Understanding interactions between native and invasive plant species in field settings and quantifying the impact of invaders in heterogeneous native ecosystems requires resolving the spatial scale on which these processes take place. Therefore, functional tracers are needed that enable resolving the alterations induced by exotic plant invasion in contrast to natural variation in a spatially explicit way. 15N isoscapes, i.e., spatially referenced representations of stable nitrogen isotopic signatures, have recently provided such a tracer. However, different processes, e.g. water, nitrogen or carbon cycles, may be affected at different spatial scales. Thus multi-isotope studies, by using different functional tracers, can potentially return a more integrated picture of invader impact. This is particularly true when isoscapes are submitted to statistical methods suitable to find homogeneous subgroups in multivariate data such as cluster analysis. Here, we used model-based clustering of spatially explicit foliar δ15N and δ13C isoscapes together with N concentration of a native indicator species, Corema album, to map regions of influence in a Portuguese dune ecosystem invaded by the N2-fixing Acacia longifolia. Cluster analysis identified regions with pronounced alterations in N budget and water use efficiency in the native species, with a more than twofold increase in foliar N, and δ13C and δ15N enrichment of up to 2‰ and 8‰ closer to the invader, respectively. Furthermore, clusters of multiple functional tracers indicated a spatial shift from facilitation through N addition in the proximity of the invader to competition for resources other than N in close contact. Finding homogeneous subgroups in multi-isotope data by means of model-based cluster analysis provided an effective tool for detecting spatial structure in processes affecting plant physiology and performance. The proposed method can give an objective measure of the spatial extent of influence of plant-plant interactions, thus improving our understanding of spatial pattern and interactions in plant communities.
Citation: Hellmann C, Werner C, Oldeland J (2016) A Spatially Explicit Dual-Isotope Approach to Map Regions of Plant-Plant Interaction after Exotic Plant Invasion. PLoS ONE 11(7): e0159403. https://doi.org/10.1371/journal.pone.0159403
Editor: Cristina Armas, Estacion Experimental de Zonas Aridas - CSIC, SPAIN
Received: March 31, 2016; Accepted: July 2, 2016; Published: July 27, 2016
Copyright: © 2016 Hellmann 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.
Data Availability: All relevant data are within the paper and its Supporting Information files.
Funding: Funding was provided by the DFG (OL 417/1-1, WE 2681/8-1, http://www.dfg.de/en) and by a scholarship of the Studienstiftung des deutschen Volkes to CH. The article processing charge was funded by the German Research Foundation (DFG) and the Albert Ludwigs University Freiburg in the funding programme Open Access Publishing. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing interests: The authors have declared that no competing interests exist.
Understanding the processes that determine spatial patterns in field data is a major goal in plant ecology . One approach to analyze spatial patterns is to group spatially explicit measurements into separable homogeneous clusters, aiming at identifying biotic and abiotic factors that explain the variation between the clusters. Spatial clustering is a suitable method which is commonly applied to large spatial datasets, such as ecoregions [2,3] or datasets in epidemiology [4–6]. However, it is seldom applied to study the spatial context of functional processes within plant communities. For example, the spatial extent in which individual plants interact with one another or with the abiotic environment is often unknown . One case where the area influenced by individual plants is of special interest is the invasion of exotic plant species into well-established native plant communities.
Invasive species are known to affect native ecosystem functioning in numerous ways and have been recognized as one of the major drivers of biodiversity loss . Plant invaders have been shown to directly alter community composition and structure, as well as to change the native environment by modifying biogeochemical cycles, notably carbon, water and nutrient cycling [9–12]. However, although it is a major objective to measure the impact of invasive species on plant communities [13,14], spatially explicit approaches in invasion ecology mostly consider large scale distribution patterns (see e.g. ), while approaches to quantify the local area of impact are rare.
Stable isotopes can provide valuable tracers for several of the processes affected by invasion at local scales. δ15N has been proposed as an integrator of N cycling [16–18] and can be used to trace N sources of plants [19,20], such as N introduced to the native system by an invasive species [21,22]. Foliar δ13C is related to photosynthetic 13C-fractionation, which depends on the ratio of internal to external CO2 partial pressure, and can thus add additional information on changes in intrinsic water use efficiency (WUEi) of C3 species , which has been used in many studies (e.g. [24,25]).
Spatially explicit representations of stable isotope values, i.e. isoscapes , allow for resolving and analyzing variations in functional tracers on multiple spatial scales. For example, δ15N isoscapes have been successfully used to quantify the impact of an N2-fixing invasive Acacia spp. . However, recent work shows that the area influenced by invasion differs depending on the tracer used, i.e. multiple tracers may detect different interaction ranges with respect to the observable processes. Hence, instead of analyzing each tracer individually, a method that includes all available tracers or isoscapes would provide a more complete picture. Such a multivariate isoscape would combine the information contributed by different tracers to characterize the region influenced by invasion, integrating the diverse processes involved and enabling to identify subregions of invader influence.
A well-established group of unsupervised methods to find subgroups in multivariate data is cluster analysis . Clustering of georeferenced isotopic values (isoscapes) has successfully been used for example to track animal migration on a continental scale [28,29], to understand trophic interactions , and to determine origins of biological materials on country level (e.g. ). However, clustering of isoscapes has mainly been applied within contexts of zoology and/ or geographic assignment while no examples with plant ecological scope are known to us from the literature. Furthermore, the mentioned studies were always conducted on large spatial scales, i.e. on country or continental scale, while studies based on e.g. individual plants in an area of less than a hectare do not exist, yet are possible.
The aim of this study was to evaluate the suitability of spatial clustering to find subregions within plant communities with different mechanisms and/ or intensity of plant-plant interactions. For this purpose, multiple raster layers representing spatially explicit measurements of informative functional tracers, i.e., isoscapes were used. Specifically, we aim to identify different regions of influence in a Portuguese dune ecosystem invaded by the N2-fixing Acacia longifolia (Andrews) Willd., a highly problematic invasive species in Mediterranean regions, using δ15N and δ13C isoscapes of a native indicator species (Corema album L.) combined with information on foliar N concentration. It has already been proven that 15N isoscapes represent an effective spatial tracer for the impact of A. longifolia [21,22]. Using a multivariate approach and including δ13C will enable to reveal additional facets of plant-plant interactions that may also differ in their spatial extent. For example, while foliar δ15N can be used to trace N input from N2-fixation by the invasive species, this may have positive or negative impacts on water use efficiency, depending on weather facilitative or competitive processes dominate the interaction. Thus, including an additional tracer will enable to distinguish between different types of interactions occurring in the community. We seek to detect homogeneous regions in the multivariate data in an objective, unsupervised way, that is, with no previous assumptions on data distribution and grouping factors used in the analysis. This will be the first study using a multivariate isoscape clustering approach for disentangling plant-plant interactions on the plant community level in the context of invasion biology.
Materials and Methods
The field site is located in a sand dune ecosystem near Pinheiro da Cruz at the Atlantic coast of Portugal (38°15.4’N, 8°46.3’ W) and was accessed with permission of the Estabelecimento Prisional de Pinheiro da Cruz. Climate is Mediterranean with Atlantic influence, with mean annual temperature of 16.6°C and mean annual precipitation of 735 mm for the nearest meteorological station in Setúbal, 38°33’N, 08°53’W, in the period of 1981–2010 . Summers are dry with high temperatures and precipitation is mostly concentrated in the winter month. Soils are arenosols (FAO classification) with poor water retention capacity , low organic matter content and low N and P availability . The native vegetation forms a sparse canopy with large proportions of bare sand. Dominant native species are the dwarf shrubs Corema album L. (Ericaceae), the N2-fixing Stauracanthus spectabilis Webb (Fabaceae), and numerous young as well as occasional adult pine trees (Pinus pinaster Aiton, Pinaceae). The area is invaded by the exotic N2-fixing Acacia longifolia (Andrews) Willd. (Fabaceae), a shrub or small tree of ca. 1–8 m height which forms several dense, monotypic stands in the studied ecosystem. These stands differ from the native vegetation in terms of structure and plant diversity and previous studies have shown that the ecosystem gets enriched with nitrogen in the surrounding of A. longifolia [21,22,34].
Three plots of 1,000 m2 area (20 x 50 m) were established in the dune system and subdivided into 2 x 5 m subplots. In the three plots, C. album occurred frequently with even spatial coverage, allowing for a well-resolved spatial sampling design. Plot 1 and 2 each comprised stands of the invasive A. longifolia, with 17% and 7% of the plot area covered by the invader, respectively. These plots were sampled in November 2009 . Additionally, a control plot (plot 3) of uninvaded native vegetation was established in April 2011. For plots 1 and 2, foliage of C. album was collected from each plant and samples were pooled per subplot. For plot 3, one random individual of C. album was sampled per subplot and the exact location of the individual was recorded. Regarding sampling strategies, we confirmed that data of individual plants sampled along a gradient corresponded well to interpolated data obtained from pooled subplots. Only current year, fully expanded, sunlit foliage was sampled on all occasions. Comparability between seasons was confirmed by comparing N concentration, δ15N and δ13C of plot 1 from spring 2008 with resampled data from November 2009, which showed no significant differences in δ15N and δ13C (Mann-Whitney-U test, W = 1171, p = 0.14 and W = 1362, p = 0.79) and only marginal deviations in N concentration, with values being slightly higher in May, showing an average enrichment of 1 g N*kg-1 (W = 1037, p = 0.02).
Analysis of isotopes and N concentration
Leaf samples were dried at 65°C for at least 48 h and then homogenized and ground to a fine powder using a ball mill (Retsch, Haan, Germany). Samples were analyzed for N concentration and C and N isotopic composition in an elemental analyzer (HEKAtech GmbH, Weinberg, Germany) coupled to a continuous flow stable isotope ratio mass spectrometer (ISOPRIME, Elementar, Hanau, Germany) at the University of Bielefeld, Germany. All samples were measured against a laboratory standard (IVA33802156, IVA Analysetechnik e.K., Meerbusch, Germany) and international standards (IAEA-NO-3 for plot 1 and 2 δ15N and IAEA-N-1 for plot 3 δ15N, International Atomic Energy Agency, Vienna, Austria). Repeated measurement precision was ≤0.5 g N*kg-1 for N concentration, ≤0.2‰ for δ15N and ≤0.1‰ for δ13C. Isotopic composition is reported in delta-notation referenced to the international IAEA standards (air N2 for δ15N and V-PDB for δ13C).
Geographic positions of the plot corners were recorded and C. album distribution and A. longifolia canopies were digitized based on hand-drawn maps in QGIS 2.4 . Foliar N concentration and δ15N of plot 1 and 2 were re-analyzed from . δ13C was measured from the same samples of . Additionally, an uninvaded control (plot 3) was sampled for both δ13C and δ15N. Foliar N concentration, δ15N and δ13C of C. album in the three plots were interpolated to continuous surfaces using variogram fit and ordinary kriging in R 3.2.1  with the package gstat . For variograms, cutoff distance was set to the default (1/3 of the longest diagonal = 17.95 m). In the variogram fits, all models proposed by the function vgm were tested with different lag distances, including five uniform (1 m, 1.2 m (default), 2 m, 3 m, 4 m) and one non-uniform segmentation (with the following boundaries: 1, 2, 3, 4, 5, 6, 7, 9, 12, 15, 18 m). The best combination of lag-distance and variogram model was chosen by means of a leave-one-out cross-validation procedure using the function krige.cv. For this purpose, the variogram fitting and the kriging was done repeatedly and each raster cell of the plot was left out from the process once and predicted from the resulting model in this run. The model that yielded the smallest root mean square error (RMSE) for predicted values and the highest R2 for the regression of predicted on measured values was chosen as the final model. For plots 1 and 2, additionally, the distance of each raster cell to the closest cell occupied by A. longifolia was calculated (R package raster, ).
To test whether the raster cells of the three plots would fall into discernable clusters based on their N concentration, δ15N and δ13C values, a model-based cluster analysis  was performed using the package mclust  in R. 3.2.1 . More conventional cluster algorithms like hierarchical clustering and k-mean partitioning approaches are usually distance-based and may be unreliable when clusters are not spherical, i.e., variable in volume, shape and/or orientation . Furthermore, it is often difficult to decide on the correct number of clusters, particularly in the presence of overlapping groups. Model-based clustering assumes that the data consist of a number of subgroups (the clusters), in each of which the variables have a different multivariate probability density function [39,40]. Model-based cluster analysis yields an estimation of the parameters of these probability density functions and calculates the posterior probabilities of cluster membership for each sample. The optimal number of clusters can then be chosen by employing a model selection criterion. The function Mclust uses the expectation-maximization (EM) algorithm for normal mixture models with a variety of covariance structures . Ten models were tested with different combinations of the following constraints: spherical, diagonal or ellipsoidal distribution; equal or varying volume; equal or varying shape; equal or varying orientation . Model selection was achieved by maximizing the Bayesian Information Criterion (BIC, ). For the three plots in our study, BIC plotted against the number of clusters increased strongly with the first four to six clusters and then levelled off and reached a plateau for some 10–20 additional clusters before decreasing (S1 Fig). Abiding by the rules of parsimony, the lowest number of clusters at the beginning of the plateau was chosen.
For the interpretation of the clusters, we produced boxplots for each model parameter, cluster and plot combination. A Kruskal-Wallis rank sum test followed by a post-hoc multiple comparison test correcting for α-inflation (function kruskalmc from the R package pgirmess, ) was used to test for significant differences between cluster medians of N concentration, δ13C and δ15N. For a better interpretation of the spatial configuration of clusters in relation to the invader, we also plotted the clusters against the median distance to the closest A. longifolia canopy within the plots.
In order to be able to compare clusters across the three plots, we used the median values of N concentration, δ15N and δ13C from the clusters retrieved by Mclust in a hierarchical cluster analysis (unweighted pair group method with arithmetic mean (UPGMA) with Euclidean distance, see  for detailed information on algorithm and distance measure) using the function agnes of the package cluster . Euclidean distance was used as all data were on the same scale. The optimal number of clusters was defined as the clustering solution with the highest Silhouette value .
The isoscapes revealed distinct spatial patterns in N concentration, δ15N and δ13C of C. album foliage (Fig 1). In the invaded plots 1 and 2, N concentration ranged between 5.8–13.5 g N*kg-1 and 6.3–9.9 g N*kg-1, respectively, and increased considerably when comparing C. album individuals growing distant and adjacent to A. longifolia (hatched area, Fig 1A and 1B). These alterations in N concentration corresponded to a more than two-fold increase for plants located close to the invader compared to the uninvaded vegetation at the borders of plot 1, and an enrichment by ca. 30% in plot 2. Similarly, δ15N of C. album became substantially enriched in the vicinity of A. longifolia, with background values of uninfluenced vegetation of ca. -11‰ (plot 1) and -8‰ (plot 2) increasing to values close to 0‰ (Fig 1D and 1E), even though C. album itself has no capacity of N2-fixation. For δ13C, a distinct spatial pattern with values enriched by ca. 2.5‰ for C. album growing close to the A. longifolia canopies was evident for plot 1, while for plot 2, pronounced small-scale variation only weakly related to the presence of the invader was observed (Fig 1G and 1H). Noticeably, enrichment in N, δ15N and δ13C associated with A. longifolia presence was evident not only in direct neighborhood of the invader, but exceeded the canopy by several meters.
Canopies of Acacia longifolia in plot 1 and 2 are indicated by white hatched polygons.
In plot 3, which is not invaded by A. longifolia, N concentration was extremely low (≤ 7.3 g N*kg-1) without much variation throughout the study plot (Fig 1C). δ15N showed weak spatial pattern, with enriched values mainly occurring in the southern part of the plot (Fig 1F). However, δ15N-enrichment was less in terms of absolute values and spatial extent compared to invaded plots 1 and 2. δ13C showed a similar pattern of enrichment, with depleted values in the northern and enriched values in the southern part of the plot and one peak showing maximal values of ca. -25.5‰ (Fig 1I).
Model-based cluster analysis resulted in optimal solutions with six clusters in plot 1 and four clusters in plot 2 and 3 according to the BIC (S1 Fig). Optimal models were ellipsoidal for all three plots, with variable volume, shape and orientation for plot 1, equal volume and shape for plot 2 and equal shape for plot 3 (S1 Fig). Fig 2 shows scatterplots of the three variables used for the cluster analyses, indicating cluster membership of each sample. In all three plots, N concentration and δ15N were correlated and clusters were arranged roughly along the concerted increase of these variables, with the exception of cluster II in plot 3 (Fig 2A–2C). Scatterplots of δ15N vs. δ13C and N concentration vs. δ13C similarly showed correlations for plot 3 (Fig 2F and 2I), with cluster II again accommodating a rather outlying group (Fig 2F). Plots 1 and 2 demonstrated a more complex relationship between δ13C and δ15N: for plot 1, in clusters I, II and III, a positive correlation between δ15N and δ13C was found, with cluster III being separated from clusters I and II by a higher enrichment in δ15N. In contrast, clusters IV, V and VI tended to decrease in δ13C with more enriched values in δ15N (Fig 2D). The same trend was evident in the scatterplot of N concentration vs. δ13C: clusters I, II and III showed increasing values in N concentration with enrichment in δ13C, while clusters IV, V and VI on average got depleted in δ13C with further increase in N concentration (Fig 2G). A similar pattern, though less pronounced, could be observed in plot 2 (Fig 2E and 2H). While across clusters I, II and III, values tended to correlate positively between δ13C and δ15N as well as δ13C and N concentration, cluster IV, with highest enrichment in δ15N and N concentration, did not show further enrichment in δ13C.
Cluster membership to cluster I to VI (for plot 1) or cluster I to IV (for plots 2 and 3) is indicated by different symbols and coloring, sorted by median N concentration, with blue to red representing low to high N. Ellipses denote the normal-probability contours at probability = 0.5. Please note different scaling of the axes.
Fig 3 shows boxplots of N concentration, δ15N and δ13C within the individual clusters. For all plots, median N concentration obviously increased with increasing cluster number, as clusters have been ordered by N concentration (Fig 3A–3C). In plot 1, δ15N similarly increased from cluster I to V, while cluster VI did not show additional enrichment (Fig 3D). Median δ13C increased from cluster I to II and then to IV, but decreased in clusters V and VI. Median δ13C of cluster III was intermediate between clusters I and II (Fig 3G). The distance to the closest A. longifolia canopy of each sample, although it was not a variable in the cluster analysis, mirrored the pattern of medians of δ15N, with members of cluster I showing the largest distance, then median distances decreased for clusters II through IV, and members of clusters IV, V and VI were located closest to A. longifolia.
Different letters indicate significant differences at P < 0.05 (Kruskal-Wallis test, non-parametric multiple comparisons corrected for α-inflation).
Patterns in plot 2, while less pronounced, were similar. N concentration increased with cluster number, though it did not differ significantly between clusters I and II (Fig 3B). For δ15N, median values were lowest in cluster II and increased in clusters III and IV (Fig 3E). δ13C increased from cluster I through III and was not significantly different between clusters III and IV, i.e. δ13C did not get further enriched with additional increase in N concentration (Fig 3H). Cluster II was the farthest and cluster IV the closest to the A. longifolia canopies, and again, the distances accurately mirrored the distribution of δ15N (Fig 3K).
In the uninvaded plot 3, i.e. without the influence of A. longifolia, δ15N and δ13C increased with increasing N concentration in clusters I, III and IV, however, in group II, relatively low N concentration was associated with the—on average—most enriched δ15N and δ13C values (Fig 3C, 3F and 3I).
Medians of the clusters from the model-based approach were submitted to a hierarchical cluster analysis with the aim to summarize clusters across the three plots. Hierarchical cluster analysis resulted in three final clusters (Fig 4). Generally, the clustering approach yielded spatially homogeneous clusters, though no information on spatial location had been included in the analyses (Fig 5). Final cluster one, which was characterized by low values in all variables and specifically, low δ15N with values close to -10‰, was represented at the northern part of plot 1 and covered roughly half of the area of uninvaded plot 3. Final cluster two showed medium δ15N and δ13C with low to medium N concentration and was present in all three plots, occupying the largest area overall. Final cluster three, with high N concentration and strongly enriched δ15N and δ13C, only occurred in invaded plots 1 and 2. In these plots, cells assigned to final cluster three spatially corresponded to the locations of A. longifolia canopies and their surroundings.
The optimal solution with k = 3 clusters as identified by highest Silhouette value is indicated by different coloring. Labels specify plot and initial cluster membership in the form plot.cluster using Arabic and Roman numerals, respectively.
Framed areas marked with Roman numerals illustrate membership of cells to clusters yielded by the initial model-based cluster analysis (within plots). Different colors indicate membership to clusters from the final hierarchical cluster analysis (across plots), which was calculated with median values derived from the model-based clustering. Canopies of Acacia longifolia in plots 1 and 2 are indicated by white polygons.
Plant invasions are known to alter the structure of plant communities by modifying nutrient flows and water regime . In particular, Acacia longifolia populations in south-west Portugal are well known for multiple impacts on plant communities through changes in nutrient, carbon and water cycling [21,22,34]. However, multivariate spatial patterns of its impact have not been analyzed until now. Model-based cluster analysis of three spatially resolved functional tracers, δ13C, δ15N, and N, was successful in partitioning an area invaded by A. longifolia into homogeneous clusters on community scale. A subsequent hierarchical cluster analysis then allowed to generalize the results across the individual study plots, yielding three subgroups that can be interpreted in terms of the multivariate impact of the invasive species and allow to distinguish between variation in the measured processes that is inherent to the native system (clusters one and two) and alterations that can be ascribed to the influence of the invader (cluster three, Fig 5). Being based on multiple spatially explicit indictors, the identified zone of influence of A. longifolia thus comprises integrated information on various processes affected by invasion.
Variation of the measured parameters between and within the uninfluenced clusters depends on intrinsic characteristics of the native system. We found pronounced small scale variation of ca. 2‰ in δ13C and up to 8‰ in δ15N in final clusters one and two on less than 50 m (Figs 1 and 3; final clusters one and two comprise clusters I-III of plots 1 and 2 and the whole of plot 3; cf. blue and yellow labeling in Figs 4 and 5). This is a large range considering that we followed a standardized sampling procedure within only one target species (cf. e.g. [45–47]). Foliar δ15N and δ13C both can be expected to vary on small scales with N and water availability, which in turn can be controlled by, e.g., topography, soil texture and plant cover [47,48,49]. Plant δ15N depends on the isotopic composition of the N source, species composition, mycorrhizal associations and the relative activity of N transformation processes [16,50,51]. δ13C provides an integrated ecological tracer of different structural, functional and phenological attributes , which are sensitive to small scale changes in abiotic and biotic environment within a plant community. In particular, plant-plant interactions can directly impact water availability and thereby intrinsic water use efficiency of the interacting individuals in a competitive  or facilitative way , which will reflect upon the carbon isotope signal. Thus, although mechanistic determinants of variation in plant δ13C and δ15N have been widely investigated, there is a large gap in data and knowledge on the range and extent of spatial variability within plant communities. Substantial background variation within and between uninvaded clusters one and two, as quantified in this study, thus emphasizes that small scale heterogeneity is highly relevant and has to be taken into account in sampling designs when attempting to use stable isotopes as community-wide tracers .
In the invaded final cluster three, all measured parameters were higher, indicating the paramount effects of the invasive species on N budget as well as on photosynthesis and water relations in the indicator species C. album (Figs 3 and 4). δ15N signatures approached the value of atmospheric nitrogen (0‰), which, together with the marked increase in leaf N concentration, suggests uptake and use of N by C. album that originated from symbiotic N2-fixiation (see also [21,22]). Notably, the increase in δ15N had a wider range compared to N concentration and accordingly, δ15N has previously been suggested as an early indicator for the impact of A. longifolia . The increase in δ13C most likely is the result of two processes both reducing photosynthetic discrimination in C. album growing close to A. longifolia: on the one hand, better N nutrition has been shown to increase photosynthetic capacity, leading to a decrease in ci/ca (the ratio of internal to ambient CO2 partial pressure) and, accordingly, reducing photosynthetic discrimination . On the other hand, as A. longifolia is a strong competitor for water [33,55], ci/ca could also be decreased due to reduced stomatal conductance in response to water stress. Both effects lead to a higher foliar δ13C of C. album in the vicinity of A. longifolia and indicate higher water use efficiency, but are not necessarily exclusively facilitative, as similarly shown in  for a Pine stand invaded by A. longifolia.
Notably, the native N2-fixer S. spectabilis had no comparable effect on C. album, as analyzed in detail in  and . The higher impact of A. longifolia compared to S. spectabilis was mainly attributed to the high growth rates, biomass turnover and litter input of the invader together with its influence on microbial processes as well as on decomposition and turnover rates [21,22].
Cluster analysis provided an objective, unsupervised means to quantify the influence of the invasive A. longifolia based on a multivariate set of functional tracers and simultaneously enabled to identify the area affected by invasion. Until now, clustering of isoscapes into functionally relevant spatial groups was mainly done for tracing animal movement [28,29], to better understand trophic interactions , and to determine origins of biological materials at country level (e.g. ). However, detecting spatial patterns with cluster analysis is not trivial because simple cluster algorithms such as hierarchical clustering always produce some sort of clustering even in the absence of any real structure . Ways to improve the analysis are to compare clustering results against a null-model , to verify cluster validity or robustness by bootstrapping  or to identify the best possible model via model-based clustering . We applied model-based clustering which identified the optimal number of significantly different clusters for each plot. The final step of clustering the median values of the measured parameters per cluster, i.e. δ13C, δ15N, and N, allowed for comparing all three plots. Hence, model-based cluster analysis proved to be a suitable tool to partition isoscapes into functionally distinct and spatially congruent clusters. In the context of plant invasion, the clusters can then be analyzed with respect to the diverse processes affected by the invader.
Within the affected area, the relationships between the measured processes differed among clusters with different degrees of A. longifolia influence, as revealed by the initial model-based cluster analysis (Figs 2 and 3). Most intriguingly, while δ13C increased with increasing N concentration in the unaffected and marginally influenced clusters, δ13C did not increase further with N enrichment in the most strongly influenced clusters. This was particularly true for the heavily invaded plot 1, where median δ13C even decreased with higher N concentration in clusters V and VI compared to cluster IV (Figs 2 and 3). Thus, simultaneously analyzing δ13C and δ15N in a multi-isotope approach revealed a non-linear relationship of N enrichment with water use efficiency that indicated a change in the dominant processes which would not be detectable by analyzing one tracer alone. This pattern might reflect a shift from facilitation by N enrichment in the vicinity of A. longifolia to competition for resources other than N inside the canopy of the invader, which could have led to a reduction in CO2 fixation rates and thus to increasing ratios of ci/ca. A similar effect was observed in Acacia-invaded Pine stand, where indeed intense competition for water can reduce CO2 fixation of species in direct neighborhood of A. longifolia . Also, a spatial change in the balance between facilitation and competition could explain why native plants are eventually outcompeted and replaced by A. longifolia [21,58,59] despite the beneficial effects on growth rates  and WUEi (Figs 1 and 3) which are evident close to the invader in an early stage of invasion. Here, model-based cluster analysis enables to detect these functional shifts within the invaded area.
Although there is emerging awareness that competition and facilitation e.g. in plant-plant, plant-pollinator or plant-microbe interactions could actually have distinct spatial distributions [60–63], the balance between different processes with potentially opposite effects as a function of spatial scale is still rarely addressed in empirical studies. Yet, by not accounting for the high spatial variability and diversity of processes involved, important aspects that drive the outcome of species interactions might be missed. Since plant-plant interactions are truly multivariate and spatially explicit, we posit that to increase our understanding of complex field situations, it will be necessary and consequential to promote the use of innovative multivariate methodologies in the future.
In conclusion, finding homogeneous subgroups in multi-isotope data by means of model-based cluster analysis with spatially resolved measurements of a multivariate set of functional tracers proved very useful in detecting spatial structure in processes affecting plant physiology and performance, including abiotic and biotic factors both, inherent to the native system and imposed by an invasive species. The proposed method can give an objective measure of the spatial extent of influence of plant-plant interactions, potentially providing evidence for shifts between facilitation and competition depending on the spatial scale. Thus, spatial partitioning of isoscapes can help to better understand spatial pattern and interactions in plant communities.
S1 Fig. Bayesian Information Criterion (BIC) as a function of number of clusters for plots 1–3.
Ten different combinations of constraints for multivariate mixture models have been tested: EII = spherical, equal volume; VII = spherical, unequal volume; EEI = diagonal, equal volume and shape; VEI = diagonal, varying volume, equal shape; EVI = diagonal, equal volume, varying shape; VVI = diagonal, varying volume and shape; EEE = ellipsoidal, equal volume, shape, and orientation; EEV = ellipsoidal, equal volume and equal shape; VEV = ellipsoidal, equal shape; VVV = ellipsoidal, varying volume, shape, and orientation.
We gratefully acknowledge contribution of Katherine G. Rascher to field sampling and initializing previous work at the field site. We thank C. Máguas for logistical support and the Estabelecimento Prisional de Pinheiro da Cruz for allowing access to the field site. Thanks to Dora Marques and Patrícia Fernandes for help during field work and to Babsi Teichner for skillful assistance in the lab. The valuable comments of two anonymous reviewers helped to improve the manuscript.
Conceived and designed the experiments: CW CH JO. Analyzed the data: CH JO. Wrote the paper: CH CW JO. Collected data: CH.
- 1. 1. Dale MRT, Fortin M-J. Spatial analysis: a guide for ecologists. 2nd ed.; New York: Cambridge University Press; 2014.
- 2. Hargrove WW, Hoffman FM. Using multivariate clustering to characterize ecoregion borders. Comput Sci Eng. 1999;1: 18–25.
- 3. Kumar J, Mills RT, Hoffman FM, Hargrove WW. Parallel k-Means clustering for quantitative ecoregion delineation using large data sets. Procedia Comput Sci. 2011;4: 1602–1611.
- 4. Ward MP, Carpenter TE. Techniques for analysis of disease clustering in space and in time in veterinary epidemiology. Prev Vet Med. 2000;45: 257–284. pmid:10821965
- 5. Brooker S, Clarke S, Njagi JK, Polack S, Mugo B, Estambale B, et al. Spatial clustering of malaria and associated risk factors during an epidemic in a highland area of western Kenya. Trop Med Int Health. 2004;9: 757–766. pmid:15228485
- 6. Tanser F, Bärnighausen T, Cooke GS, Newell M-L. Localized spatial clustering of HIV infections in a widely disseminated rural South African epidemic. Int J Epidemiol. 2009; dyp148.
- 7. Berger U, Piou C, Schiffers K, Grimm V. Competition among plants: Concepts, individual-based modelling approaches, and a proposal for a future research strategy. Perspect Plant Ecol Evol Syst. 2008;9: 121–135.
- 8. Keller RP, Geist J, Jeschke JM, Kühn I. Invasive species in Europe: ecology, status, and policy. Environ Sci Eur. 2011;23: 1–17.
- 9. Liao C, Peng R, Luo Y, Zhou X, Wu X, Fang C, et al. Altered ecosystem carbon and nitrogen cycles by plant invasion: a meta-analysis. New Phytol. 2008;177: 706–714. pmid:18042198
- 10. Gaertner M, Den Breeyen A, Cang H, Richardson DM. Impacts of alien plant invasions on species richness in Mediterranean-type ecosystems: a meta-analysis. Prog Phys Geogr. 2009;33: 319–338.
- 11. Ehrenfeld JG. Ecosystem consequences of biological invasions. Annu Rev Ecol Evol Syst. 2010;41: 59–80.
- 12. Pyšek P, Jarosik V, Hulme PE, Pergl J, Hejda M, Schaffner U, et al. A global assessment of invasive plant impacts on resident species, communities and ecosystems: the interaction of impact measures, invading species’ traits and environment. Glob Change Biol. 2012;18: 1725–1737.
- 13. Parker IM, Simberloff D, Lonsdale WM, Goodell K, Wonham M, Kareiva PM, et al. Impact: Toward a framework for understanding the ecological effects of invaders. Biol Invasions. 1999;1: 3–19.
- 14. Thiele J, Kollmann J, Markussen B, Otte A. Impact assessment revisited: improving the theoretical basis for management of invasive alien species. Biol Invasions. 2010;12: 2025–2035.
- 15. Pyšek P, Hulme PE. Spatio-temporal dynamics of plant invasions: Linking pattern to process. Ecoscience. 2005;12: 302–315.
- 16. Högberg P. Tansley Review No. 9515N natural abundance in soil-plant systems. New Phytol. 1997;137: 179–203.
- 17. Craine JM, Elmore AJ, Aidar MPM, Bustamante M, Dawson TE, Hobbie EA, et al. Global patterns of foliar nitrogen isotopes and their relationships with climate, mycorrhizal fungi, foliar nutrient concentrations, and nitrogen availability. New Phytol. 2009;183: 980–992. pmid:19563444
- 18. Kleinebecker T, Hoelzel N, Prati D, Schmitt B, Fischer M, Klaus VH. Evidence from the real world: 15N natural abundances reveal enhanced nitrogen use at high plant diversity in Central European grasslands. J Ecol. 2014;102: 456–465.
- 19. Handley LL, Raven JA. The use of natural abundance of nitrogen isotopes in plant physiology and ecology. Plant Cell Environ. 1992;15: 965–985.
- 20. Stahl VM, Beyschlag W, Werner C. Dynamic niche sharing in dry acidic grasslands -a 15N-labeling experiment. Plant Soil. 2011;344: 389–400.
- 21. Hellmann C, Sutter R, Rascher KG, Máguas C, Correia O, Werner C. Impact of an exotic N2-fixing Acacia on composition and N status of a native Mediterranean community. Acta Oecologica. 2011;37: 43–50.
- 22. Rascher KG, Hellmann C, Máguas C, Werner C. Community scale 15N isoscapes: tracing the spatial impact of an exotic N2-fixing invader. Ecol Lett. 2012;15: 484–491. pmid:22409424
- 23. Farquhar GD, Hubick KT, Condon AG, Richards RA. Carbon isotope fractionation and plant water-use-efficiency. In: Rundel PW, Ehleringer JR, Nagy KH, editors. Stable Isotopes in Ecological Research. Berlin: Springer-Verlag; 1989. pp. 21–40.
- 24. Seibt U, Rajabi A, Griffiths H, Berry JA. Carbon isotopes and water use efficiency: sense and sensitivity. Oecologia. 2008;155: 441–454. pmid:18224341
- 25. Werner C, Máguas C. Carbon isotope discrimination as a tracer of functional traits in a Mediterranean macchia plant community. Funct Plant Biol. 2010;37: 467–477.
- 26. West JB, Sobek A, Ehleringer JR. A simplified GIS approach to modeling global leaf water isoscapes. PLoS ONE. 2008;3: e2447. pmid:18560592
- 27. Kaufman L, Rousseeuw PJ. Finding groups in data: An introduction to cluster analysis. John Wiley & Sons; 2009.
- 28. Hobson KA, Van Wilgenburg SL, Wassenaar LI, Powell RL, Still CJ, Craine JM. A multi-isotope (δ13C, δ15N, δ2H) feather isoscape to assign Afrotropical migrant birds to origins. Ecosphere. 2012;3: art44.
- 29. García-Pérez B, Hobson KA. A multi-isotope (δ2H, δ13C, δ15N) approach to establishing migratory connectivity of Barn Swallow (Hirundo rustica). Ecosphere. 2014;5: art21.
- 30. Guerreiro M, Phillips R, Cherel Y, Ceia F, Alvito P, Rosa R, et al. Habitat and trophic ecology of Southern Ocean cephalopods from stable isotope analyses. Mar Ecol Prog Ser. 2015;530: 119–134.
- 31. Meier-Augenstein W, Kemp HF, Schenk ER, Almirall JR. Discrimination of unprocessed cotton on the basis of geographic origin using multi-element stable isotope signatures. Rapid Commun Mass Spectrom RCM. 2014;28: 545–552. pmid:24497293
- 32. IPMA—019 [Internet]. [cited 23 Mar 2016]. Available: http://www.ipma.pt/pt/oclima/normais.clima/1981-2010/019/
- 33. Rascher KG, Máguas C, Große-Stoltenberg A, Werner C. Understory invasion of A. longifolia in a Mediterranean pine forest negatively affects the water use and carbon assimilation rates of native trees. Ecosystems. 2011;14: 904–919.
- 34. Rascher KG, Große-Stoltenberg A, Máguas C, Meira-Neto JAA, Werner C. Acacia longifolia invasion impacts vegetation structure and regeneration dynamics in open dunes and pine forests. Biol Invasions. 2011;13: 1099–1113.
- 35. QGIS Development Team. QGIS Geographic Information System. Open Source Geospatial Foundation Project [Internet]. 2014. Available: http://qgis.osgeo.org
- 36. R Core Team. R: a language and environment for statistical computing. R Foundation for Statistical Computing: Vienna, Austria [Internet]. 2016. Available: http://www.R-project.org
- 37. Pebesma EJ. Multivariable geostatistics in S: the gstat package. Comput Geosci. 2004;30: 683–691.
- 38. Hijmans RJ. raster: Geographic data analysis and modeling. R package version 2.3–40. [Internet]. 2015. Available: http://CRAN.R-project.org/package=raster
- 39. Fraley C, Raftery AE. Model-based clustering, discriminant analysis and density estimation. J Am Stat Assoc. 2002; 611–631.
- 40. Fraley C, Raftery AE, Murphy TB, Scrucca L. mclust Version 4 for R: Normal mixture modeling for model-based clustering, classification, and density estimation. Technical Report No. 597, Department of Statistics, University of Washington; 2012.
- 41. Everitt BS, Landau S, Leese M, Stahl D. Cluster Analysis. John Wiley & Sons; 2011.
- 42. Schwarz G. Estimating the dimension of a model. Ann Stat. 1978;6: 461–464.
- 43. Giraudoux P. pgirmess: Data analysis in Ecology. R package version 1.6.2 [Internet]. 2015. Available: http://CRAN.R-project.org/package=pgirmess
- 44. Maechler M, Rousseeuw P, Struyf A, Hubert M, Hornik K. cluster: Cluster analysis basics and extensions. R package version 2.0.3. [Internet]. 2015. Available: http://CRAN.R-project.org/package=cluster
- 45. Rousseeuw PJ. Silhouettes: A graphical aid to the interpretation and validation of cluster analysis. J Comput Appl Math. 1987; 53–65.
- 46. Peñuelas J, Filella I, Terradas J. Variability of plant nitrogen and water use in a 100-m transect of a subdesertic depression of the Ebro valley (Spain) characterized by leaf δ13C and δ15N. Acta Oecologica. 1999;20: 119–123.
- 47. Bai E, Boutton T, Liu F, Wu X, Archer S, Hallmark C. Spatial variation of the stable nitrogen isotope ratio of woody plants along a topoedaphic gradient in a subtropical savanna. Oecologia. 2009;159: 493–503. pmid:19085012
- 48. Hook PB, Burke IC. Biogeochemistry in a shortgrass landscape: Control by topography, soil texture, and microclimate. Ecology. 2000;81: 2686–2703.
- 49. Hartman G, Danin A. Isotopic values of plants in relation to water availability in the Eastern Mediterranean region. Oecologia. 2010;162: 837–852. pmid:19956974
- 50. Pardo LH, Nadelhoffer KJ. Using nitrogen isotope ratios to assess terrestrial ecosystems at regional and global scales. In: West JB, Bowen GJ, Dawson TE, Tu KP, editors. Isoscapes. Springer Netherlands; 2010. pp. 221–249.
- 51. Craine JM, Brookshire ENJ, Cramer MD, Hasselquist NJ, Koba K, Marin-Spiotta E, et al. Ecological interpretations of nitrogen isotope ratios of terrestrial plants and soils. Plant Soil. 2015;396: 1–26.
- 52. Grossiord C, Forner A, Gessler A, Granier A, Pollastrini M, Valladares F, et al. Influence of species interactions on transpiration of Mediterranean tree species during a summer drought. Eur J For Res. 2014;134: 365–376.
- 53. Yang Y, Siegwolf RTW, Körner C. Species specific and environment induced variation of δ13C and δ15N in alpine plants. Front Plant Sci. 2015;6.
- 54. Cernusak LA, Ubierna N, Winter K, Holtum JAM, Marshall JD, Farquhar GD. Environmental and physiological determinants of carbon isotope discrimination in terrestrial plants. New Phytol. 2013;200: 950–965.
- 55. Werner C, Zumkier U, Beyschlag W, Máguas C. High competitiveness of a resource demanding invasive acacia under low resource supply. Plant Ecol. 2010;206: 83–96.
- 56. Kulldorff M. A spatial scan statistic. Commun Stat—Theory Methods. 1997;26: 1481–1496.
- 57. Suzuki R, Shimodaira H. Pvclust: an R package for assessing the uncertainty in hierarchical clustering. Bioinformatics. 2006;22: 1540–1542. pmid:16595560
- 58. Marchante H, Marchante E, Freitas H. Invasion of the Portuguese dune ecosystems by the exotic species Acacia longifolia (Andrews) Willd.: effects at the community level. In: Child LE, Brock JH, Brundu G, Prach K, Pyšek P, Wade PM, et al., editors. Plant invasions: Ecological threats and management solutions. Leiden: Backhuys Publishers; 2003. pp. 75–85.
- 59. Marchante H, Marchante E, Freitas H, Hoffmann JH. Temporal changes in the impacts on plant communities of an invasive alien tree, Acacia longifolia. Plant Ecol. 2015;216: 1481–1498.
- 60. Barbier N, Couteron P, Lefever R, Deblauwe V, Lejeune O. Spatial decoupling of facilitation and competition at the origin of gapped vegetation patterns. Ecology. 2008;89: 1521–1531. pmid:18589517
- 61. Yannarell AC, Busby RR, Denight ML, Gebhart DL, Taylor SJ. Soil bacteria and fungi respond on different spatial scales to invasion by the legume Lespedeza cuneata. Front Microbiol. 2011;2: 127. pmid:21687434
- 62. Segoli M, Ungar ED, Giladi I, Arnon A, Shachak M. Untangling the positive and negative effects of shrubs on herbaceous vegetation in drylands. Landsc Ecol. 2012;27: 899–910.
- 63. Hegland SJ. Floral neighbourhood effects on pollination success in red clover are scale-dependent. Funct Ecol. 2014;28: 561–568.