Using resistance distance from circuit theory to model dispersal through habitat corridors

Using resistance distance from circuit theory to model dispersal through habitat corridors Abstract Aims Resistance distance (RD), based on circuit theory, is a promising metric for modelling effects of landscape configuration on dispersal of organisms and the resulting population and community patterns. The values of RD reflect the likelihood of a random walker to reach from a source to a certain destination in the landscape. Although it has successfully been used to model genetic structures of animal populations, where it most often outperforms other isolation metrics, there are hardly any applications to plants and, in particular, to plant community data. Our aims were to test if RD was a suitable metric for studying dispersal processes of plants in narrow habitat corridors (linear landscape elements [LLE]). This would be the case, if dispersal processes (seed dispersal and migration) resembled random walks. Further, we compared the model performance of RD against least-cost distance (LCD) and Euclidean distance (ED). Finally, we tested the suitability of different cost surfaces for calculations of LCD and RD. Methods We used data from 50 vegetation plots located on semi-natural LLE (field margins, ditches, road verges) in eight agricultural landscapes of Northwest Germany. We mapped LLE, including hedges and tree rows, from aerial images in a Geographic Information System, converted the maps into raster layers, and assigned resistance values to the raster cells, where all cells outside of LLE received infinite resistance and, thus, represented barriers to dispersal. For all pairs of plots within study areas, we calculated Jaccard similarity assuming that it was a proxy (or correlate) of dispersal events between plots. Further, we calculated RD and LCD of the network of LLE and ED between the plots. We modelled the effects of distance metrics on community similarity using binomial generalized linear mixed models. Important Findings ED was clearly the least suitable isolation metrics. Further, we found that RD performed better than LCD at modelling Jaccard similarity. Predictions varied markedly between the two distance metrics suggesting that RD comprises additional information about the landscape beyond spatial distance, such as the possible presence of multiple pathways between plots. Cost surfaces with equal cell-level resistances for all types of LLE performed better than more complex ones with habitat-specific resistances. We conclude that RD is a highly suitable measure of isolation or, inversely, connectivity for studying dispersal processes of plants within habitat corridors. It is likely also suitable for assessing landscape permeability in other landscape types with areal habitats instead of narrow corridors. RD holds the potential to improve assessments of isolation (or connectivity) for models of regional population and meta-community dynamics. connectivity, floristic similarity, isolation, landscape, migration, least-cost distance INTRODUCTION For a dispersing organism or propagule, the likelihood of reaching a certain location generally decreases with distance from the source (Hanski and Gilpin 1997). Hence, the Euclidean distance (ED) between two points or patches is a classical measure of their isolation from each other that may serve well in case the intervening landscape is uniformly suitable for dispersal (isolation by distance, Jenkins et al. 2010). However, in many cases the landscape in between habitats is heterogeneous, consisting of different land-cover or ecosystem types, which may vary considerably in how much they impede dispersal. Hence, dispersal of organisms between suitable habitats may strongly depend on the quality and structure of the landscape matrix (Prevedello and Vieira 2010; Storfer et al. 2010). Some types of areas may be absolute barriers for a given organism (e.g., mountain ranges, harsh environments), while others may allow for movement of individuals or dispersal of diaspores, and yet others may even serve as additional habitat (e.g., habitat corridors). Then, the shortest line between two points in the landscape may actually not be the most likely route of dispersal and, hence, indices based on ED may be poor predictors of dispersal likelihood or frequency (McRae 2006). Least-cost distance (LCD) is an established measure of isolation of habitats that only considers routes where movement or dispersal is possible (i.e., it excludes barriers) and, potentially, incorporates variable suitability for dispersal by assigning different cost values to different land-cover types (Adriaensen et al. 2003). However, LCD considers only one path between two points or patches, although there may often be several parallel routes. Theoretically, the likelihood of a random walker to reach from one point to another would increase linearly with the number of connecting paths (given equal length, width and quality; McRae et al. 2008). Hence, LCD may fail to capture the total likelihood of dispersal in cases where there are multiple connections between habitats (Fletcher et al. 2014; McRae and Beier 2007). Resistance distance (RD) based on circuit theory, also called ‘isolation by resistance’ or ‘effective resistance’, is a measure of isolation that considers both multiple connections and variable suitability of land-cover for dispersal (McRae 2006). Hence, it may be more appropriate than LCD for modelling dispersal-related processes in landscape settings with multiple pathways between habitat patches. Calculations of RD are based on raster maps where each cell is considered as a node in an electrical network that has a certain resistance. Low resistance values correspond to low cost of movement or dispersal through that cell, whereas high resistance represents high cost, and positive infinity represents absolute barriers. Then, it is possible to calculate the effective resistance between two points in the network, considering all serial and parallel lines between them, using Ohm’s law (McRae 2006). Regarding ecological interpretation, the values of effective resistance are linearly related with, e.g., equilibrium genetic differentiation of populations, while their inverses, i.e., effective conductance, are linearly related with effective migration, if the underlying dispersal process is essentially a random walk (McRae et al. 2008). The likelihood of dispersal between habitats affects patterns of populations and ecological communities, such as genetic distance, patch occupancy and taxonomic similarity (Thompson and Townsend 2006). Hence, such population or community patterns can be used as proxies of dispersal frequency to analyse the effect of landscape structure on the underlying dispersal processes, and to test the appropriateness of different isolation metrics and parameterisations of landscape-resistance surfaces for certain species or species groups (Spear et al. 2010; Zeller et al. 2012), if environmental variation is controlled for in the analysis. Although hitherto only few studies directly compared the performance of RD with other isolation metrics (Kershenbaum et al. 2014), there is evidence that RD may substantially outperform ED and LCD at modelling genetic distance of populations (e.g., McRae and Beier 2007; Kershenbaum et al. 2014). However, there are also some contradictory results. For instance, a continental-scale study of the wolverine (Gulo gulo) in North America found markedly better prediction of genetic differentiation when using RD as compared to LCD (McRae and Beier 2007), whereas another study of the same species, conducted at regional scale, found LCD to perform better (Schwartz et al. 2009). Yet other studies found only minor differences in the performance of LCD and RD, e.g., studying reptiles and amphibians at regional and landscape scale ( Moore et al. 2011; Row et al. 2010). Thus, there seems to be a high potential in the application of RD, but the relative performance of different measures of isolation appears to vary among types of organisms and scales, which calls for further comparative empirical testing. Numerous studies applied RD to model genetic distance of animal populations, but only few studies have tested its applicability and relative performance at modelling plants. RD performed better at modelling genetic distance of populations of American mahogany (Swietenia macrophylla) and Pitcher’s thistle (Cirsium pitcheri) compared to LCD (Fant et al. 2014; McRae and Beier 2007). Further, RD correlated stronger with genetic distance in studies of prairie sunflower (Helianthus petiolaris) and canyon live oak (Quercus chrysolepis) compared to ED (Andrew et al. 2012; Ortego et al. 2015). These studies were conducted at different scales from supra-regional (Central America, American mahogany) to landscape scale (Great Sand Dunes in Colorado, prairie sunflower), respectively. Another supra-regional study, conducted in coastal marshes, found RD to outperform LCD and ED with salt marsh grass (Puccinellia maritima), but there was no substantial difference between RD and LCD with sea arrowgrass (Triglochin maritima; Rouger and Jump 2014). Hence, there is some evidence that dispersal or migration processes of plants may reflect random walk and, thus, can be modelled using RD, but this does not seem to be true for all species, landscape types and spatial scales. Regarding the spatial arrangement of habitat, most previous studies were conducted in landscapes that represented patch mosaics, patch-corridor-matrix mosaics or the island-biogeographic model, but—to our knowledge—no study investigated landscapes that consisted exclusively of networks of narrow habitat corridors within an entirely inhospitable matrix. However, many agricultural landscapes worldwide are dominated by hostile environments to most species, e.g., arable fields, intensively used grasslands, while areas for dispersal or migration are often constrained to linear strips alongside field margins, roads or rivers. Classical connectivity measures are likely to fail in such landscape settings and, hence, we need a new method for modelling connectivity of the landscape matrix between core habitat areas or nature reserves in human-influenced landscapes. By far, the most studies that applied RD or LCD used genetic distance among populations as target variable in order to test their significance or predictive power. Indices of population genetic structure are often good proxies of functional connectivity or isolation (Boulet et al. 2007; Spear et al. 2010), but sampling and analysis effort put limits to their application when the aim is to study larger groups of species or whole communities. Taxonomic similarity of local communities may be an alternative for modelling dispersal processes. Generally, similarity will increase with the number of successful dispersal events between sites. This relationship is not linear because only dispersal of species that were previously limited to one of the compared communities will increase taxonomic similarity, while dispersal events of species already present in both communities are ignored. Nevertheless, transformations of similarity indices (in this study we used the logit of the Jaccard index) may show a sufficiently linear relationship with dispersal rate to investigate how landscape affects dispersal processes (see online supplementary Fig. S1). However, to our knowledge RD has not been tested on similarity of plant communities so far and only once on animal communities (aquatic invertebrates, Morán-Ordóñez et al. 2015). The main aim of our study was to test the applicability of RD, based on circuit theory, to modelling dispersal or migration of plants through habitat corridors in otherwise hostile landscape matrices using taxonomic similarity (Jaccard index) as a proxy of dispersal frequency. This comprises the questions whether dispersal and migration processes of plants generally reflect a random walk through the available corridor area and if, as a consequence, logit-transformed community similarity shows a near-linear relationship with RD. This can only be tested empirically. A further aim was to compare the performance of RD, LCD and ED at predicting community similarity and, hence, dispersal likelihood. Moreover, we also compared different parameterizations of cost/resistance surfaces for the modelling of isolation using both equal resistance values for all types of corridors and specific resistances that supposedly reflected availability of suitable microhabitats within different corridor types. Finally, we tested the performance of isolation metrics for species groups with different dispersal abilities (short versus long-distance dispersed species) because species with limited dispersal can be expected to react more strongly to spatial isolation (Thompson and Townsend 2006). MATERIALS AND METHODS Study areas and field work The study was carried out in eight study areas, each 1 km2, in Northwest Germany (see online supplementary Table S1). The regional climate is temperate oceanic with average annual temperature of around 10°C and annual precipitation around 800 mm (period 1981–2000; Klimaatlas Nordrhein-Westfalen, http://www.klimaatlas.nrw.de). The landform of the study areas is mostly plain at altitudes between 40 and 80 m.a.s.l., but slightly hilly in the southernmost area at 200–220 m.a.s.l. Soils of the study areas are sandy in the western and northeastern part of the study region, loamy in the central part and loess dominated in the southern part, but always lime-free. The landscapes of the region are characterized by intensive agricultural land use and conversion of permanent grassland to arable land since the 1960s and particularly during the last 15 years. The few remaining grassland parcels are mown four to six times per year and, thus, are no suitable habitat for almost all of the typical grassland plant species. Hence, the agricultural landscape matrix is a hostile environment for virtually all plant species except for some ruderal annuals and few extremely mowing tolerant species (e.g., Lolium multiflorum Lam., L. perenne L., Trifolium repens L.). The density of linear landscape elements (LLE)—hedges, tree rows, field margins, ditches—that serve as habitat corridors for plant species is comparatively high in some parts of the study region, but low in others. Hence, there is a marked density gradient of LLE and a high variation of their areal proportions between 2.5% and 10% of the total area among study areas. The locations of the study areas were selected by random points using Geographic Information System (GIS). We wanted the study areas to represent the prevailing agricultural landscapes of the region and, hence, excluded larger settlements, extensive forests, lakes, rivers and areas of markedly different geology from the random sampling based on Corine Land Cover (http://www.eea.europa.eu/publications/COR0-landcover) and general soil maps. In each study area, we selected 5–8 plots that were randomly located in open (treeless) LLE stratified by two classes (field margins, including road verges, and ditches) using random points in GIS with a minimum distance of 100 m between them. All LLE that were at least 2 m wide were considered for random sampling, whereas narrower ones were excluded. Variation in the number of plots per study area occurred because some plots were disturbed by maintenance measures or access was forbidden by land owners. Vegetation sampling was conducted according to the Braun-Blanquet method using elongated plots of 1 × 25 m2 due to the narrow shape of the LLE. We recorded all vascular plant species of the herb layer in spring and in summer of 2012. The total number of vegetation plots was 50. The plant communities of field margins belonged to mesic ruderal grasslands (order Arrhenatheretalia; Ellenberg 2009) with some species typical of nitrophilous tall-herb stands (order Glechometalia) and had on average 22.6 species (SD ± 7.6) per 25 m2. Ditches contained plant assemblages intermediate between mesic (Arrhenatheretalia) and wet grasslands (Molinietalia) with some species typical of fens and marshes and had a mean species richness of 24.6 (SD ± 10.6). Calculation of community similarity We calculated the unweighted Jaccard similarity index for all possible pairs of plots within each study area. Additionally, we calculated Jaccard indices using only species with limited dispersal capabilities, here referred to as “short-distance dispersal” and, likewise, only those with long-distance dispersal mechanisms in order to test for differential response of these dispersal trait groups to isolation. The group of “short-distance dispersal” comprised those species with unspecific dispersal syndrome (mostly barochorous), capsules shedding seeds, and with only aquatic dispersal, whereas “long- distance dispersal” included species with epizoochory and endozoochory and with wind-dispersal by pappi or due to minute seeds according to Hodgson et al. (1995). Calculations of isolation metrics LLE were mapped from aerial images in GIS within the core study areas (1 km2) plus a buffer zone of 500 m in order to avoid boundary effects that may bias estimates of landscape resistance (Koen 2010). We discerned different categories of LLE: tracks between fields, field margins, hedges/tree rows and ditches with or without shading (Fig. 1A). The maps were rasterized at 1-m resolution and we assigned a conductivity value between >0 and 100 to all cells representing LLE, whereas cells representing the agricultural landscape matrix received zero. We used two variants of conductivity surfaces for calculating LCD and RD: (i) all cells located on LLE received an equal conductivity value of 100 and (ii) different LLE categories received different habitat-specific conductivity values. For calculations of RD, the conductivity values were converted to resistances (R = 1/conductivity) that were also used as cost values for calculating LCD. Figure 1: View largeDownload slide configuration, classification and parameterization of linear landscape elements (LLE) for calculation of least-cost and resistance distance. (A): vector map of a section of one study area (‘Osterbauerschaft’). (B): corresponding raster map with habitat-specific cell-level resistances (costs) for calculation of least-cost and resistance distance. LLE were buffered by 5 m on both sides in order to close small gaps due to roads or lengthwise interruptions. Buffers and, thus, filled gaps received doubled resistance. Figure 1: View largeDownload slide configuration, classification and parameterization of linear landscape elements (LLE) for calculation of least-cost and resistance distance. (A): vector map of a section of one study area (‘Osterbauerschaft’). (B): corresponding raster map with habitat-specific cell-level resistances (costs) for calculation of least-cost and resistance distance. LLE were buffered by 5 m on both sides in order to close small gaps due to roads or lengthwise interruptions. Buffers and, thus, filled gaps received doubled resistance. RD was calculated as the effective resistance of LLE raster cells between two points (in this case plots) considering all serial and parallel connections among raster cells based on Ohm’s law (McRae et al. 2008) where the total resistance of resistors in series is the sum of single resistors,  Rtotal=R1+R2+…+Rn and the total resistance of resistors in parallel is the sum of the reciprocals of single resistors,  1Rtotal=1R1+1R2+…+1Rn LCD was calculated as the sum of cost values (R; the same as the resistance values, in this study) of all LLE raster cells located on the shortest path between the two points, i.e.,  LCD=∑i=1nRi We calculated both LCD and RD between the plots within each study area using the python console of QGIS 2.6 (QGIS Development Team 2014) with the GRASS-GIS function ‘r.cost’, and the plugin ‘Circuitscape for Processing 0.1.1’ (https://github.com/alexbruy/processing_circuitscape), respectively. The suitability of LLE types for dispersal/migration of species may vary. For instance, species of open habitats may more readily disperse/migrate through field margins compared to narrow edges alongside hedges or tree rows. Therefore, we used conductivity values in the range of >0 to 100 that were scaled to the estimated percentage of suitable microhabitat for light-demanding plant species within the LLE. For instance, hedge rows received a cell-level conductivity of 25 because ~25% of their area consisted of grass or tall-herb dominated strips on their edges. These conductivity values were meant to represent the putative suitability of the LLE categories for dispersal or migration based on expert opinion. The corresponding resistance values were used to calculate variants of LCD and RD with habitat-specific costs or resistances, respectively (Fig. 1B; see online supplementary Table S2). Small gaps between LLE (i.e., cells with zero conductivity) are a practical problem for calculating LCD and RD, because they result in missing values or infinite resistance, respectively, thus only reflecting that there is no connection. However, gap sizes of few meters will not be effective dispersal barriers for most species. Thus, small gaps need to be closed in order to enable the calculations. Here, we assumed that gaps of up to 10 m can be passed even by short-distance dispersed species. Hence, we buffered the LLE with a radius of 5 m and used the gross area (LLE + buffer) for the calculations. We tested two variants of conductivity for the raster cells that were located on LLE buffers (i.e., outside of the real LLE): (i) buffer cells received the same conductivity value as the adjacent LLE and (ii) buffers and, thus, small gaps received only half the conductivity. Statistical analyses We modelled the relationship between Jaccard similarity of plot pairs and ED, LCD or RD with generalized linear mixed models (GLMM) using the function ‘glmer’ of the package ‘lme4 1.1–9’ in R 3.2.3 (R Core Team 2015). We used the binomial distribution with logit link because Jaccard indices are proportion data. The GLMM included fixed effects of one of the variants of distance metrics and of the LLE types that were compared (three levels: field margin with field margin, field margin with ditch and ditch with ditch) in order to take differences in environmental conditions and plant community composition into account. Due to the nested design of the study, the GLMM included a random intercept of ‘study area’ (eight levels). Additionally, we included an observation-level (‘plot pair’) random effect in order to account for overdispersion in the data (Agresti 2002, sec. 13.5; http://glmm.wikidot.com/faq). The total number of plot pairs was 136, but we omitted four plot pairs that were not connected by LLE, so that the final sample size was 132. Distance metrics were z-transformed (centred and scaled) in order to get standardized regression coefficients. The significance of the fixed effects was tested with parametric bootstraps (1000 resamples) because each plot was involved in several plot pairs and, thus, the Jaccard-index values were not independent. The assumption of linearity of the relationship between the response (on logit scale) and the predictor was validated using the ‘cumres’ function of the R package ‘gof 0.9.1’. As ‘cumres’ does not work with GLMM, we calculated GLMs with the same fixed effects and additional fixed effects of study area (but without observation-level effects) for each GLMM. There was no case of significant deviation from linearity. In order to test if the model fits of different isolation metrics were significantly different, we conducted Vuong tests (Vuong 1989) using the function ‘vuongtest’ from the ‘nonnest2’ package (Merkle and You 2016). For this purpose, we also used the GLM because the Vuong test cannot be conducted with GLMM. RESULTS LCD and RD were significantly correlated (P < 0.001) with Pearson coefficients of 0.76 for variants with equal as well as LLE-type specific cell-level resistances. Both metrics were significantly correlated with ED (all P values < 0.001) with LCD showing correlation coefficients of 0.75 and 0.71 for variants with equal and habitat-specific costs, while RD showed coefficients of 0.48 and 0.54, respectively. All three isolation metrics showed a significant linear relationship with logits of Jaccard similarity of vegetation plots throughout all variants of parameterisation of cost/resistance surfaces (Table 1; for detailed model output see online supplementary Tables S4–S13). In general, variants of LCD and RD that were calculated with halved conductivities for gaps (<10 m) fit better to the data than those calculated with full connectivity of gaps. Hence, the following results refer to the variants with reduced gap connectivity, while the others can be found in the online supplementary Table S3. LCD and RD showed lower Akaike’s information criterion (AIC) values than ED (Table 1). Several variants of LCD and RD had a significantly better model fit than ED, in particular those with equal cost/resistance values (Table 2). All variants of RD performed significantly better than ED, whereas LCD with habitat-specific cost values did not (Table 2). When using all species in Jaccard calculations, the performances of LCD and RD were similar with regard to AIC values (δAIC for RD compared to LCD of +0.2 and −0.7 for equal and habitat-specific resistance values, respectively; Table 1), and the differences in model fit between these two metrics were not significant (Table 2). However, when using only short-distance dispersed plant species, RD performed consistently better than LCD (δAIC −1.4 and −2.1; Table 1; Fig. 2). The better model fit of RD was marginally significant with both equal and habitat-specific resistance values (P values of 0.08; Table 2). In contrast, long-distance dispersed species showed no significant effect of isolation regardless of isolation metric. Table 1: modelling results for Euclidean, least-cost and resistance distance Isolation metric  Regression coefficient (B)  Standard error of B  AIC  P (bootstrap)  Jaccard similarity calculated with all species   Euclidean distance  −0.146  0.082  850.8  0.013   Least-cost distance (equal cost)  −0.253  0.083  845.2  <0.001   Resistance distance (equal resistance)  −0.289  0.096  845.4  <0.001   Least-cost distance (habitat-specific cost)  −0.218  0.088  848.0  <0.001   Resistance distance (habitat-specific resistance)  −0.242  0.092  847.3  0.003  Jaccard similarity calculated with short-distance dispersed species   Euclidean distance  −0.252  0.124  899.3  0.011   Least-cost distance (equal cost)  −0.374  0.128  895.0  <0.001   Resistance distance (equal resistance)  −0.464  0.149  893.6  <0.001   Least-cost distance (habitat-specific cost)  −0.326  0.133  897.3  <0.001   Resistance distance (habitat-specific resistance)  −0.399  0.141  895.2  <0.001  Isolation metric  Regression coefficient (B)  Standard error of B  AIC  P (bootstrap)  Jaccard similarity calculated with all species   Euclidean distance  −0.146  0.082  850.8  0.013   Least-cost distance (equal cost)  −0.253  0.083  845.2  <0.001   Resistance distance (equal resistance)  −0.289  0.096  845.4  <0.001   Least-cost distance (habitat-specific cost)  −0.218  0.088  848.0  <0.001   Resistance distance (habitat-specific resistance)  −0.242  0.092  847.3  0.003  Jaccard similarity calculated with short-distance dispersed species   Euclidean distance  −0.252  0.124  899.3  0.011   Least-cost distance (equal cost)  −0.374  0.128  895.0  <0.001   Resistance distance (equal resistance)  −0.464  0.149  893.6  <0.001   Least-cost distance (habitat-specific cost)  −0.326  0.133  897.3  <0.001   Resistance distance (habitat-specific resistance)  −0.399  0.141  895.2  <0.001  The latter two were calculated with equal and habitat-specific cell-level resistances or costs, respectively. Each line represents one separate generalized linear mixed model. The dependent variable was Jaccard similarity calculated with all vascular plant species or with only short-distance dispersed species. For calculations of isolation metrics, small gaps between linear landscape elements (LLE) were closed by buffers of 5 m width that received doubled cell-level resistances compared to the adjacent LLE. Regression coefficients refer to standardized (z-transformed) values of isolation indices. P values from parametric bootstrap with 1000 resamples. Abbreviation: AIC = Akaike’s information criterion. View Large Table 2: pairwise tests of model fit (Vuong tests) of competing generalized linear models of Jaccard similarity that used different isolation metrics (Euclidean, least-cost and resistance distance) in the predictors, but otherwise the same model setup Models compared  Z  P  Jaccard similarity calculated with all species   Euclidean versus least-cost distance (equal cost)  −2.184  0.015   Euclidean versus resistance distance (equal resistance)  −2.071  0.019   Least-cost versus resistance distance (equal cost/resistance)  −0.904  0.183   Euclidean versus least-cost distance (habitat-specific cost)  −1.317  0.094   Euclidean versus resistance distance (habitat-specific resistance)  −1.750  0.040   Least-cost versus resistance distance (habitat-specific cost/resistance)  −1.128  0.130  Jaccard similarity calculated with short-distance dispersed species   Euclidean versus least-cost distance (equal cost)  −1.605  0.054   Euclidean versus resistance distance (equal resistance)  −1.927  0.027   Least-cost versus resistance distance (equal cost/ resistance)  −1.386  0.083   Euclidean versus least-cost distance (habitat-specific cost)  −1.086  0.139   Euclidean versus resistance distance (habitat-specific resistance)  −1.712  0.043   Least-cost versus resistance distance (habitat-specific cost/resistance)  −1.403  0.080  Models compared  Z  P  Jaccard similarity calculated with all species   Euclidean versus least-cost distance (equal cost)  −2.184  0.015   Euclidean versus resistance distance (equal resistance)  −2.071  0.019   Least-cost versus resistance distance (equal cost/resistance)  −0.904  0.183   Euclidean versus least-cost distance (habitat-specific cost)  −1.317  0.094   Euclidean versus resistance distance (habitat-specific resistance)  −1.750  0.040   Least-cost versus resistance distance (habitat-specific cost/resistance)  −1.128  0.130  Jaccard similarity calculated with short-distance dispersed species   Euclidean versus least-cost distance (equal cost)  −1.605  0.054   Euclidean versus resistance distance (equal resistance)  −1.927  0.027   Least-cost versus resistance distance (equal cost/ resistance)  −1.386  0.083   Euclidean versus least-cost distance (habitat-specific cost)  −1.086  0.139   Euclidean versus resistance distance (habitat-specific resistance)  −1.712  0.043   Least-cost versus resistance distance (habitat-specific cost/resistance)  −1.403  0.080  Each row represents a test of two competing models. P values below 0.05 indicate that the second model fitted significantly better. Least-cost and resistance distance were calculated with equal and habitat-specific cell-level resistances or costs. Jaccard similarity was calculated using all plant species or only short-distance dispersed species. View Large Figure 2: View largeDownload slide Jaccard similarity vs. (A) least-cost distance and (B) resistance distance of pairs of vegetation plots located on linear landscape elements (LLE). Jaccard similarity was calculated using only species with short-distance dispersal. Both isolation metrics were calculated using resistance surfaces with equal cell-level resistance for all types of LLE, but with doubled resistance for small gaps (<10 m). Prediction curves were calculated with generalized linear mixed models (see Table 1). AIC: Akaike’s Information Criterion; B: standardized regression coefficient for least-cost or resistance distance; P: p-value from parametric bootstrap of the model. Open circles: comparisons of two field margins; black circles: two ditches; grey circles: field margin and ditch. Figure 2: View largeDownload slide Jaccard similarity vs. (A) least-cost distance and (B) resistance distance of pairs of vegetation plots located on linear landscape elements (LLE). Jaccard similarity was calculated using only species with short-distance dispersal. Both isolation metrics were calculated using resistance surfaces with equal cell-level resistance for all types of LLE, but with doubled resistance for small gaps (<10 m). Prediction curves were calculated with generalized linear mixed models (see Table 1). AIC: Akaike’s Information Criterion; B: standardized regression coefficient for least-cost or resistance distance; P: p-value from parametric bootstrap of the model. Open circles: comparisons of two field margins; black circles: two ditches; grey circles: field margin and ditch. RD always had larger standardized regression coefficients and, thus, a stronger ‘effect’ on Jaccard similarity compared to LCD with all species and with short-distance dispersed species. Plots pairs with similar LCD could vary markedly in RD. At low RD, i.e., high density of LLE with multiple connections between plots, predicted floristic similarity was higher when using RD compared to LCD. At high RD, this pattern was reversed (Fig. 3). Figure 3: View largeDownload slide maps of current through linear landscape elements (LLE) between pairs of vegetation plots (circles). Grey-scale colours represent the strength of current (in Ampere) which was calculated based on circuit theory using the software ‘Circuitscape for Processing’. Stronger current indicates a higher likelihood of an organism or propagule to pass through the respective cell based on the assumption of random movement. Least-cost distances are similar in both examples, but resistance distances are markedly different. (A) Low resistance distance due to high density of LLE with several connections between the plots. (B) High resistance distance. While expected floristic similarity of plots (Jaccard index) was the same when using least-cost distance as predictor, resistance distance yielded substantially higher or lower predictions depending on the density of the LLE network. Figure 3: View largeDownload slide maps of current through linear landscape elements (LLE) between pairs of vegetation plots (circles). Grey-scale colours represent the strength of current (in Ampere) which was calculated based on circuit theory using the software ‘Circuitscape for Processing’. Stronger current indicates a higher likelihood of an organism or propagule to pass through the respective cell based on the assumption of random movement. Least-cost distances are similar in both examples, but resistance distances are markedly different. (A) Low resistance distance due to high density of LLE with several connections between the plots. (B) High resistance distance. While expected floristic similarity of plots (Jaccard index) was the same when using least-cost distance as predictor, resistance distance yielded substantially higher or lower predictions depending on the density of the LLE network. Variants of distance metrics with specific cell-level resistances for each LLE type (see online supplementary Table S2) performed worse regarding AIC values and effect estimates compared to equal resistances (Table 1). DISCUSSION Isolation measures that consider the spatial configuration of LLE, such as LCD and RD, are more suitable than ED to model dispersal-related processes between habitat patches connected by LLE or between different points in the LLE network. This is in line with several studies that showed ED to perform rather poorly at modelling population processes in situations where the landscape matrix between patches or populations contains barriers as well as additional (suboptimal) habitat, or different densities of habitat and dispersal corridors (e.g., Andrew et al. 2012; Bani et al. 2015; Coulon et al. 2015; Fant et al. 2014; Morán-Ordóñez et al. 2015; Ortego et al. 2015). Further, RD performs better than LCD in predicting floristic similarity (Jaccard index) of vegetation stands in networks of habitat corridors, particularly with respect to short-distance dispersed species. This likely reflects the possibility of dispersal or migration of plants between two points in the network along multiple pathways which are ignored by LCD. The differences in AIC values between LCD and RD were <2 for variants with equal resistances and 2.1 for variants with habitat-specific resistances in this empirical test (Table 1; Fig. 2), and the differences in model fit were only marginally significant (Table 2). Hence, it could be argued that LCD does not perform substantially worse and might be sufficient for modelling dispersal-related processes of plant species in corridors. However, we advocate that RD is the superior isolation measure for two reasons: (i) it captures more variation in the community data and its predictions differ substantially from those of LCD, if corridor density deviates from the average (Fig. 3) and (ii) it can account for multiple sources of dispersing organisms, if the connectivity of habitat patches to (multiple) neighbouring patches is to be modelled which is likely the most prevalent application in science and conservation planning. In our study landscapes, dispersal of species was severely constrained to the narrow LLE, whereas the landscape matrix did not serve as potential habitat for most of the species. Many plot pairs were connected by one comparatively short direct LLE corridor and had just few additional connections with substantially longer travel path that probably contributed only a moderate proportion of dispersal events among the plots. In such situations, LCD could be expected to be an almost equally good predictor as RD (Row et al. 2010). Nevertheless, we could show that RD is likely better than LCD at modelling community processes of dispersal limited plant species, even if dispersal is constrained to a small number of narrow corridors. All of the few studies that applied isolation metrics based on circuit theory to plant species found that RD was better or as good as other measures in a large range of landscape types (contiguous to highly fragmented habitat) and spatial scales (landscape to continental; Andrew et al. 2012; Fant et al. 2014; McRae and Beier 2007; Ortego et al. 2015; Rouger and Jump 2014). Therefore, it is surprising that this approach has not been used more often in studies of plants’ population genetics, distribution and diversity. Current evidence suggests that migration of plant species over several generations may well resemble random walk that is an implicit assumption of RD based on circuit theory. Thus, there seems to be a high potential to apply this method in future research on plant populations and meta-communities. There is also a marked shortage of applications of circuit theory to community-level patterns, such as taxonomic similarity, regarding both animals and plants. We know of only one study on aquatic invertebrates that detected significant influence of landscape structure on community similarity using RD and, further, could show that dispersal trait groups reacted differently to landscape patterns (Morán-Ordóñez et al. 2015). Taxonomic similarity may not be the most accurate proxy of dispersal rates, but it has got the advantage of easy data acquisition and the possibility to simultaneously study all species or to compare different trait groups of species within the same study system. In agreement with other studies (Morán-Ordóñez et al. 2015; Thompson and Townsend 2006), we found strong effects of isolation on short-distance dispersed species, whereas long-distance dispersed species were unaffected. Thus, it is necessary to extend studies on the effects of landscape structure on dispersal-related processes from populations to entire communities, and to search for trait groups with similar response in order to build differentiated quantitative theories. The use of community data in combination with RD will strongly facilitate this endeavour. When the landscape under study comprises different types of habitats or landscape elements, such as field margins, ditches and hedges, it would be a reasonable assumption that resistances to dispersal (or migration) vary among these types. For instance, a hedgerow offers only narrow edges as suitable habitat for light-demanding plant species (as studied here) and, thus, the likelihood of dispersal or migration may be lower compared to field margins. Consequently, we hypothesized that variants of isolation metrics with specific cell-level resistances would perform better than equal resistances. However, we found the opposite pattern in this study. The specific resistance values that we applied (see online supplementary Table S2) were expert opinions based on the estimated area proportion of suitable microhabitat for open-country species. For example, hedge rows received ~4 times higher resistance than open field margins (0.040 versus 0.011) as we supposed that only about a quarter of the total hedge strip would be suitable edge habitat. The fact that LCD and RD with habitat-specific cost/resistance values performed less well than equal cost/resistance, suggests that resistance is not linearly related to the area proportion of suitable microhabitat for open-country plant species in LLE. Reasons for this may lie in wrong estimates of average cover percentages of suitable microhabitat, which we deem unlikely, or marked variability of those percentages within LLE habitat types which, however, we did not notice in the field. In any case, the spatial configuration of microhabitat within LLE may play an important role. For instance, our parameterization of hedges yielded a 4-fold increase of resistance compared to the equal cost/resistance variants. But if we had set the edges of the hedge to conductivity of 100, while considering the interior of the hedge as barrier, the increase in total resistance of the hedge would have been much stronger due to the lack of lateral connections between the two edges. Therefore, the fine-scale spatial configuration of microsites within habitat corridors may be an important point to tackle in future studies. Resistance surfaces based on expert opinion do not always perform well (Beier et al. 2008; Shirk et al. 2015), but there are several approaches to estimate and to validate resistance models using empirical data that may substantially improve model performance (Peterman et al. 2014; Shirk et al. 2010; Zeller et al. 2012). Hence, empirical modelling of habitat-specific resistances may hold potential to further improve models of dispersal-related processes in corridors of variable quality. Another advantage of RD is its flexibility to cope with many different kinds of landscapes (i.a., patch mosaic, patch-corridor-matrix mosaic, habitat networks) as long as there are any connections between the plots or patches under study. For instance, RD can be used to assess the likelihood of dispersal into patches that are connected to multiple source patches through corridor networks which cannot be done using either LCD or classical connectivity metrics, such as the proximity index and similar ones. In conclusion, RD is more suitable than LCD for modelling the effect of connectivity, or landscape permeability, on dispersal of plant (and animal) species in a great variety of landscape types, from patch mosaics to situations where the landscape matrix predominantly consists of hostile environment. There is a high potential in using RD in combination with easily acquired plant community data, such as simple species lists, in order to quantify the relationship between isolation or, inversely, connectivity and dispersal for all species or for different trait groups in an ecosystem simultaneously. In this way, this methodological approach can help to build a coherent framework of quantitative theory, to enhance models of regional population and meta-community dynamics and to improve the theoretical basis of corridor and habitat connectivity planning. SUPPLEMENTARY MATERIAL Supplementary data are available at Journal of Plant Ecology online. AUTHOR CONTRIBUTIONS JT, SB and JS conceived and designed the study. JT and JS conducted the field work. JT analysed the data and wrote the manuscript. SB and JS provided editorial advice. ACKNOWLEDGEMENTS We thank Simon Kellner, Henrike Ruhmann and Alexander Terstegge for their help in the field work and Bo Markussen for statistical advice. We also thank Alexander Bruy for developing the QGIS plugin ‘Circuitscape for Processing’ that we used for calculating resistance distances. Last but not least, we thank two anonymous referees for their helpful comments on an earlier version of this paper. Conflict of interest statement. None declared. REFERENCES Adriaensen F Chardon JP De Blust Get al.  ( 2003) The application of ‘least-cost’ modelling as a functional landscape model. Landsc Urban Plan  64: 233– 47. Google Scholar CrossRef Search ADS   Agresti A( 2002) Categorical Data Analysis, 2nd edn . Hoboken, NJ: Wiley. Google Scholar CrossRef Search ADS   Andrew RL Ostevik KL Ebert DPet al.  ( 2012) Adaptation with gene flow across the landscape in a dune sunflower. Mol Ecol  21: 2078– 91. Google Scholar CrossRef Search ADS PubMed  Bani L Pisa G Luppi Met al.  ( 2015) Ecological connectivity assessment in a strongly structured fire salamander (Salamandra salamandra) population. Ecol Evol  5: 3472– 85. 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Using resistance distance from circuit theory to model dispersal through habitat corridors

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© The Author(s) 2017. Published by Oxford University Press on behalf of the Institute of Botany, Chinese Academy of Sciences and the Botanical Society of China. All rights reserved. For permissions, please email: journals.permissions@oup.com
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Abstract

Abstract Aims Resistance distance (RD), based on circuit theory, is a promising metric for modelling effects of landscape configuration on dispersal of organisms and the resulting population and community patterns. The values of RD reflect the likelihood of a random walker to reach from a source to a certain destination in the landscape. Although it has successfully been used to model genetic structures of animal populations, where it most often outperforms other isolation metrics, there are hardly any applications to plants and, in particular, to plant community data. Our aims were to test if RD was a suitable metric for studying dispersal processes of plants in narrow habitat corridors (linear landscape elements [LLE]). This would be the case, if dispersal processes (seed dispersal and migration) resembled random walks. Further, we compared the model performance of RD against least-cost distance (LCD) and Euclidean distance (ED). Finally, we tested the suitability of different cost surfaces for calculations of LCD and RD. Methods We used data from 50 vegetation plots located on semi-natural LLE (field margins, ditches, road verges) in eight agricultural landscapes of Northwest Germany. We mapped LLE, including hedges and tree rows, from aerial images in a Geographic Information System, converted the maps into raster layers, and assigned resistance values to the raster cells, where all cells outside of LLE received infinite resistance and, thus, represented barriers to dispersal. For all pairs of plots within study areas, we calculated Jaccard similarity assuming that it was a proxy (or correlate) of dispersal events between plots. Further, we calculated RD and LCD of the network of LLE and ED between the plots. We modelled the effects of distance metrics on community similarity using binomial generalized linear mixed models. Important Findings ED was clearly the least suitable isolation metrics. Further, we found that RD performed better than LCD at modelling Jaccard similarity. Predictions varied markedly between the two distance metrics suggesting that RD comprises additional information about the landscape beyond spatial distance, such as the possible presence of multiple pathways between plots. Cost surfaces with equal cell-level resistances for all types of LLE performed better than more complex ones with habitat-specific resistances. We conclude that RD is a highly suitable measure of isolation or, inversely, connectivity for studying dispersal processes of plants within habitat corridors. It is likely also suitable for assessing landscape permeability in other landscape types with areal habitats instead of narrow corridors. RD holds the potential to improve assessments of isolation (or connectivity) for models of regional population and meta-community dynamics. connectivity, floristic similarity, isolation, landscape, migration, least-cost distance INTRODUCTION For a dispersing organism or propagule, the likelihood of reaching a certain location generally decreases with distance from the source (Hanski and Gilpin 1997). Hence, the Euclidean distance (ED) between two points or patches is a classical measure of their isolation from each other that may serve well in case the intervening landscape is uniformly suitable for dispersal (isolation by distance, Jenkins et al. 2010). However, in many cases the landscape in between habitats is heterogeneous, consisting of different land-cover or ecosystem types, which may vary considerably in how much they impede dispersal. Hence, dispersal of organisms between suitable habitats may strongly depend on the quality and structure of the landscape matrix (Prevedello and Vieira 2010; Storfer et al. 2010). Some types of areas may be absolute barriers for a given organism (e.g., mountain ranges, harsh environments), while others may allow for movement of individuals or dispersal of diaspores, and yet others may even serve as additional habitat (e.g., habitat corridors). Then, the shortest line between two points in the landscape may actually not be the most likely route of dispersal and, hence, indices based on ED may be poor predictors of dispersal likelihood or frequency (McRae 2006). Least-cost distance (LCD) is an established measure of isolation of habitats that only considers routes where movement or dispersal is possible (i.e., it excludes barriers) and, potentially, incorporates variable suitability for dispersal by assigning different cost values to different land-cover types (Adriaensen et al. 2003). However, LCD considers only one path between two points or patches, although there may often be several parallel routes. Theoretically, the likelihood of a random walker to reach from one point to another would increase linearly with the number of connecting paths (given equal length, width and quality; McRae et al. 2008). Hence, LCD may fail to capture the total likelihood of dispersal in cases where there are multiple connections between habitats (Fletcher et al. 2014; McRae and Beier 2007). Resistance distance (RD) based on circuit theory, also called ‘isolation by resistance’ or ‘effective resistance’, is a measure of isolation that considers both multiple connections and variable suitability of land-cover for dispersal (McRae 2006). Hence, it may be more appropriate than LCD for modelling dispersal-related processes in landscape settings with multiple pathways between habitat patches. Calculations of RD are based on raster maps where each cell is considered as a node in an electrical network that has a certain resistance. Low resistance values correspond to low cost of movement or dispersal through that cell, whereas high resistance represents high cost, and positive infinity represents absolute barriers. Then, it is possible to calculate the effective resistance between two points in the network, considering all serial and parallel lines between them, using Ohm’s law (McRae 2006). Regarding ecological interpretation, the values of effective resistance are linearly related with, e.g., equilibrium genetic differentiation of populations, while their inverses, i.e., effective conductance, are linearly related with effective migration, if the underlying dispersal process is essentially a random walk (McRae et al. 2008). The likelihood of dispersal between habitats affects patterns of populations and ecological communities, such as genetic distance, patch occupancy and taxonomic similarity (Thompson and Townsend 2006). Hence, such population or community patterns can be used as proxies of dispersal frequency to analyse the effect of landscape structure on the underlying dispersal processes, and to test the appropriateness of different isolation metrics and parameterisations of landscape-resistance surfaces for certain species or species groups (Spear et al. 2010; Zeller et al. 2012), if environmental variation is controlled for in the analysis. Although hitherto only few studies directly compared the performance of RD with other isolation metrics (Kershenbaum et al. 2014), there is evidence that RD may substantially outperform ED and LCD at modelling genetic distance of populations (e.g., McRae and Beier 2007; Kershenbaum et al. 2014). However, there are also some contradictory results. For instance, a continental-scale study of the wolverine (Gulo gulo) in North America found markedly better prediction of genetic differentiation when using RD as compared to LCD (McRae and Beier 2007), whereas another study of the same species, conducted at regional scale, found LCD to perform better (Schwartz et al. 2009). Yet other studies found only minor differences in the performance of LCD and RD, e.g., studying reptiles and amphibians at regional and landscape scale ( Moore et al. 2011; Row et al. 2010). Thus, there seems to be a high potential in the application of RD, but the relative performance of different measures of isolation appears to vary among types of organisms and scales, which calls for further comparative empirical testing. Numerous studies applied RD to model genetic distance of animal populations, but only few studies have tested its applicability and relative performance at modelling plants. RD performed better at modelling genetic distance of populations of American mahogany (Swietenia macrophylla) and Pitcher’s thistle (Cirsium pitcheri) compared to LCD (Fant et al. 2014; McRae and Beier 2007). Further, RD correlated stronger with genetic distance in studies of prairie sunflower (Helianthus petiolaris) and canyon live oak (Quercus chrysolepis) compared to ED (Andrew et al. 2012; Ortego et al. 2015). These studies were conducted at different scales from supra-regional (Central America, American mahogany) to landscape scale (Great Sand Dunes in Colorado, prairie sunflower), respectively. Another supra-regional study, conducted in coastal marshes, found RD to outperform LCD and ED with salt marsh grass (Puccinellia maritima), but there was no substantial difference between RD and LCD with sea arrowgrass (Triglochin maritima; Rouger and Jump 2014). Hence, there is some evidence that dispersal or migration processes of plants may reflect random walk and, thus, can be modelled using RD, but this does not seem to be true for all species, landscape types and spatial scales. Regarding the spatial arrangement of habitat, most previous studies were conducted in landscapes that represented patch mosaics, patch-corridor-matrix mosaics or the island-biogeographic model, but—to our knowledge—no study investigated landscapes that consisted exclusively of networks of narrow habitat corridors within an entirely inhospitable matrix. However, many agricultural landscapes worldwide are dominated by hostile environments to most species, e.g., arable fields, intensively used grasslands, while areas for dispersal or migration are often constrained to linear strips alongside field margins, roads or rivers. Classical connectivity measures are likely to fail in such landscape settings and, hence, we need a new method for modelling connectivity of the landscape matrix between core habitat areas or nature reserves in human-influenced landscapes. By far, the most studies that applied RD or LCD used genetic distance among populations as target variable in order to test their significance or predictive power. Indices of population genetic structure are often good proxies of functional connectivity or isolation (Boulet et al. 2007; Spear et al. 2010), but sampling and analysis effort put limits to their application when the aim is to study larger groups of species or whole communities. Taxonomic similarity of local communities may be an alternative for modelling dispersal processes. Generally, similarity will increase with the number of successful dispersal events between sites. This relationship is not linear because only dispersal of species that were previously limited to one of the compared communities will increase taxonomic similarity, while dispersal events of species already present in both communities are ignored. Nevertheless, transformations of similarity indices (in this study we used the logit of the Jaccard index) may show a sufficiently linear relationship with dispersal rate to investigate how landscape affects dispersal processes (see online supplementary Fig. S1). However, to our knowledge RD has not been tested on similarity of plant communities so far and only once on animal communities (aquatic invertebrates, Morán-Ordóñez et al. 2015). The main aim of our study was to test the applicability of RD, based on circuit theory, to modelling dispersal or migration of plants through habitat corridors in otherwise hostile landscape matrices using taxonomic similarity (Jaccard index) as a proxy of dispersal frequency. This comprises the questions whether dispersal and migration processes of plants generally reflect a random walk through the available corridor area and if, as a consequence, logit-transformed community similarity shows a near-linear relationship with RD. This can only be tested empirically. A further aim was to compare the performance of RD, LCD and ED at predicting community similarity and, hence, dispersal likelihood. Moreover, we also compared different parameterizations of cost/resistance surfaces for the modelling of isolation using both equal resistance values for all types of corridors and specific resistances that supposedly reflected availability of suitable microhabitats within different corridor types. Finally, we tested the performance of isolation metrics for species groups with different dispersal abilities (short versus long-distance dispersed species) because species with limited dispersal can be expected to react more strongly to spatial isolation (Thompson and Townsend 2006). MATERIALS AND METHODS Study areas and field work The study was carried out in eight study areas, each 1 km2, in Northwest Germany (see online supplementary Table S1). The regional climate is temperate oceanic with average annual temperature of around 10°C and annual precipitation around 800 mm (period 1981–2000; Klimaatlas Nordrhein-Westfalen, http://www.klimaatlas.nrw.de). The landform of the study areas is mostly plain at altitudes between 40 and 80 m.a.s.l., but slightly hilly in the southernmost area at 200–220 m.a.s.l. Soils of the study areas are sandy in the western and northeastern part of the study region, loamy in the central part and loess dominated in the southern part, but always lime-free. The landscapes of the region are characterized by intensive agricultural land use and conversion of permanent grassland to arable land since the 1960s and particularly during the last 15 years. The few remaining grassland parcels are mown four to six times per year and, thus, are no suitable habitat for almost all of the typical grassland plant species. Hence, the agricultural landscape matrix is a hostile environment for virtually all plant species except for some ruderal annuals and few extremely mowing tolerant species (e.g., Lolium multiflorum Lam., L. perenne L., Trifolium repens L.). The density of linear landscape elements (LLE)—hedges, tree rows, field margins, ditches—that serve as habitat corridors for plant species is comparatively high in some parts of the study region, but low in others. Hence, there is a marked density gradient of LLE and a high variation of their areal proportions between 2.5% and 10% of the total area among study areas. The locations of the study areas were selected by random points using Geographic Information System (GIS). We wanted the study areas to represent the prevailing agricultural landscapes of the region and, hence, excluded larger settlements, extensive forests, lakes, rivers and areas of markedly different geology from the random sampling based on Corine Land Cover (http://www.eea.europa.eu/publications/COR0-landcover) and general soil maps. In each study area, we selected 5–8 plots that were randomly located in open (treeless) LLE stratified by two classes (field margins, including road verges, and ditches) using random points in GIS with a minimum distance of 100 m between them. All LLE that were at least 2 m wide were considered for random sampling, whereas narrower ones were excluded. Variation in the number of plots per study area occurred because some plots were disturbed by maintenance measures or access was forbidden by land owners. Vegetation sampling was conducted according to the Braun-Blanquet method using elongated plots of 1 × 25 m2 due to the narrow shape of the LLE. We recorded all vascular plant species of the herb layer in spring and in summer of 2012. The total number of vegetation plots was 50. The plant communities of field margins belonged to mesic ruderal grasslands (order Arrhenatheretalia; Ellenberg 2009) with some species typical of nitrophilous tall-herb stands (order Glechometalia) and had on average 22.6 species (SD ± 7.6) per 25 m2. Ditches contained plant assemblages intermediate between mesic (Arrhenatheretalia) and wet grasslands (Molinietalia) with some species typical of fens and marshes and had a mean species richness of 24.6 (SD ± 10.6). Calculation of community similarity We calculated the unweighted Jaccard similarity index for all possible pairs of plots within each study area. Additionally, we calculated Jaccard indices using only species with limited dispersal capabilities, here referred to as “short-distance dispersal” and, likewise, only those with long-distance dispersal mechanisms in order to test for differential response of these dispersal trait groups to isolation. The group of “short-distance dispersal” comprised those species with unspecific dispersal syndrome (mostly barochorous), capsules shedding seeds, and with only aquatic dispersal, whereas “long- distance dispersal” included species with epizoochory and endozoochory and with wind-dispersal by pappi or due to minute seeds according to Hodgson et al. (1995). Calculations of isolation metrics LLE were mapped from aerial images in GIS within the core study areas (1 km2) plus a buffer zone of 500 m in order to avoid boundary effects that may bias estimates of landscape resistance (Koen 2010). We discerned different categories of LLE: tracks between fields, field margins, hedges/tree rows and ditches with or without shading (Fig. 1A). The maps were rasterized at 1-m resolution and we assigned a conductivity value between >0 and 100 to all cells representing LLE, whereas cells representing the agricultural landscape matrix received zero. We used two variants of conductivity surfaces for calculating LCD and RD: (i) all cells located on LLE received an equal conductivity value of 100 and (ii) different LLE categories received different habitat-specific conductivity values. For calculations of RD, the conductivity values were converted to resistances (R = 1/conductivity) that were also used as cost values for calculating LCD. Figure 1: View largeDownload slide configuration, classification and parameterization of linear landscape elements (LLE) for calculation of least-cost and resistance distance. (A): vector map of a section of one study area (‘Osterbauerschaft’). (B): corresponding raster map with habitat-specific cell-level resistances (costs) for calculation of least-cost and resistance distance. LLE were buffered by 5 m on both sides in order to close small gaps due to roads or lengthwise interruptions. Buffers and, thus, filled gaps received doubled resistance. Figure 1: View largeDownload slide configuration, classification and parameterization of linear landscape elements (LLE) for calculation of least-cost and resistance distance. (A): vector map of a section of one study area (‘Osterbauerschaft’). (B): corresponding raster map with habitat-specific cell-level resistances (costs) for calculation of least-cost and resistance distance. LLE were buffered by 5 m on both sides in order to close small gaps due to roads or lengthwise interruptions. Buffers and, thus, filled gaps received doubled resistance. RD was calculated as the effective resistance of LLE raster cells between two points (in this case plots) considering all serial and parallel connections among raster cells based on Ohm’s law (McRae et al. 2008) where the total resistance of resistors in series is the sum of single resistors,  Rtotal=R1+R2+…+Rn and the total resistance of resistors in parallel is the sum of the reciprocals of single resistors,  1Rtotal=1R1+1R2+…+1Rn LCD was calculated as the sum of cost values (R; the same as the resistance values, in this study) of all LLE raster cells located on the shortest path between the two points, i.e.,  LCD=∑i=1nRi We calculated both LCD and RD between the plots within each study area using the python console of QGIS 2.6 (QGIS Development Team 2014) with the GRASS-GIS function ‘r.cost’, and the plugin ‘Circuitscape for Processing 0.1.1’ (https://github.com/alexbruy/processing_circuitscape), respectively. The suitability of LLE types for dispersal/migration of species may vary. For instance, species of open habitats may more readily disperse/migrate through field margins compared to narrow edges alongside hedges or tree rows. Therefore, we used conductivity values in the range of >0 to 100 that were scaled to the estimated percentage of suitable microhabitat for light-demanding plant species within the LLE. For instance, hedge rows received a cell-level conductivity of 25 because ~25% of their area consisted of grass or tall-herb dominated strips on their edges. These conductivity values were meant to represent the putative suitability of the LLE categories for dispersal or migration based on expert opinion. The corresponding resistance values were used to calculate variants of LCD and RD with habitat-specific costs or resistances, respectively (Fig. 1B; see online supplementary Table S2). Small gaps between LLE (i.e., cells with zero conductivity) are a practical problem for calculating LCD and RD, because they result in missing values or infinite resistance, respectively, thus only reflecting that there is no connection. However, gap sizes of few meters will not be effective dispersal barriers for most species. Thus, small gaps need to be closed in order to enable the calculations. Here, we assumed that gaps of up to 10 m can be passed even by short-distance dispersed species. Hence, we buffered the LLE with a radius of 5 m and used the gross area (LLE + buffer) for the calculations. We tested two variants of conductivity for the raster cells that were located on LLE buffers (i.e., outside of the real LLE): (i) buffer cells received the same conductivity value as the adjacent LLE and (ii) buffers and, thus, small gaps received only half the conductivity. Statistical analyses We modelled the relationship between Jaccard similarity of plot pairs and ED, LCD or RD with generalized linear mixed models (GLMM) using the function ‘glmer’ of the package ‘lme4 1.1–9’ in R 3.2.3 (R Core Team 2015). We used the binomial distribution with logit link because Jaccard indices are proportion data. The GLMM included fixed effects of one of the variants of distance metrics and of the LLE types that were compared (three levels: field margin with field margin, field margin with ditch and ditch with ditch) in order to take differences in environmental conditions and plant community composition into account. Due to the nested design of the study, the GLMM included a random intercept of ‘study area’ (eight levels). Additionally, we included an observation-level (‘plot pair’) random effect in order to account for overdispersion in the data (Agresti 2002, sec. 13.5; http://glmm.wikidot.com/faq). The total number of plot pairs was 136, but we omitted four plot pairs that were not connected by LLE, so that the final sample size was 132. Distance metrics were z-transformed (centred and scaled) in order to get standardized regression coefficients. The significance of the fixed effects was tested with parametric bootstraps (1000 resamples) because each plot was involved in several plot pairs and, thus, the Jaccard-index values were not independent. The assumption of linearity of the relationship between the response (on logit scale) and the predictor was validated using the ‘cumres’ function of the R package ‘gof 0.9.1’. As ‘cumres’ does not work with GLMM, we calculated GLMs with the same fixed effects and additional fixed effects of study area (but without observation-level effects) for each GLMM. There was no case of significant deviation from linearity. In order to test if the model fits of different isolation metrics were significantly different, we conducted Vuong tests (Vuong 1989) using the function ‘vuongtest’ from the ‘nonnest2’ package (Merkle and You 2016). For this purpose, we also used the GLM because the Vuong test cannot be conducted with GLMM. RESULTS LCD and RD were significantly correlated (P < 0.001) with Pearson coefficients of 0.76 for variants with equal as well as LLE-type specific cell-level resistances. Both metrics were significantly correlated with ED (all P values < 0.001) with LCD showing correlation coefficients of 0.75 and 0.71 for variants with equal and habitat-specific costs, while RD showed coefficients of 0.48 and 0.54, respectively. All three isolation metrics showed a significant linear relationship with logits of Jaccard similarity of vegetation plots throughout all variants of parameterisation of cost/resistance surfaces (Table 1; for detailed model output see online supplementary Tables S4–S13). In general, variants of LCD and RD that were calculated with halved conductivities for gaps (<10 m) fit better to the data than those calculated with full connectivity of gaps. Hence, the following results refer to the variants with reduced gap connectivity, while the others can be found in the online supplementary Table S3. LCD and RD showed lower Akaike’s information criterion (AIC) values than ED (Table 1). Several variants of LCD and RD had a significantly better model fit than ED, in particular those with equal cost/resistance values (Table 2). All variants of RD performed significantly better than ED, whereas LCD with habitat-specific cost values did not (Table 2). When using all species in Jaccard calculations, the performances of LCD and RD were similar with regard to AIC values (δAIC for RD compared to LCD of +0.2 and −0.7 for equal and habitat-specific resistance values, respectively; Table 1), and the differences in model fit between these two metrics were not significant (Table 2). However, when using only short-distance dispersed plant species, RD performed consistently better than LCD (δAIC −1.4 and −2.1; Table 1; Fig. 2). The better model fit of RD was marginally significant with both equal and habitat-specific resistance values (P values of 0.08; Table 2). In contrast, long-distance dispersed species showed no significant effect of isolation regardless of isolation metric. Table 1: modelling results for Euclidean, least-cost and resistance distance Isolation metric  Regression coefficient (B)  Standard error of B  AIC  P (bootstrap)  Jaccard similarity calculated with all species   Euclidean distance  −0.146  0.082  850.8  0.013   Least-cost distance (equal cost)  −0.253  0.083  845.2  <0.001   Resistance distance (equal resistance)  −0.289  0.096  845.4  <0.001   Least-cost distance (habitat-specific cost)  −0.218  0.088  848.0  <0.001   Resistance distance (habitat-specific resistance)  −0.242  0.092  847.3  0.003  Jaccard similarity calculated with short-distance dispersed species   Euclidean distance  −0.252  0.124  899.3  0.011   Least-cost distance (equal cost)  −0.374  0.128  895.0  <0.001   Resistance distance (equal resistance)  −0.464  0.149  893.6  <0.001   Least-cost distance (habitat-specific cost)  −0.326  0.133  897.3  <0.001   Resistance distance (habitat-specific resistance)  −0.399  0.141  895.2  <0.001  Isolation metric  Regression coefficient (B)  Standard error of B  AIC  P (bootstrap)  Jaccard similarity calculated with all species   Euclidean distance  −0.146  0.082  850.8  0.013   Least-cost distance (equal cost)  −0.253  0.083  845.2  <0.001   Resistance distance (equal resistance)  −0.289  0.096  845.4  <0.001   Least-cost distance (habitat-specific cost)  −0.218  0.088  848.0  <0.001   Resistance distance (habitat-specific resistance)  −0.242  0.092  847.3  0.003  Jaccard similarity calculated with short-distance dispersed species   Euclidean distance  −0.252  0.124  899.3  0.011   Least-cost distance (equal cost)  −0.374  0.128  895.0  <0.001   Resistance distance (equal resistance)  −0.464  0.149  893.6  <0.001   Least-cost distance (habitat-specific cost)  −0.326  0.133  897.3  <0.001   Resistance distance (habitat-specific resistance)  −0.399  0.141  895.2  <0.001  The latter two were calculated with equal and habitat-specific cell-level resistances or costs, respectively. Each line represents one separate generalized linear mixed model. The dependent variable was Jaccard similarity calculated with all vascular plant species or with only short-distance dispersed species. For calculations of isolation metrics, small gaps between linear landscape elements (LLE) were closed by buffers of 5 m width that received doubled cell-level resistances compared to the adjacent LLE. Regression coefficients refer to standardized (z-transformed) values of isolation indices. P values from parametric bootstrap with 1000 resamples. Abbreviation: AIC = Akaike’s information criterion. View Large Table 2: pairwise tests of model fit (Vuong tests) of competing generalized linear models of Jaccard similarity that used different isolation metrics (Euclidean, least-cost and resistance distance) in the predictors, but otherwise the same model setup Models compared  Z  P  Jaccard similarity calculated with all species   Euclidean versus least-cost distance (equal cost)  −2.184  0.015   Euclidean versus resistance distance (equal resistance)  −2.071  0.019   Least-cost versus resistance distance (equal cost/resistance)  −0.904  0.183   Euclidean versus least-cost distance (habitat-specific cost)  −1.317  0.094   Euclidean versus resistance distance (habitat-specific resistance)  −1.750  0.040   Least-cost versus resistance distance (habitat-specific cost/resistance)  −1.128  0.130  Jaccard similarity calculated with short-distance dispersed species   Euclidean versus least-cost distance (equal cost)  −1.605  0.054   Euclidean versus resistance distance (equal resistance)  −1.927  0.027   Least-cost versus resistance distance (equal cost/ resistance)  −1.386  0.083   Euclidean versus least-cost distance (habitat-specific cost)  −1.086  0.139   Euclidean versus resistance distance (habitat-specific resistance)  −1.712  0.043   Least-cost versus resistance distance (habitat-specific cost/resistance)  −1.403  0.080  Models compared  Z  P  Jaccard similarity calculated with all species   Euclidean versus least-cost distance (equal cost)  −2.184  0.015   Euclidean versus resistance distance (equal resistance)  −2.071  0.019   Least-cost versus resistance distance (equal cost/resistance)  −0.904  0.183   Euclidean versus least-cost distance (habitat-specific cost)  −1.317  0.094   Euclidean versus resistance distance (habitat-specific resistance)  −1.750  0.040   Least-cost versus resistance distance (habitat-specific cost/resistance)  −1.128  0.130  Jaccard similarity calculated with short-distance dispersed species   Euclidean versus least-cost distance (equal cost)  −1.605  0.054   Euclidean versus resistance distance (equal resistance)  −1.927  0.027   Least-cost versus resistance distance (equal cost/ resistance)  −1.386  0.083   Euclidean versus least-cost distance (habitat-specific cost)  −1.086  0.139   Euclidean versus resistance distance (habitat-specific resistance)  −1.712  0.043   Least-cost versus resistance distance (habitat-specific cost/resistance)  −1.403  0.080  Each row represents a test of two competing models. P values below 0.05 indicate that the second model fitted significantly better. Least-cost and resistance distance were calculated with equal and habitat-specific cell-level resistances or costs. Jaccard similarity was calculated using all plant species or only short-distance dispersed species. View Large Figure 2: View largeDownload slide Jaccard similarity vs. (A) least-cost distance and (B) resistance distance of pairs of vegetation plots located on linear landscape elements (LLE). Jaccard similarity was calculated using only species with short-distance dispersal. Both isolation metrics were calculated using resistance surfaces with equal cell-level resistance for all types of LLE, but with doubled resistance for small gaps (<10 m). Prediction curves were calculated with generalized linear mixed models (see Table 1). AIC: Akaike’s Information Criterion; B: standardized regression coefficient for least-cost or resistance distance; P: p-value from parametric bootstrap of the model. Open circles: comparisons of two field margins; black circles: two ditches; grey circles: field margin and ditch. Figure 2: View largeDownload slide Jaccard similarity vs. (A) least-cost distance and (B) resistance distance of pairs of vegetation plots located on linear landscape elements (LLE). Jaccard similarity was calculated using only species with short-distance dispersal. Both isolation metrics were calculated using resistance surfaces with equal cell-level resistance for all types of LLE, but with doubled resistance for small gaps (<10 m). Prediction curves were calculated with generalized linear mixed models (see Table 1). AIC: Akaike’s Information Criterion; B: standardized regression coefficient for least-cost or resistance distance; P: p-value from parametric bootstrap of the model. Open circles: comparisons of two field margins; black circles: two ditches; grey circles: field margin and ditch. RD always had larger standardized regression coefficients and, thus, a stronger ‘effect’ on Jaccard similarity compared to LCD with all species and with short-distance dispersed species. Plots pairs with similar LCD could vary markedly in RD. At low RD, i.e., high density of LLE with multiple connections between plots, predicted floristic similarity was higher when using RD compared to LCD. At high RD, this pattern was reversed (Fig. 3). Figure 3: View largeDownload slide maps of current through linear landscape elements (LLE) between pairs of vegetation plots (circles). Grey-scale colours represent the strength of current (in Ampere) which was calculated based on circuit theory using the software ‘Circuitscape for Processing’. Stronger current indicates a higher likelihood of an organism or propagule to pass through the respective cell based on the assumption of random movement. Least-cost distances are similar in both examples, but resistance distances are markedly different. (A) Low resistance distance due to high density of LLE with several connections between the plots. (B) High resistance distance. While expected floristic similarity of plots (Jaccard index) was the same when using least-cost distance as predictor, resistance distance yielded substantially higher or lower predictions depending on the density of the LLE network. Figure 3: View largeDownload slide maps of current through linear landscape elements (LLE) between pairs of vegetation plots (circles). Grey-scale colours represent the strength of current (in Ampere) which was calculated based on circuit theory using the software ‘Circuitscape for Processing’. Stronger current indicates a higher likelihood of an organism or propagule to pass through the respective cell based on the assumption of random movement. Least-cost distances are similar in both examples, but resistance distances are markedly different. (A) Low resistance distance due to high density of LLE with several connections between the plots. (B) High resistance distance. While expected floristic similarity of plots (Jaccard index) was the same when using least-cost distance as predictor, resistance distance yielded substantially higher or lower predictions depending on the density of the LLE network. Variants of distance metrics with specific cell-level resistances for each LLE type (see online supplementary Table S2) performed worse regarding AIC values and effect estimates compared to equal resistances (Table 1). DISCUSSION Isolation measures that consider the spatial configuration of LLE, such as LCD and RD, are more suitable than ED to model dispersal-related processes between habitat patches connected by LLE or between different points in the LLE network. This is in line with several studies that showed ED to perform rather poorly at modelling population processes in situations where the landscape matrix between patches or populations contains barriers as well as additional (suboptimal) habitat, or different densities of habitat and dispersal corridors (e.g., Andrew et al. 2012; Bani et al. 2015; Coulon et al. 2015; Fant et al. 2014; Morán-Ordóñez et al. 2015; Ortego et al. 2015). Further, RD performs better than LCD in predicting floristic similarity (Jaccard index) of vegetation stands in networks of habitat corridors, particularly with respect to short-distance dispersed species. This likely reflects the possibility of dispersal or migration of plants between two points in the network along multiple pathways which are ignored by LCD. The differences in AIC values between LCD and RD were <2 for variants with equal resistances and 2.1 for variants with habitat-specific resistances in this empirical test (Table 1; Fig. 2), and the differences in model fit were only marginally significant (Table 2). Hence, it could be argued that LCD does not perform substantially worse and might be sufficient for modelling dispersal-related processes of plant species in corridors. However, we advocate that RD is the superior isolation measure for two reasons: (i) it captures more variation in the community data and its predictions differ substantially from those of LCD, if corridor density deviates from the average (Fig. 3) and (ii) it can account for multiple sources of dispersing organisms, if the connectivity of habitat patches to (multiple) neighbouring patches is to be modelled which is likely the most prevalent application in science and conservation planning. In our study landscapes, dispersal of species was severely constrained to the narrow LLE, whereas the landscape matrix did not serve as potential habitat for most of the species. Many plot pairs were connected by one comparatively short direct LLE corridor and had just few additional connections with substantially longer travel path that probably contributed only a moderate proportion of dispersal events among the plots. In such situations, LCD could be expected to be an almost equally good predictor as RD (Row et al. 2010). Nevertheless, we could show that RD is likely better than LCD at modelling community processes of dispersal limited plant species, even if dispersal is constrained to a small number of narrow corridors. All of the few studies that applied isolation metrics based on circuit theory to plant species found that RD was better or as good as other measures in a large range of landscape types (contiguous to highly fragmented habitat) and spatial scales (landscape to continental; Andrew et al. 2012; Fant et al. 2014; McRae and Beier 2007; Ortego et al. 2015; Rouger and Jump 2014). Therefore, it is surprising that this approach has not been used more often in studies of plants’ population genetics, distribution and diversity. Current evidence suggests that migration of plant species over several generations may well resemble random walk that is an implicit assumption of RD based on circuit theory. Thus, there seems to be a high potential to apply this method in future research on plant populations and meta-communities. There is also a marked shortage of applications of circuit theory to community-level patterns, such as taxonomic similarity, regarding both animals and plants. We know of only one study on aquatic invertebrates that detected significant influence of landscape structure on community similarity using RD and, further, could show that dispersal trait groups reacted differently to landscape patterns (Morán-Ordóñez et al. 2015). Taxonomic similarity may not be the most accurate proxy of dispersal rates, but it has got the advantage of easy data acquisition and the possibility to simultaneously study all species or to compare different trait groups of species within the same study system. In agreement with other studies (Morán-Ordóñez et al. 2015; Thompson and Townsend 2006), we found strong effects of isolation on short-distance dispersed species, whereas long-distance dispersed species were unaffected. Thus, it is necessary to extend studies on the effects of landscape structure on dispersal-related processes from populations to entire communities, and to search for trait groups with similar response in order to build differentiated quantitative theories. The use of community data in combination with RD will strongly facilitate this endeavour. When the landscape under study comprises different types of habitats or landscape elements, such as field margins, ditches and hedges, it would be a reasonable assumption that resistances to dispersal (or migration) vary among these types. For instance, a hedgerow offers only narrow edges as suitable habitat for light-demanding plant species (as studied here) and, thus, the likelihood of dispersal or migration may be lower compared to field margins. Consequently, we hypothesized that variants of isolation metrics with specific cell-level resistances would perform better than equal resistances. However, we found the opposite pattern in this study. The specific resistance values that we applied (see online supplementary Table S2) were expert opinions based on the estimated area proportion of suitable microhabitat for open-country species. For example, hedge rows received ~4 times higher resistance than open field margins (0.040 versus 0.011) as we supposed that only about a quarter of the total hedge strip would be suitable edge habitat. The fact that LCD and RD with habitat-specific cost/resistance values performed less well than equal cost/resistance, suggests that resistance is not linearly related to the area proportion of suitable microhabitat for open-country plant species in LLE. Reasons for this may lie in wrong estimates of average cover percentages of suitable microhabitat, which we deem unlikely, or marked variability of those percentages within LLE habitat types which, however, we did not notice in the field. In any case, the spatial configuration of microhabitat within LLE may play an important role. For instance, our parameterization of hedges yielded a 4-fold increase of resistance compared to the equal cost/resistance variants. But if we had set the edges of the hedge to conductivity of 100, while considering the interior of the hedge as barrier, the increase in total resistance of the hedge would have been much stronger due to the lack of lateral connections between the two edges. Therefore, the fine-scale spatial configuration of microsites within habitat corridors may be an important point to tackle in future studies. Resistance surfaces based on expert opinion do not always perform well (Beier et al. 2008; Shirk et al. 2015), but there are several approaches to estimate and to validate resistance models using empirical data that may substantially improve model performance (Peterman et al. 2014; Shirk et al. 2010; Zeller et al. 2012). Hence, empirical modelling of habitat-specific resistances may hold potential to further improve models of dispersal-related processes in corridors of variable quality. Another advantage of RD is its flexibility to cope with many different kinds of landscapes (i.a., patch mosaic, patch-corridor-matrix mosaic, habitat networks) as long as there are any connections between the plots or patches under study. For instance, RD can be used to assess the likelihood of dispersal into patches that are connected to multiple source patches through corridor networks which cannot be done using either LCD or classical connectivity metrics, such as the proximity index and similar ones. In conclusion, RD is more suitable than LCD for modelling the effect of connectivity, or landscape permeability, on dispersal of plant (and animal) species in a great variety of landscape types, from patch mosaics to situations where the landscape matrix predominantly consists of hostile environment. There is a high potential in using RD in combination with easily acquired plant community data, such as simple species lists, in order to quantify the relationship between isolation or, inversely, connectivity and dispersal for all species or for different trait groups in an ecosystem simultaneously. In this way, this methodological approach can help to build a coherent framework of quantitative theory, to enhance models of regional population and meta-community dynamics and to improve the theoretical basis of corridor and habitat connectivity planning. SUPPLEMENTARY MATERIAL Supplementary data are available at Journal of Plant Ecology online. AUTHOR CONTRIBUTIONS JT, SB and JS conceived and designed the study. JT and JS conducted the field work. JT analysed the data and wrote the manuscript. SB and JS provided editorial advice. ACKNOWLEDGEMENTS We thank Simon Kellner, Henrike Ruhmann and Alexander Terstegge for their help in the field work and Bo Markussen for statistical advice. 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Journal of Plant EcologyOxford University Press

Published: Jun 1, 2018

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