasian haplotype as a strong competitor is reported to override the native American haplotype (Saltonstall 2002(Saltonstall , 2003 by, for example, a more aggressive shoot initiation from rhizomes and higher salinity tolerance than the native haplotype (Vasquez et al. 2005). In central Europe, on the other hand, the native reed beds have undergone significant deterioration known as the reed dieback syndrome (e.g., Koppitz 1999). This reed decline has been associated with excess eutrophication leading to deterioration of the rhizomes (Ostendorp 1989) and decline of genetic diversity of reed beds (Koppitz et al. 1997). On the coastal areas of the Baltic Sea, Phragmites australis is a native wide-spread helophyte playing an important role in the ecosystem dynamics of shallow coastal areas (Meriste et al. 2012).
In the Baltic Sea, the reed beds, situated at the landwater interface, protect the shoreline from wave-induced bank erosion, mitigate sediment-borne internal nutrient loading, and act as buffers for catchment-borne external loading (Kaitaranta et al. 2013). Phragmites distribution is also a corner stone in coastal ecology, as reed belts sustain high biodiversity by providing nesting areas for birds (Huhta 2009;Meriste et al. 2012) and spawning areas for fish Lappalainen et al. 2008). The role of Phragmites on the functioning of coastal areas is, however, contradictory, as during the last decades, Phragmites has spread along the shore areas of the Baltic Sea and is claimed to also have negative feedbacks on coastal ecosystems due to its rapid spread (Huhta 2009;Pitk€ anen et al. 2013). Phragmites is a strong competitor and once established in an area often outcompetes and shades other plant species decreasing local biodiversity (Munsterhjelm 1997). In the coastal area of the Gulf of Finland (GOF) and the Archipelago Sea, the increase in Phragmites distribution during the last few decades has been associated with multiple changes in human activities (Ojala and Louekari 2002) and has raised the interest and concern of local people (IBAM 2011;Lamp en 2012).
A number of studies have examined the causes of Phragmites intensive expansion in different regions. As a worldwide common factor, human disturbance in coastal areas has been found to facilitate Phragmites dispersal (Burdick and Konisky 2003;Silliman and Bertness 2004;Bart et al. 2006;King et al. 2007;Chambers et al. 2008). There is evidence of pronounced Phragmites prevalence on shorelines adjacent to urbanized (King et al. 2007) and agricultural land (Chambers et al. 2008). Maheu-Giroux and De Blois (2007) presented point pattern analysis of Phragmites expansion in linear wetlands. They found that Phragmites expanded with higher rates in linear anthropogenic habitats compared with natural wetlands. Additionally, Phragmites is a pioneer species, being among the first species to settle on virgin soil after mechanical alterations of land, such as dredging and near-shore building (Pitk€ anen et al. 2013). Along the Baltic coast, the increasing eutrophication due to excess nutrient runoff from land together with decreased grazing pressure has led to the spread of large perennial species such as Phragmites (Jutila 2001;von Numers 2011;Pitk€ anen et al. 2013). In the Finnish Archipelago, the expansion of Phragmites has been rapid in soft and sheltered areas where reed belts have become denser and wider (Pitk€ anen et al. 2013). Phragmites is also witnessed to expand outward in new areas in the archipelago (von Numers 2011). This suggests the establishment of new suitable habitats through organic matter settlement to formerly soil-poor outer archipelago areas. It also reflects the absence of the spread controlling role of grazing (Jutila 2001;von Numers 2011) as annual cutting of reed beds by cattle controlled the vegetative growth and conceivably the probability of seed formation of Phragmites.
Phragmites is known to spread both generatively through seed formation and seedling growth and vegetatively by rhizome growth of clones (Koppitz 1999;Belzile et al. 2010). Seed production may be abundant and occurs in the fall, and seeds can be dispersed by wind during ice cover or through wave transportation during ice-free time (Baldwin et al. 2010), with dispersal distance up to 10 km (F er and Hroudov a 2009). The seeds of Phragmites can float for several days (F er and Hroudov a 2009), and germination time is one year (Baldwin et al. 2010). Sexual dispersal through seed settlement can occur in new suitable growing sites at the shoreline with optimum sediment property and moisture and space free of vegetation. This is known as the settlement phase (Koppitz and K€ uhl 2000) after which the seedlings propagate vegetatively to occupy the free niches, a phase known as the propagation stage. During the last stationary phase, the various genotypes compete for space and the bestadapted clones to the site prevail (Koppitz and K€ uhl 2000). Therefore, the genetic diversity in old reed bed is quite low, and the stands consist of only few best-adapted vegetatively dispersing clones (Koppitz et al. 1997). As seed germination and seedling growth cannot occur in submerged conditions  or under heavy shading and competition for space, usually local close-range spread of Phragmites beds is due to vegetative horizontal growth of rhizomes. Vegetative growth rate can vary from 1 to 4 m yearly (Weisner 1987;Clevering and Van der Toorn 2000). In the coastal areas of Finland, new areas of long-distance colonization can be inhabited by seed dispersal and seedling establishment, or alternatively vegetatively through rhizome bits cut out of reed beds and transported by waves, but close-range colonization and dispersal occur mainly through clonal growth (Koppitz et al. 1997;Mal and Narine 2004;F er and Hroudov a 2009;Kettenring and Mock 2012).
Topographic factors can influence the occurrence of Phragmites. Having a stiff and strong stem, Phragmites is more resistant to wave exposure at shallow water than other helophytes , which partly explains the ability to colonize new sites in the sea area. However, open shorelines prone to heavy surfs are unfavorable habitats for Phragmites von Numers 2011). Additionally, increasing water depth is a strong selective force in limiting reed dispersion because internal aeration pathways suffer as transportation of oxygen to the roots becomes more difficult when the plant grows deeper (Huhta 2009;Engloner and Major 2011). Water depth therefore regulates the seaward expansion (Meriste et al. 2012) as maximum growth depth of Phragmites in sheltered areas is ca. 2 m (Luther 1951;L. Nurminen, pers. obs.). Understanding the reasons behind and mechanisms of the spreading of Phragmites on coastal ecosystems of the Baltic Sea is of timely importance for modeling this phenomenon. Targeted management and planning of the area can greatly benefit from predictive modeling of Phragmites distribution.
Species distribution modeling/models (SDMs) are useful and widely applied tools in environmental conservation and management (Guisan and Zimmermann 2000;Austin 2002). A SDM attempts to spatially predict the occurrence or abundance of a species mostly by relating data on the species distribution with the environmental and topographic characteristics of associated locations (Elith and Leathwick 2009). Various approaches and methods are used for modeling species distributions, and new trends are emerging in SDM (Zimmermann et al. 2010). Novel methods, including machine learning (ML) techniques, are increasingly adopted in SDM and found to improve prediction capabilities (Elith et al. 2006;Hochachka et al. 2007;Elith and Graham 2009). Advances in algorithms and computation power facilitate the use of these methods and allow handling large data, both in the number of instances and predictors. Advancement, although to a lesser extent, has also occurred in different directions such as the use of dynamic models in studies of species distributions (Robinson et al. 2011).
A correlative approach to SDM utilizes data of species occurrences, environmental gradients, and topographic variables to delineate potentially suitable habitats and predict species occurrences in unsampled geographic locations. In spatial analysis, the effect of the geographic vicinity on a location's characteristics is well established (Tobler 1970). Significant parts of spatial processes are explained by the surrounding influence. The realization of this influence in geographic space causes a phenomenon known as autocorrelation. Legendre (1993) defines autocorrelation as "the property of random variables taking values, at pairs of locations a certain distance apart, that are more similar (positive autocorrelation) or less similar (negative autocorrelation) than expected for randomly associated pairs of observations." Autocorrelation can occur in both space (SAC) and time. In ecology, autocorrelation is intrinsic to species distributions by means of dispersal (Wintle and Bardos 2006;Dormann 2007a). In species with close-range vegetative/clonal dispersal such as Phragmites, spatial dependency is more pronounced due to the vegetative expansion with rhizomes. Therefore, it is important for the study of Phragmites dynamics to consider the close-range neighborhood effect together with the influential environmental and topographic variables.
A number of coastal ecosystem studies of the Finnish coasts addressed the prevalence and expansion of Phragmites (e.g., Ojala and Louekari 2002;Ikonen and Hagelberg 2007;Huhta 2009), its role in the ecosystem and interaction with other species (e.g., H€ arm€ a et al. 2008;Lappalainen et al. 2008;Kaitaranta et al. 2013), and the social interest and concern that it raises (IBAM 2011;Lamp en 2012). However, few studies have attempted to map Phragmites occurrences (Luther 1951;Suominen 1998;Pitk€ anen 2006), and yet fewer attempted to model its distribution in the area (von Numers 2011;Pitk€ anen et al. 2013). Suominen (1998) delineated Phragmites colonies for three sites in the Archipelago Sea from aerial photographs which date back to the second half of the last century. Pitk€ anen (2006) used satellite imagery to map reed colonies along the whole Finnish coast of the GOF, the Archipelago Sea, and areas Northeast Estonia. They reported that although Phragmites colonies were successfully mapped in some areas, the overall accuracy of the resultant map has significant error rates that prevent its use in other applications. Pitk€ anen et al. (2013) examined contemporary records of the occurrence of a number of species in comparison with historical data from 1930s and 1940s surveyed by Luther (1951). They observed significant increase in Phragmites occurrences in the contemporary survey records compared with the historical data. von Numers (2011) compared the occurrence of a number of species in historical and contemporary data and used logistic regression to test variables that exert influence on the occurrence and colonization of species. He found significant Phragmites prevalence at nonrocky and sheltered shores, although a shift in Phragmites occurrences toward less sheltered islands was observed.
Despite the contribution of these studies to the effort of understanding the dynamics of Phragmites spread on the Finnish coasts, a number of questions are still to be investigated. There is a need for quantifying endogenous and exogenous factors playing roles in the colonization of shores by Phragmites, as a basis for a predictive SDM. Compared to static mapping, a SDM utilizes input of Phragmites occurrences (provided, e.g., by manual delineation or spectral analysis of aerial photographs or satellite imagery) to build a model capable of predicting distributions of Phragmites in unsampled geographic locations and/or time frames. Moreover, evaluation of various scenarios for the purpose of managing and planning of the coastal ecosystem becomes possible using a SDM. We present here an analysis of Phragmites occurrence and spread in four sites on the Finnish coast of the GOF and the Archipelago Sea. We examine environmental and topographic predictors of Phragmites occurrence and test spatial patterns of its dynamics. We adopt a cellular representation of the phenomenon and consider multiple scales in the analysis. Laying a foundation for a spatiotemporal model of Phragmites distribution, the objectives of this study were as follows: (i) to examine the occurrence of Phragmites in relation to a number of environmental predictors, (ii) to examine and quantify the effect of close-range dispersal on Phragmites expansion, and (iii) to develop a predictive model of Phragmites distribution and produce maps of habitat suitability.

Study area and data
Our study area consisted of four sites located in the Archipelago Sea and the Finnish coast of the GOF (Fig. 1). The area has witnessed significant Phragmites spread both seaward and into clear shores in the last few decades (Huhta 2009;von Numers 2011;Pitk€ anen et al. 2013). Sites located in the Archipelago Sea are near the city of Turku, at Ruissalo, Kramppi, and Redamo islands. The fourth site is in Svartb€ ack (Purola), on the Eastern part of the Finnish coast of the GOF, close to the outlet of River Kymijoki, which is one of the major rivers flowing into the GOF. In addition to data availability, the choice of the study sites took in consideration representation of different zones, such as the inner (Ruissalo), outer (Redamo), and intermediate (Kramppi) Archipelago as well as the Eastern part of the Finnish coast of the GOF (Svartb€ ack). These zones have varying coastal characteristics including shore openness, water quality, and shore development.
Maps of Phragmites distributions in different years for each site (Fig. 2) were provided by the Finnish Environment Institute (SYKE). Maps of Phragmites in the Archipelago sites were delineated by Suominen (1998) from aerial photographs that were taken in spring and early summer (April 24 to June 16). He introduced corrections on some of the delineations after a boat visit to the field in 1997. The smallest reed patches identified were about 25 m 2 in area (Suominen 1998). Svartb€ ack Phragmites maps were delineated by experts in SYKE from aerial photographs taken in July 2003 and August 2006. Bathymetry grids with pixel resolution of 5 m were derived for all sites, using ANU-DEM program (Hutchinson 1988(Hutchinson , 1989 in ArcGIS 10 (ESRI 2011), from elevation and depth contour lines and depth measurement points in the topographic maps available from the National Land Survey of Finland. Grids of relative shore openness with pixel resolution of 10 m were derived from the abstraction of fetch lines, the stretch of water surface over which waves can develop freely (Lundqvist et al. 2006). In addition, grids of the Euclidean distance to the closest river outlet with pixel resolution of 5 m were calculated for each site. River outlets were manually located for all basins that appear in the National Land Survey topographic maps. Finally, we extended coastal land cover classes [given by the second level classes of CORINE map (http://www.eea.europa.eu/publications/COR0-landcover)] offshore so that the shorelines and marine waters with less than 3 m of water depth (the analysis area) are assigned the land cover class of the adjacent land. CORINE land cover maps, with a minimum mapping unit of 25 ha, from years 2000 (for the Archipelago sites) and 2006 (for Svartb€ ack) were provided by SYKE.
Vector maps of Phragmites distributions were converted to binary grids of raster format indicating Phragmites presence and absence. Setting the grid size for conversion took into account the spatial resolution of the predictor grids. As the predictor grids in our case were derived and interpolated at grid sizes of 5 and 10 m, converting maps of Phragmites distributions to smaller grid size would result in bulky files with redundant information. However, the bigger the grid size used to convert vector maps to raster layers, the higher the loss of information on Phragmites distributions because small patches of Phragmites might disappear. In order to minimize the loss of information on Phragmites distribution, we computed the depth index, defined as the average distance from the polygon's interior point to the nearest point on the perimeter (Angel et al. 2010), for all Phragmites patches in each site. A maximum of one patch in each site was with a depth index less than 0.5 m. Therefore, Phragmites distribution maps were converted to raster grids of 2 m cell size, ensuring negligible loss of accuracy of Phragmites distribution. We then used a Latin Hypercube Sampling procedure (LHS) (Minasny and McBratney 2006;Falk et al. 2011) to draw samples of 10,000 and 100,000 instances from each site for different analysis purposes as explained below. LHS procedure samples variables from their multivariate distributions so that the range of each variable is fully covered by maximally stratifying its marginal distribution. In order to ensure representativeness, the samples were maximally stratified for Phragmites occurrence (presence/absence), each predictor and the geographic space (given by x and y coordinates).

Analysis of Phragmites distribution
Phragmites spread into certain locations and its disappearance from others over years is a function of dispersion mechanism and location characteristics. While vegetative growth with rhizomes is said to be the major method by which Phragmites propagates (Bart and Hartman 2003;Gucker 2008), part of Phragmites dynamics is explained by seed germination and seedling growth (Alvarez et al. 2005;McCormick et al. 2010). When suitable conditions exist, reed colonies can establish on clear shores (settlement phase) and start propagating vegetatively (Koppitz and K€ uhl 2000). We analyzed changes in the areal cover of reed colonies between time periods in each site using the logarithmic growth equation given by Wilson and Bossert (1971;Rice et al. 2000). The equation is given as follows: N = N 0 e rt , where N 0 is the area of reed patches at time 0, N is the area of reed patches at time 1, e is the base of the natural logarithm, t is the difference in years between time 1 and time 0, and r is the intrinsic rate of natural increase per year, for which the equation is solved. This allows comparing figures of reed growth in different geographic areas over time because the formula normalizes change for different areas and time periods. In this section, we analyze the occurrence and spread of Phragmites in relation to environmental factors and neighborhood effect.

Phragmites occurrence and suitability factors
Four environmental variables were used to examine the habitat suitability for Phragmites. These variables are motivated by the review of Phragmites ecology presented in the Introduction. The first variable is the distance to the closest river outlet, which is used as a surrogate variable for nutrient content in sediments. Excessive amount of nutrients is washed out to rivers and transported to the land-sea interface. A fraction of river-transported matter is accumulated in the sediments, and further dispersed matter is diluted and mixed with the sea water as the distance offshore grows (Rodrigues et al. 2009), making shorelines and waters close to river outlets suitable for Phragmites spread. The second variable is the land cover given by CORINE maps. The third variable is the water depth, which is included in the predictors because it limits the ability of Phragmites to expand seaward (Huhta 2009;Meriste et al. 2012). Finally, shore openness is included in the predictors as an indication of wave exposure, an essential factor for Phragmites ability to colonize shores von Numers 2011), and for the ecological structure of shoreline communities (Ekebom et al. 2003;Tolvanen and Suominen 2005).
We examined distributions of these variables for reedoccupied and reed-clear calls in the sites using the samples with 100,000 instances. Locations that hosted Phragmites in any year were considered reed-occupied, and those where Phragmites never existed (according to the data at hand) were labeled unoccupied. This allows exploring the occurrence of Phragmites at different ranges of the tested variables in different geographic areas. In order to examine the progression of Phragmites over time in relation to the variables, we created density plots for the reed-occupied cells in each year for every site. We note that the latter analysis included only the static predictors, namely the water depth, the relative openness, and the distance to river mouths; land cover is varying over time, and the data we have are from years 2000 and 2006, which is why it was not included in this analysis.

Phragmites expansion and neighborhood effect
Dispersal is a major cause of intrinsic SAC in ecology (Dormann 2007a). Species distribution is strongly influenced by the ability of propagules to reach suitable habitats. In clonal species such as Phragmites, vegetative growth leads to the occurrence of large clusters of colonies once established in a location. In an aggregative process, the state of the neighborhood is an important determinant of the future state of the location in question. In addition to the endogenous source of autocorrelation (i.e., dispersal), an exogenous component of spatial dependency (Legendre et al. 2002) also exists as most environmental variables are autocorrelated. Therefore, the presence of Phragmites in a location can indicate the suitability of its surrounding (where similar conditions are likely to be found) for Phragmites takeover.
We used Svartb€ ack Phragmites data to analyze the influence of the neighborhood on the future of a location with respect to Phragmites presence/absence. The choice of this site was because of the short time lag (3 years) between the available Phragmites maps, which allows detecting the effect of the neighborhood composition on Phragmites progression, unlike the long time periods (13-20 years) separating maps of Phragmites in the Archipelago sites. We examined the neighborhood effect on multiple scale settings because the representation of phenomena and variables in the analysis environment can greatly influence the results (Higgins et al. 1996;Roddick and Lees 2009). Different sizes and shapes of cells and neighborhood analysis windows can result in confounding conclusions on the autocorrelation of variables. Analysis of the influence of neighbors beyond the first order is advised (Cliff and Ord 1969;cited in Fortin and Dale 2009), and an appropriate setting of the neighborhood window allows capturing the operational range of the process being modeled (White and Engelen 2000). We examined diameters of the maximum inscribed circle (Angel et al. 2010) in patches that emerged or disappeared in the period from 2003 to 2006 in order to determine the appropriate cell size for the analysis. The lower and upper quartiles were 2 and 10 m, based on which the analysis was conducted on Phragmites grids with cell sizes of 3, 5, 7, and 9 m. We also considered various sizes of neighborhood windows, including 3 9 3, 5 9 5, 7 9 7, and 9 9 9.
The approach to exploring the neighborhood effect on Phragmites dynamics is illustrated in Fig. 3 1->0), and cells that were occupied by Phragmites in both time steps (denoted 1->1). Another set of grids are those holding the number of reed-occupied neighbors for each cell in 2003, using different neighborhood windows. Those were, separately, cross-tabulated with the grid holding the state transition producing four two-way tables. Each table was then split based on the state of 2003 (0->0 with 0->1 and 1->0 with 1->1). A picture of the neighborhood effect can thus be depicted; the likelihood of a location to become occupied by Phragmites is given by the proportion of locations with the same neighborhood composition to which Phragmites had expanded, and the likelihood of Phragmites to disappear from a location is given by the proportion of locations with the same neighborhood composition from which Phragmites had disappeared.

Modeling Phragmites distribution
Aiming at a predictive SDM, we adopted the boosted regression trees (BRT) method (De'ath 2007;Elith et al. 2008). Although BRT techniques stem from both statistical and ML approaches (Elith et al. 2008), the dependence on algorithmic learning, the focus on predictive accuracy, and the use of large datasets for learning characterize it as a ML approach (Hochachka et al. 2007;Olden et al. 2008). BRT comprises decision trees for classification and regression and boosting optimization for combining a collection of models (Elith et al. 2008). In a tree-based model, the predictor space is repeatedly divided into areas, using split points that minimize prediction errors. Each area is then assigned to the most probable class. Instead of building a single tree with best prediction, boosting optimizes accuracy (Ridgeway 1999;Sutton 2005) by gradually adding up trees that best reduce the loss in prediction performance. When training a BRT model, the bag fraction (bf), the learning rate (lr), and the tree complexity (tc) parameters should be set. The bf introduces stochasticity into BRT by specifying the proportion of training data to be selected at each step of the model building. The lr determines the contribution of each new added tree to the model deviance reduction, and the tc determines whether predictor interactions are to be fitted by defining the number of nodes in each tree. Although a slower lr and a higher number of trees are generally preferable (Elith et al. 2008), there is no concrete definition of best combinations of those parameters. For a comprehensive description of BRT particularly for ecological applications, the reader can refer to De'ath (2007), Elith et al. (2008), and Elith and Graham (2009).
We used the samples with 10,000 instances to build BRT models for each site with various combinations of lr (0.05, 0.01, 0.005, 0.001), tc (3, 5, 7, 10, 20), and bf (0.25, 0.50, 0.75, 0.90) parameters. A bf of 0.75, a lr of 0.005, and a tc of 10 almost consistently yielded higher performance than other combinations. We used these values of parameters to build models for Phragmites prediction. We used the extension of R gbm (Ridgeway 2006) for BRT developed by Elith et al. (2008) for building BRT models. We tested the models for both interpolation and extrapolation of Phragmites occurrences. For the interpolation, the sample drawn from each site was used to classify independent cells from the same site. As available CORINE land cover maps are from years 2000 and 2006, we used Phragmites distributions of 1996 in Ruissalo, 1995in Kramppi, 1995in Redamo, and 2006 in Svartb€ ack to build and test the models for interpolation. For the extrapolation, we used the model trained with the sample of Ruissalo 1996 to predict Phragmites distributions of 1995 in Kramppi, 1995 in Redamo, and2003 in Svartb€ ack. The choice of Ruissalo model for extrapolation was because the land cover grid of Ruissalo is inclusive of all land cover classes that appear in other sites.
Models and predictions were evaluated using a number of measures (Pearce and Ferrier 2000). For BRT models, we present the mean and standard error of ten-fold crossvalidation (CV) statistics including correlation and the area under the receiver operative characteristic (ROC) curve (AUC). AUC statistic was also calculated for the interpolated and extrapolated maps of Phragmites distribution using R ROCR (Sing et al. 2005). Probability estimates of Phragmites occurrence were dichotomized to binary data of presence/absence using the minimized difference threshold criteria (Jim enez-Valverde and Lobo 2007). Sensitivity and specificity performance measures were computed using a cell-by-cell comparison of predicted distributions with truth.

Figures of Phragmites spread over years
Analysis of Phragmites distribution in different years in the study sites showed an increased Phragmites colonization of clear waters and shoreline segments. Various Phragmites prevalence (Table 1) and annual intrinsic rates of increase (Table 2) were observed in different geographic areas and time periods. Expansion of Phragmites was the dominant trend in most examined periods. An exception was in Kramppi between 1977 and 1995 where the area of reed colonies shrank with a small annual rate of 0.4%. However, over the whole period , Kramppi witnessed a significant growth of reed colonies. Highest reed prevalence and annual expansion rate occurred in Svartb€ ack where Phragmites covered one-fifth and one-fourth of the area in 2003 and 2006, respectively.

Relationships between Phragmites occurrence and predictor variables
Differences were observed in Phragmites prevalence in relation to the same variable in different geographic areas (Fig. 4) and, to a lesser extent, in different time periods (Fig. 5). Notable prevalence of reed is found on the shorelines and shallow waters. Majority (3 quartiles) of the reed colonies in all examined sites existed in waters with less than 1 m in depth. However, the distribution of Phragmites over time shows progression into deeper waters, especially in Kramppi and Svartb€ ack. Phragmites also dominated sheltered shorelines and bays, although on the temporal scale seemed to have expanded to slightly less sheltered areas, especially in Ruissalo and Kramppi. Areas in the vicinity of river outlets are also observed to provide suitable habitats for Phragmites. It is worth noting the distance lag from river outlets before Phragmites occurs in high prevalence. Areas right at the outlets of river basins show lower or no suitability for Phragmites compared to those within proximity of 250 m (in Ruissalo and Redamo) to 600 m (in Svartb€ ack). Phragmites appears to colonize shores adjacent to various land cover types ( Fig. 6) with slightly varying prevalence. Most sites had low representation of land cover classes. Heterogeneous agricultural areas (land cove class 2.4) seem to have high prevalence of Phragmites on their shores. Phragmites prevalence exhibited strong association with artificial, nonagricultural vegetated areas (class 1.4), and the scrub and herbaceous vegetation (class 3.2) in Ruissalo.

Neighborhood effect on Phragmites expansion
Effect of the neighborhood composition on the transition of cells is illustrated in Fig. 7. The neighborhood composition, given by the number of reed-occupied cells surrounding the cell in question, is found influential on the likelihood of Phragmites to spread or disappear from a location. Generally, clear water cells with prevalence of Phragmites in the surrounding are more susceptible for Phragmites takeover. On the contrary, the likelihood of disappearance is higher for small standalone patches than it for patches surrounded by large Phragmites colonies. While the same general picture of neighborhood effect is reflected in all combinations of cell sizes and neighborhood windows analyzed, differences can be noticed in the level of information and noise in curves from different combinations. Considering the 0->1 state transition (the solid circles in Fig. 7), a small cell size (3 m), and a small neighborhood window (3 9 3) yielded no clear distinction in the probability of a cell to become colonized by Phragmites when 1 or 8 neighbors are already colonized. Enlarging the cell size and including neighbors beyond Moore neighborhood in the analysis gradually reflects a clearer picture of the neighborhood influence. However, when both the cell size and the neighborhood window are very large (9 m and 9 9 9), noise is introduced in the relationship curves, especially at high neighbor counts. Relationships for the 1->0 state transition (the open circles in Fig. 7) reflected a trend of Phragmites disappearing when few adjacent colonies occur within the vicinity. When the neighborhood window is extended (7 9 7 and 9 9 9), noise is introduced at low neighbor counts.

Modeling Phragmites distribution
BRT models performed differently in predicting Phragmites distributions in different geographic areas. AUC scores from model CV were relatively high with values of 0.97 for Ruissalo and Redamo, 0.96 for Kramppi, and 0.89 for Svartb€ ack models. Table 3 lists the number of trees and statistics of model performance using CV. The influence of variables on the prediction of Phragmites occurrence is illustrated in Fig. 8 for each site. The depth of water (in Ruissalo and Svartb€ ack) and the distance to river mouths (in Kramppi and Redamo) were the most influential variables in predicting reed occurrences. Openness came third in variable importance in all sites, followed by the land cover, which was in some cases of negligible influence on the prediction.

Discussion
The intrinsic rate of increase in Phragmites areal cover varied between study sites. The intensive progression of Phragmites in Svartb€ ack indicates the existence of highly suitable conditions for Phragmites proliferation. This is in line with figures showing that nutrient concentrations increase eastward in the GOF (SYKE 2009). While the increase in area was the observed trend, decrease in Phragmites areal cover and disappearance of reed patches occurred in some locations, most notably in Kramppi in the period 1977-1995. Those patches were mostly small in area and were not surrounded by other settlements of Phragmites. Increased Phragmites area eightfold in Kramppi, most of the reed patches that appear in the map of 1977 were not observed in the map of 1962. In the period from 1977 to 1995, most patches appeared in both maps with different areas (Fig. 2). This may suggest that changes in the reed distribution in Kramppi occurred by seed/seedling establishment in earlier years and by vegetative spread with rhizomes in following years. The predictors used were all proxies to more functionally relevant variables, resulting in models for prediction rather than explanation. Predictors exhibited different levels of separation between the reed-occupied and clear locations. In Kramppi, for instance, the distributions of reed-occupied and clear cells almost overlap with respect to the openness and the distance to river mouths. We investigated this on a topographic map of Kramppi and found that it might be due to the presence of a relatively close bay (called Vanhankyl€ anlahti) to which a number of rivers flow with no records of Phragmites occurrence in our data although recent Satellite Imagery from Google Maps (maps.google.com) indicates the presence of large reed colonies in that bay. This is likely what caused the two populations (reed-occupied and reed-free cells) to exhibit large overlap in their distributions. Based on this observation and given the good performance of the models, we argue that these variables have high potential in predicting Phragmites occurrences.
The suggested occurrence of Phragmites in locations where water depth exceeds 2 m in Fig. 4 should be treated critically as literature and personal observations indicate that it is unlikely for Phragmites to progress into waters deeper than 2 m (Luther 1951;Munsterhjelm 1997;L. Nurminen, pers. obs.). As no ground truthing was conducted to validate these particular data records, they should be regarded erroneous, and no conclusions about the limit of water depth at which Phragmites can occur should be drawn on their basis. Possible error sources that may have caused this are (i) errors in the interpolated bathymetry model, (ii) errors in the input maps of reed due to possible difficulties in distinguishing Phragmites on the aerial photographs, and/or (iii) errors due to the resolution inconsistency of Phragmites grids (2 m) and the bathymetry grid (5 m). It should be noted, however, that such possible errors in data have minimum effect on the results of BRT models due to their robustness to noisy data, as illustrated by the low error rates of the predictions. The use of binomial deviance, rather than AdaBoost, as BRT loss functions is likely to yield better performance where classes may be mislabeled (Elith et al. 2008), as the case may be here.
Similar to results from the exploratory analysis (Fig. 6), fitted values from the BRT model for Phragmites presence next to different land cover types (Fig. 10) show influence of agricultural areas in Ruissalo on the prevalence of Phragmites. In BRT models, the land cover was found to be the least influential of all variables in predicting reed occurrences. This may be due to the low resolution of the land cover grid, which was not detailed enough to (1) depict changes in the prevalence of Phragmites in areas adjacent to different classes of land cover or (2) include a wider range of land cover classes. Nonetheless, land cover types have diverse effects on ecological niches on the regional scale (Dormann 2007b;Hirzel and Le Lay 2008).
Refining the predictor variables and adding additional relevant predictors may enhance prediction and model performance. Some studies have suggested that land use and nutrient loading influence the prevalence of Phragmites on the local scale (Bertness et al. 2002;Silliman and Bertness 2004), while other studies have found their effect to be on the catchment scale (King et al. 2007;Kettenring et al. 2010). Therefore, improvement of the model results could be achieved by accounting for the river basin size and adjacent land use in order to define the magnitude and range of their impact on coastal areas. Also, more detailed bathymetry and openness models could result in a more accurate spatial prediction of areas suitable for Phragmites. Finally, seabed type in shallow waters can be a good indicator of a location's suitability for Phragmites (Coops and van der Velde 1995;Kaitaranta et al. 2013).
Neighborhood state was found influential in Phragmites dynamics. With vegetative proliferation, Phragmites is likely to overtake areas adjacent to existing colonies, provided favorable conditions exist (Koppitz and K€ uhl 2000). Considering cells beyond Moore neighborhood (the eight nearest cells) was useful for capturing the neighborhood influence on the expansion and disappearance of reed. However, very large neighborhood windows yielded trends with noise at high (in the 0->1 case) and low (in the 1->0 case) occupied-neighbor counts. We expect this to be a result of a strong clustering in Phragmites distribution in space which makes it unlikely to find many small patches of Phragmites standing alone in open waters or many spots of clear water in the middle of large reed colonies. Therefore, with few records for these cases, no clear trend could be depicted. Regardless of the settings chosen in this study, however, high likelihood of Phragmites spread into adjacent locations was found when significant prevalence of Phragmites occurs in the neighborhood.
Using a cellular data model in this type of studies has a number of advantages. It is compatible with the raster format widely used in GIS, which makes a range of free and open source software and libraries available for the computation and data manipulation. We used R gbm package (Ridgeway 2006;Elith et al. 2008) for modeling Phragmites distributions, R ggplot2 (Wickham 2009) for illustrations, and Python Numpy (http://www.numpy.org/) for data manipulation and per-processing. The computational power of Numpy allows efficient development and running of dynamic models such as the cellular automata for spatial processes (Altartouri and Jolma 2012).
From an ecological point of view, this data model is suitable for incorporating mechanisms of dispersal in SDM. The flexibility in setting the size and shape of the neighborhood window allows accounting for both closerange and long-distance dispersion. However, the ability to correctly model such processes is conditioned on the adequate choice of scale parameters such as the cell size and neighborhood window. Examining a range of settings for these parameters is important for choosing an adequate scale that maintains balance between model accuracy and generality. A disadvantage of this data model arises from the necessary conversion between vector and raster formats, as species distribution data are usually collected in a point or a polygon vector format. This may lead to accuracy reduction during the conversion. However, the loss of information can be minimized if landscape metrics and proper sampling techniques are considered in the conversion process.
Phragmites distribution was successfully modeled using BRT, with variation in the performance between the interpolation and extrapolation, and in extrapolating to different time periods and geographic locations. For the interpolation cases, BRT models for the Archipelago sites performed highly with AUC greater than 0.96. Lower but acceptable performance was observed in Svartb€ ack with an AUC of 0.89. This can be due to the presence of variables influencing Phragmites distribution in this site that were not included in our predictors. Also, we notice disappearance of Phragmites next to the shoreline in Svartb€ ack in 2006 compared with 2003, which might be due to manual removal of reeds, a factor not incorporated in the model. Nonetheless, our results concur with earlier work (Caruana and Niculescu-Mizil 2006;Elith et al. 2006Elith et al. , 2008Elith and Graham 2009), suggesting the high potential of BRT in modeling species distributions.
Phragmites distributions were extrapolated on the spatial and temporal axes of model generalization (Hirzel  and Le Lay 2008). Extrapolation of Ruissalo model to predict Phragmites distributions of Kramppi and Redamo yielded better performance compared with its performance in Svartb€ ack. Due to their spatial and temporal proximity to Ruissalo, conditions in the Archipelago sites (in the extrapolated years) are expected to be more similar than those in Svartb€ ack located in the Eastern part of the GOF. Extrapolation is usually burdened with uncertainty (Dormann 2007b;Elith and Leathwick 2009) and lower prediction performance in this case can be attributed to differences in the influential factors and their magnitude of influence in different sites. While the extrapolation of Ruissalo model in other sites demonstrates the potential of the methods presented in this study for predictive mapping of Phragmites, the direct application of the model along the whole Finnish coast is not suggested. For such task, we recommend zonation of the area into smaller areas with comparable characteristics, for example water quality figures, and training a model of each individual area in order to achieve accurate predictions.
Adequate interpretation of SDM results is important in order to avoid misuse (Keating and Cherry 2004;Jim enez-Valverde et al. 2008). Our study is correlative and employs a ML approach, which emphasizes prediction and utilizes any predictor that is potentially informative (Hochachka et al. 2007). The correct interpretation of the resulting maps is not an absolute probability of Phragmites occurrence but rather a relative ranking of habitat suitability (Keating and Cherry 2004;Morisette et al. 2006). Using datasets relatively easy to obtain, our study can help delineating suitable habitats for Phragmites along the Southern Finnish coasts, allowing early management plans to be made (Bart et al. 2006;King et al. 2007). Predicting habitat suitability is essential also for ecological studies on species distribution and habitat diversity Pitk€ anen et al. 2013) and timely predictions on the catchment-borne nutrient loading of coastal areas (Kaitaranta et al. 2013), given the key role of reed beds on littoral communities in shallow and sheltered coastal ecosystems (Meriste et al. 2012).
In conclusion, the dynamics of Phragmites at the Southern coastal zone of Finland has shown both expansion and disappearance of local patches, but clearly expansive growth has been the dominant trend, observed also by other studies from the Northern Baltic area (von Numers 2011; Meriste et al. 2012). Showing variation in different geographic locations, the progression of Phragmites resulted in an increase in the colonies areal cover by more than 1% per year in all analyzed sites, reaching 8% in some sites. The depth of water, shore openness, and proximity to river mouths were useful predictors of Phragmites occurrence. Our results indicate that shallow shores located nearby river outlets represent suitable habitats for Phragmites establishment and expansion. In concordance with von Numers (2011), over the last few decades, Phragmites has shown progression into slightly deeper waters and relatively more open shores. Although in the Baltic Sea, the potential seaward expansion of Phragmites is ultimately regulated by sea-level fluctuation and wave action reflecting the windiness and storminess of the sea area (Meriste et al. 2012). We also found the state of a location's surrounding in terms of Phragmites occurrence to influence the likelihood of Phragmites progression to that location. The resulting habitat suitability maps suggest the existence of places potentially suitable for Phragmites colonization. Extensive research in North America (Lambertini et al. 2008;Belzile et al. 2010) and Central Europe (Koppitz 1999;Koppitz and K€ uhl 2000;F er and Hroudov a 2009) has shown Phragmites to expand and colonize new areas mainly through close-range vegetative growth and long-distance generative dispersal by seeds. Nevertheless, close-range seedling dispersal may occur when seedling establishment is enabled, for example, by dredging or by settlement of organic matter on sandy shores through eutrophication, and, on the other hand, long-distant vegetative dispersal is enabled by detached rhizome bits of old stands (F er and Hroudov a 2009). To reveal the expansion dynamics of Phragmites in more detail in the Northern Baltic and the coastal area of Southern Finland, a detailed study on the population structure, genetic diversity, and reproduction mode of the reed stands would be timely and provide important supplementing information for the modeling approach.