Landscape Graphs Research Articles

Assessing the strategic role of urban green spaces for habitat connectivity in multi-family residential plots

Urban green spaces are key for maintaining and restoring habitat connectivity within cities. Despite substantial investigations on the contribution to connectivity of different types of urban green spaces, the specific contribution of green spaces located in multifamily residential (MFR) plots has yet to be assessed. Estimating this contribution is crucial given the multiple roles fulfilled by these green spaces in urban planning. To achieve this goal, we focused on four taxa: the European hedgehog (Erinaceus europaeus), the Red squirrel (Sciurus vulgaris), forest passerine birds and moths. We assessed the potential habitat connectivity for each taxon across the metropolitan urban area of Lyon (France), with landscape graphs built using 1-metre resolution land cover maps. Considering the current state as a reference, we then designed five land cover change scenarios affecting habitat distribution in the MFR plots: (i) maximum and (ii) minimum theoretical connectivity (references), (iii) improve quality of existing green spaces, (iv) improve quantity of green spaces with sub-optimal quality and, (v) maximum restoration (management scenarios). The taxon- and scenario-specific impacts highlight the crucial contribution of private spaces to habitat connectivity. For all taxa, while the MFR only cover 8 % of the study area, connectivity would increase by up to 60 % if these plots were greened. In contrast, sealing these plots could reduce overall connectivity by up to 40 %. The interpolation of local connectivity metrics for each habitat patch and each MFR plot allowed us to identify the most relevant plots for urban greening. Because our approach can improve habitat connectivity at different scales, from neighbourhoods to entire urban areas, it could prove useful for landscape planning in most urban settings.

Topological Approach for Detection of Structural Breakpoints in Philippine Stock Price Data Surrounding the COVID-19 Pandemic

Topological data analysis (TDA) is a novel but rigorous framework used to identify the underlying shape and structure of a huge data set. In this study, we demonstrated how TDA can be useful in analyzing and predicting stock market movement. The study collected time-series data from the Philippine Stock Exchange of companies that were heavily affected by lockdown measures implemented during the COVID-19 pandemic and those that thrived. The study found that during market crashes, persistence diagrams revealed a presence of persistence weakening phenomenon. Moreover, by analyzing the stock price movement given an interval of time, the persistence landscape graphs produced high points or bumps during a market drop, which corresponds to structural breakpoints in the time series. Indeed, persistent homology can be used to predict early warning signs of probable market crashes.

Evaluation of the Functional Connectivity between the Mangomarca Fog Oasis and the Adjacent Urban Area Using Landscape Graphs

Evaluation of the Functional Connectivity between the Mangomarca Fog Oasis and the Adjacent Urban Area Using Landscape Graphs

Riparian habitat connectivity restoration in an anthropized landscape: A multi-species approach based on landscape graph and soil bioengineering structures.

In urbanized areas, rivers and riparian ecosystems are often the only ecological corridors available for wildlife movement. There, riverbanks are often stabilised by civil engineering structures (dykes, riprap). This can lead to habitat degradation and loss of landscape connectivity. Fascines (willow bundles tied together) could be an alternative to riprap, since they maintain the quality of the natural ecosystems by using native vegetal species instead of rocks, but their potential positive impact needs to be assessed. We proposed a landscape-scale decision-making method for river managers who want to restore banks by transforming riprap into fascines to improve landscape connectivity. We applied our methodology to a case study involving a 25 km-stretch of the Arve River, France. We selected four target vertebrate species based on biological traits to cover a wide range of dispersal capacities. For each species, we used landscape graphs to assess habitat connectivity under different contrasted riverbank scenarios. Scenarios included replacing all-natural banks with ripraps or replacing all ripraps with fascines. In addition, we systematically tested the effect of replacing individual 100 or 500 m sections of ripraps by fascines, to locate where riverbank restoration would maximize connectivity gain. The four species selected responded very differently to the scenarios (up to +14% and +46% change in Probability of Connectivity for common toads and Eurasian beavers, respectively, 0% for common sandpipers and barred grass snakes). The restoration of specific riverbank sections could result in important gains in PC (up to +33% for one single section for one species) but no section maximized connectivity gain for all the target species.

Landscape properties of the very large-scale and the variable neighborhood search metaheuristics for the multidimensional assignment problem

We study the recent metaheuristic search algorithm for the multidimensional assignment problem (MAP) using fitness landscape theory. The analyzed algorithm performs a very large-scale neighborhood search on a set of feasible solutions to the problem. We derive properties of the landscape graphs that represent these very large-scale search algorithms acting on the solutions of the MAP. In particular, we show that the search graph is a generalization of a hypercube. We extend and generalize the original very large-scale neighborhood search to develop the variable neighborhood search. The new search is capable of searching even larger large-scale neighborhoods. We perform numerical analyses of the search graph structures for various problem instances of the MAP and different neighborhood structures of the MAP algorithm based on a very large-scale search. We also investigate the correlation between fitness (i.e., objective values) and distance (i.e., path lengths) of the local minima (i.e., sinks of the landscape). Our results can be used to design improved search-based metaheuristics for the MAP.

Validating graph-based connectivity models with independent presence-absence and genetic data sets.

Habitat connectivity is a key objective of current conservation policies and is commonly modeled by landscape graphs (i.e., sets of habitat patches [nodes] connected by potential dispersal paths [links]). These graphs are often built based on expert opinion or species distribution models (SDMs) and therefore lack empirical validation from data more closely reflecting functional connectivity. Accordingly, we tested whether landscape graphs reflect how habitat connectivity influences gene flow, which is one of the main ecoevolutionary processes. To that purpose, we modeled the habitat network of a forest bird (plumbeous warbler [Setophaga plumbea]) on Guadeloupe with graphs based on expert opinion, Jacobs' specialization indices, and an SDM. We used genetic data (712 birds from 27 populations) to compute local genetic indices and pairwise genetic distances. Finally, we assessed the relationships between genetic distances or indices and cost distances or connectivity metrics with maximum-likelihood population-effects distance models and Spearman correlations between metrics. Overall, the landscape graphs reliably reflected the influence of connectivity on population genetic structure; validation R2 was up to 0.30 and correlation coefficients were up to 0.71. Yet, the relationship among graph ecological relevance, data requirements, and construction and analysis methods was not straightforward because the graph based on the most complex construction method (species distribution modeling) sometimes had less ecological relevance than the others. Cross-validation methods and sensitivity analyzes allowed us to make the advantages and limitations of each construction method spatially explicit. We confirmed the relevance of landscape graphs for conservation modeling but recommend a case-specific consideration of the cost-effectiveness of their construction methods. We hope the replication of independent validation approaches across species and landscapes will strengthen the ecological relevance of connectivity models.

Role of green roofs in urban connectivity, an exploratory approach using landscape graphs in the city of Paris, France

Green roofs provide many ecosystem services, but little is known about the way they contribute to urban functional connectivity. This paper has the following four objectives: (1) to compare the potential green roofs’ role to connectivity in relation to other urban green spaces, (2) to specify the green roofs contribution’s type, (3) to explore the influence of building height integration method and finally (4) to assess the impact on connectivity of simulated greening new roofs. Using a landscape graph approach, we modeled ecological networks of three species groups with different dispersion capacities in the Paris region (France). Then, we computed several connectivity metrics to assess the potential contribution of green roofs to functional connectivity. At a large scale (metropole scale), our results show that green roofs can slightly improve the global connectivity largely through the connections rather than the addition of habitat area. More than a stepping stone function, green roofs would have a dispersion flux function at a local scale. Furthermore, when the difficulty of crossing movement is exponential to the height of buildings, green roofs over 20 m high are mostly disconnected from the ecological networks. In addition to the green roof’s height, our analysis highlights the very strong role played by buildings’ configuration. This study raises promising directions for the integration of building height into the analysis of urban connectivity. Detailed research and long-term biological data from green roofs and green spaces are needed to confirm our results.

Importance of climate‐induced tree species composition changes in forecasting the amount of reachable habitat for forest birds

AbstractAimBird and tree species distributions will shift along with future climatic conditions through direct effects related to species responses to bioclimatic variables. In addition, tree species composition changes should indirectly drive changes in forest bird habitats. Here, we predicted the effects of climate changes on the amount of reachable habitat for forest birds and teased apart the role of the indirect effects.LocationFrance.MethodsWe projected tree and bird species distributions (2020 and 2050) using generalized additive models which accounted for climatic conditions at a large scale (France) and local environmental conditions at regional scale. The projections combined two scenarios of climate changes (RCP 2.6 and 8.5) and two scenarios of forest management (increase in either deciduous or coniferous stands). We modelled the amount of reachable habitat with landscape graphs and the equivalent connectivity index (EC) for five birds associated to the main forest types of the study area. To differentiate the sources of EC change between 2020 and 2050, we compared two future landscape graphs including only the indirect effect, or the direct and indirect effects of climate changes.ResultsFor birds with low and intermediate thermal maxima, climate‐based distributions were nearly stable over time (absence of direct effects), EC change was only attributed to indirect effects. In contrast, for bird species with high thermal maximum, EC change was mostly driven by direct effects (more favourable climatic conditions) and little by indirect effects.Main conclusionsUsing an innovative modelling framework that bind species distribution and connectivity models with climate and land use changes in forest, we showed that EC dynamics could be completely due to climate‐driven changes in tree species composition. Our results highlight the importance of accounting for the indirect effects of climate changes, especially in forests where major shifts in tree species composition are expected.

Behind the scenes of landscape connectivity: Optimization, thresholding

Optimization is underlying technique of many graph-theoretic algorithms, including shortest paths and minimum spanning tree and hence – hidden component of landscape connectivity methods. Optimization solutions have different selectivity but it remains unexplored. Indeterminate solutions happen without warning and may be spatially biased. Errors are hidden. These issues may undermine connectivity measures and conclusions.Two optimization targets may be distinguished: mobile agent and connectivity provider, with different requirements. Review of how are they handled in literature finds them entangled and often misspecified, owing to inconclusive results, especially pronounced when conservation and explanatory goals are mixed. I categorize graph structures against targets and show how initial choice of structure introduces implicit optimization. Allowing for stochasticity of mobile agent resolves omniscience problem.Lastly, I advocate against creating landscape graphs with thresholds in favor of complete planar graphs. Thresholding is impractical, biased by design and yields non-optimal solutions due to simplistic partitioning.

Assessing the influence of the amount of reachable habitat on genetic structure using landscape and genetic graphs.

Genetic structure, i.e. intra-population genetic diversity and inter-population genetic differentiation, is influenced by the amount and spatial configuration of habitat. Measuring the amount of reachable habitat (ARH) makes it possible to describe habitat patterns by considering intra-patch and inter-patch connectivity, dispersal capacities and matrix resistance. Complementary ARH metrics computed under various resistance scenarios are expected to reflect both drift and gene flow influence on genetic structure. Using an empirical genetic dataset concerning the large marsh grasshopper (Stethophyma grossum), we tested whether ARH metrics are good predictors of genetic structure. We further investigated (i) how the components of the ARH influence genetic structure and (ii) which resistance scenario best explains these relationships. We computed local genetic diversity and genetic differentiation indices in genetic graphs, and ARH metrics in the unified and flexible framework offered by landscape graphs, and we tested the relationships between these variables. ARH metrics were relevant predictors of the two components of genetic structure, providing an advantage over commonly used habitat metrics. Although allelic richness was significantly explained by three complementary ARH metrics in the best PLS regression model, private allelic richness and MIW indices were essentially related with the ARH measured outside the focal patch. Considering several matrix resistance scenarios was also key for explaining the different genetic responses. We thus call for further use of ARH metrics in landscape genetics to explain the influence of habitat patterns on the different components of genetic structure.

Graphab: An application for modeling and managing ecological habitat networks

<h2>Abstract</h2> Landscape graphs are increasingly used in ecology, conservation, and landscape planning for modeling habitat connectivity of wildlife species. We present here the follow-up of Graphab, a software application for modeling habitat networks. This application has been recently enhanced by advanced functions of spatial analysis, command-line facilities, and connections with other software applications. It has been used in many studies, first in ecological studies for analyzing the role of landscape connectivity on biological responses measured in the field, second for supporting decisions concerning biodiversity preservation. Future improvements could be made to make the links more realistic with respect to ecological processes.

Integrating ecological networks modelling in a participatory approach for assessing impacts of planning scenarios on landscape connectivity

This research aims at integrating ecological networks modelling in a participatory approach in order to assess impacts of land-use planning scenarios on landscape connectivity. This approach was applied to the metropolitan area of Bordeaux, a highly dynamic territory that has been modified by several decades of rapid urbanization. Whilst ecological network modelling is widely used in the academic spheres, the concept of ecological network itself also rose within operational stakeholders acting in land-use planning. However, exchanges between scientists and stakeholders about this concept and its modelling and decision-making applications remain rare and generally relate to discussions about results of analyzes carried out by scientists on their own. To our knowledge, no studies to date have involved stakeholders throughout the whole modelling process. In this purpose, we developed an adapted companion modelling approach bringing together scientists and stakeholders for co-constructing (1) a multi-species approach based on ecoprofiles, (2) a conceptual model of the territory’s social-ecological functioning and (3) five land-use planning scenarios over a 15-years horizon. In parallel, we used a landscape graphs approach for modelling ecological networks of ecoprofiles, computing local and global connectivity metrics and estimating scenarios’ impacts on multi-species connectivity. The results globally showed negative impacts of dystopian scenarios or anticipated trends in planning on landscape connectivity (from −20.5% to −8.1% on average, respectively), and in a lesser extent positive impacts of utopian or transformative scenarios (+1.5% and 4.5% on average, respectively). Scenarios’ impacts also varied among ecoprofiles, with some ecoprofiles showing similar or antagonistic effects. These results served as a support of debates between stakeholders on the consequences of policy decisions and actions on connectivity, and on the possibilities of translating connectivity modelling in land-use planning and biodiversity conservation in an urban context.

Graph4lg: A package for constructing and analysing graphs for landscape genetics in R

Abstract In landscape genetics, habitat connectivity and population genetic structure have been analysed using graph‐theoretic approaches to understand how landscape features influence demography (i.e. dispersal and population size). Despite substantial advances in enhancing both genetic and landscape graph use, a software tool bringing together a large range of construction and analysis parameters for these two types of graphs was lacking in the landscape genetic toolbox. Moreover, although these two types of graphs appear complementary for answering landscape genetic questions, methods for comparing them have not been forthcoming. We have developed an R package to improve and encourage the use of these graphs. It includes functions for converting and importing genetic data and for genetic distance computing. It also implements time‐efficient geodesic and cost‐distance calculations from spatial data. A large range of parameters can be used to create genetic and landscape graphs from these data, including several graph pruning methods. We made available to R users the command‐line facilitaties of Graphab software to easily model landscape graphs in R. The package functions perform preliminary analysis to adapt methodological choices to research questions. Landscape and genetic graphs created can be analysed with node‐level metrics as well as link‐level and modularity analyses. Users can compare and visualise these graphs and export them to shapefiles to facilitate interpretation and subsequent analyses. graph4lg contributes to expanding landscape and genetic graph potential for analysing ecological connectivity while encouraging further investigations on methodological implications related to these tools.

Comparison of landscape graph modelling methods for analysing pond network connectivity

Landscape fragmentation negatively impacts species populations by isolating them. Assessing landscape connectivity could help to improve biodiversity conservation. Among various methods available to model and analyse connectivity, graph-theoretic approaches are recognized as powerful tools, even if their ecological significance may be questionable in some cases. Indeed, there are many ways to construct a landscape graph and their impacts on the assessment of connectivity are rarely explored. Our aim was to compare three methods of constructing landscape graphs to identify differences and similarities in the resulting network connectivity. The methods can be distinguished according to the type of data used: expert opinions, field data or a combination of the two. The methodological framework was applied to seven pond-dwelling species (Alytes obstetricans, Bufo bufo, Epidalea calamita, Hyla arborea, Natrix natrix, Rana temporaria, Triturus cristatus) in the Ile-de-France region (France). Three common methods were applied to construct landscape graphs: (1) using a land cover map (LM) and expert opinions to define nodes and links; (2) using a habitat suitability model (HSM) and species occurrence data to define nodes and links; and (3) using a HSM to define nodes and a land cover map to define links (HSM_LM). To carry out our study, we produced a land cover map, collected and prepared input data for HSMs, generated HSMs to map the probability of species occurrence and constructed landscape graphs from the three methods. For each of them, several connectivity metrics were calculated and compared. The results revealed large differences in the statistical distribution of connectivity values, even though the spatial location of the main areas of low and high connectivity was roughly the same. In general, the LM method provided lower values of connectivity and smaller areas of high values than the other two, regardless of species. Conversely, the HSM method had the highest connectivity values, while the combined HSM_LM method appeared to be intermediate. Our study was not intended to conclude whether one method is better than another; only to point out that results vary greatly depending on the graph construction method. To evaluate the predictive performance of each model, a validation process should be conducted with another independent biological dataset, which was not available in our study. The high variability of results argues for taking care to ensure that the construction of models is carefully consistent with ecological assumptions and the objective pursued.

Coupling landscape graph modeling and biological data: a review

Landscape graphs are widely used to model networks of habitat patches. As they require little input data, they are particularly suitable for supporting conservation decisions (and decisions about other issues as e.g. disease spread) taken by land planners. However, it may be problematic to use these methods in operational contexts without validating them with empirical data on species or communities. Since little is known about methodological alternatives for coupling landscape graphs with biological data, we have made an exhaustive review of these methods to analyze links between the main purposes of the studies, the way landscape graphs are constructed and used, the type of field data, and the way these data are integrated into the analysis. We systematically describe a corpus of 71 scientific papers dealing with terrestrial species, with particular emphasis on methodological choices and contexts of the studies. Despite a great variability of types of biological data and coupling strategies, our analyses reveal a dichotomy according to the objective of the studies, between (i) approaches aimed at improving ecological knowledge, mainly based on land-cover maps and using biological data to test the influence of landscape connectivity on biological responses, and (ii) approaches with an operational aim, in which biological data are directly integrated into the graph construction and assuming a positive effect of connectivity. Beyond these main contrasts, the review shows that landscape graphs can benefit from field data of different types at varying scales. The great variability of approaches adopted reveals the flexible nature of these tools.

Modelling in the Context of an Environmental Mobilisation: A Graph-Based Approach for Assessing the Landscape Ecological Impacts of a Highway Project

Abstract The construction of highways leads to several environmental and landscape impacts, including the fragmentation of natural habitats for many animal species. Highway projects are therefore generally accompanied by mobilisations from the inhabitants of the areas concerned and environmental associations. This work aims to model the potential impacts of a highway project in France on ecological networks and to study the reception of the results by the opponents of this project. We have adopted a three-step approach. First, a land-cover map of the study area was produced at a fine scale of 10 m resolution. Second, we developed a multi-species approach by defining fifteen species groups representative of different habitats of our study area. Third, the design of landscape graphs and the resulting calculation of connectivity metrics allowed mapping the impact of the highway on multi-species ecological connectivity. Reflexive feedback from comments on these results by the public during a mobilisation day against the highway project allows assessment of the relevance of such a modelling approach in this context.

Environmental mitigation hierarchy and biodiversity offsets revisited through habitat connectivity modelling

Biodiversity loss is accelerating because of unceasing human activity and land clearing for development projects (urbanisation, transport infrastructure, mining and quarrying …). Environmental policy-makers and managers in different countries worldwide have proposed the mitigation hierarchy to ensure the goal of “no net loss (NNL) of biodiversity” and have included this principle in environmental impact assessment processes. However, spatial configuration is hardly ever taken into account in the mitigation hierarchy even though it would greatly benefit from recent developments in habitat connectivity modelling incorporating landscape graphs. Meanwhile, national, European and international commitments have been made to maintain and restore the connectivity of natural habitats to face habitat loss and fragmentation.Our objective is to revisit the mitigation hierarchy and to suggest a methodological framework for evaluating the environmental impact of development projects, which includes a landscape connectivity perspective. We advocate the use of the landscape connectivity metric equivalent connectivity (EC), which is based on the original concept of “amount of reachable habitat”. We also refine the three main levels of the mitigation hierarchy (impact avoidance, reduction and offset) by integrating a landscape connectivity aspect.We applied this landscape connectivity framework to a simple, virtual habitat network composed of 14 patches of varying sizes. The mitigation hierarchy was addressed through graph theory and EC and several scenarios of impact avoidance, reduction and compensation were tested.We present the benefits of a habitat connectivity framework for the mitigation hierarchy, provide practical recommendations to implement this framework and show its use in real case studies that had previously been restricted to one or two steps of the mitigation hierarchy. We insist on the benefits of a habitat connectivity framework for the mitigation hierarchy and for ecological equivalence assessment. In particular, we demonstrate why it is risky to use a standard offset ratio (the ratio between the amount of area negatively impacted and the compensation area) without performing a connectivity analysis that includes the landscape surrounding the zone impacted by the project. We also discuss the limitations of the framework and suggest potential improvements. Lastly, we raise concerns about the need to rethink the strategy for biodiversity protection. Given that wild areas and semi-natural habitats are becoming scarcer, in particular in industrialised countries, we are convinced that the real challenge is to quickly reconsider the current vision of “developing first, then assessing the ecological damage”, and instead urgently adopt an upstream protection strategy that would identify and protect the land that must not be lost if we wish to maintain viable species populations and ecological corridors allowing them the mobility necessary to their survival.

How ecological networks could benefit from landscape graphs: A response to the paper by Spartaco Gippoliti and Corrado Battisti

Ecological networks are tools for conservation planning that rely on the concept of connectivity. Criticisms leveled at them are that they are widely used in a dogmatic way regardless of how they compare against other tools and that their efficiency is rarely assessed. I propose to include landscape graphs in the debate because they are designed to be operational models of ecological networks. I outline the key features of landscape graphs that can be matched with some of these criticisms: weighting of patches and links to take the landscape matrix into account, integrated metrics dealing with both connectivity and amount of habitat, and the possibility of including them in a decision-support system based on scenario analyses. I conclude that criticisms of ecological networks reveal the lack of diffusion of modeling tools such as landscape graphs, and that approaches such as participatory modeling bringing together scientists and practitioners could be one way to improve matters.

An ex-post evaluation approach to assess the impacts of accomplished urban structure shift on landscape connectivity

Many studies have been conducted to evaluate the effects of different urban structures on landscape connectivity, and most of them rely on the comparison approach or ex-ante scenario analysis. However, we still lack an ex-post method to capture the consequences of accomplished urban structure shift (from monocentric to polycentric), which is guided by the land use planning. To fill this gap, we develop an ex-post evaluation approach which integrates counterfactual analysis and landscape graphs. Counterfactual analysis is combined with cellular automata simulation model, to uncover what the city might look like, if it had continued to expand in a monocentric structure; and the landscape graphs enable us to reveal the possible landscape connectivity in actual and counterfactual scenarios. We select Nanjing city as the study area and 4 target species, to delve into the varying impacts of the urban structure shift on different taxonomic groups. Our case study demonstrates that: (1) the impact of urban structure shift is more relevant to the long disperser; (2) the actual landscape (polycentric) would facilitate the bird's dispersal, while (3) forest mammals have higher connectivity in the counterfactual scenario (monocentric), and the possible reasons are discussed. Finally, we demonstrate that the urban structure shift might not necessarily cause the connectivity decline, on condition that the key connectivity providers are identified by integrating ecological network analysis into the land use planning, and well preserved in the shift.

Pinpointing cryptic borders: Fine-scale phylogeography and genetic landscape analysis of the Hormogaster elisae complex (Oligochaeta, Hormogastridae)

Spatial and temporal aspects of the evolution of cryptic species complexes have received less attention than species delimitation within them. The phylogeography of the cryptic complex Hormogaster elisae (Oligochaeta, Hormogastridae) lacks knowledge on several aspects, including the small-scale distribution of its lineages or the palaeogeographic context of their diversification. To shed light on these topics, a dense specimen collection was performed in the center of the Iberian Peninsula – resulting in 28 new H. elisae collecting points, some of them as close as 760m from each other- for a higher resolution of the distribution of the cryptic lineages and the relationships between the populations. Seven molecular regions were amplified: mitochondrial subunit 1 of cytochrome c oxidase (COI), 16S rRNA and tRNA Leu, Ala, and Ser (16S t-RNAs), one nuclear ribosomal gene (a fragment of 28S rRNA) and one nuclear protein-encoding gene (histone H3) in order to infer their phylogenetic relationships. Different representation methods of the pairwise divergence in the cytochrome oxidase I sequence (heatmap and genetic landscape graphs) were used to visualize the genetic structure of H. elisae. A nested approach sensu Mairal et al. (2015) (connecting the evolutionary rates of two datasets of different taxonomic coverage) was used to obtain one approximation to a time-calibrated phylogenetic tree based on external Clitellata fossils and a wide molecular dataset. Our results indicate that limited active dispersal ability and ecological or biotic barriers could explain the isolation of the different cryptic lineages, which never co-occur. Rare events of long distance dispersal through hydrochory appear as one of the possible causes of range expansion.