Landscape and Urban Planning 124 (2014) 140–150
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Landscape and Urban Planning journal homepage: www.elsevier.com/locate/landurbplan
Research Paper
A methodological framework for the use of landscape graphs in land-use planning Jean-Christophe Foltête ∗ , Xavier Girardet, Céline Clauzel ThéMA, UMR 6049 CNRS – Université de Franche-Comté, 32 rue Mégevand, F-25030 Besanc¸on, France
h i g h l i g h t s • • • •
The use of landscape graphs is investigated through routine land-planning issues. Landscape graphs can help to identify optimal locations for increasing connectivity. Mitigation of a barrier effect may be guided by landscape-graph analysis. Diachronic analysis of graphs is useful for including landscape connectivity in impact assessment.
a r t i c l e
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Article history: Received 24 April 2013 Received in revised form 12 December 2013 Accepted 19 December 2013 Available online 17 January 2014 Keywords: Functional connectivity Decision support Ecological network Prioritisation Mitigation Impact assessment
a b s t r a c t Landscape graphs are now widely used for representing and analysing ecological networks. Although several studies have provided methodological syntheses of how to use these tools to quantify functional connectivity, it is still unclear how landscape graphs can be used for decision support in land planning. This paper outlines the different types of application that may provide relevant responses to the main questions arising in land planning about ecological networks. Three approaches are distinguished according to their objective: (1) to support prioritisation within an ecological network from a conservationist perspective; (2) to increase connectivity by identifying the best locations for adding new elements to the network, either when starting from the current state of the network or when seeking to mitigate the barrier effect engendered by a development project; (3) to assess the potential impact of a development project in terms of decreased connectivity. The computations based on connectivity metrics are explained for each of these three approaches. Then each approach is illustrated in the context of a pond network near the town of Belfort, in eastern France. The results show how the same connectivity metric used in the different approaches may serve different purposes. This emphasises the potential value of landscape graphs for the land-planning decision-support process and not just for conservation purposes (i.e. prioritisation). © 2013 Elsevier B.V. All rights reserved.
1. Introduction For several decades now biodiversity has been observed to be in decline in many parts of the world as a result of anthropogenic factors such as urban sprawl and more intensive farming (Barbault, 2001). In response to this threat, several strategies have been applied to reduce the impact of human activities on natural resources. Many countries have implemented a conservation strategy by legislating to protect areas in the form of nature reserves. However, even if methods have been developed to designate protected areas on a scientific basis (McDonnell, Possingham, Ball, & Cousins, 2002), questions have been raised about the effectiveness of conservation policies based exclusively on protected-area planning (Bishop, Philipps, & Warren, 1995). At the same time,
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landscape ecologists have noticed that populations living in fragmented habitats are forced to adopt specific dynamics (patchy populations or metapopulations) making them highly dependent on fluxes between their habitat patches (Hanski & Ovaslaken, 2000). Consequently, more attention has been paid to common landscapes and to connections between significant reservoirs of biodiversity (Noss & Harris, 1986). This context has highlighted landscape connectivity (Taylor, Fahrig, & With, 2006) and led to the concepts of ecological network and greenway being integrated into land-use-planning policies (Ahern, 1995; Boitani, Falcucci, Maiorano, & Rondinini, 2007). Following Ahern (1995), the term ‘ecological networks’ is used here to designate a spatial system of habitat cores connected by functional corridors rather than the set of energy fluxes within ecosystems (Fath, Scharler, Ulanowisz, & Hannon, 2007). Since ecological networks are relevant objects to integrate into environmental management strategies (Ahern, 1995), new needs have appeared in land-use planning, reflecting the different actions
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likely to be taken by practitioners (Bergsten & Zetterberg, 2013). Such needs have strong geographical implications because the central question asked of landscape managers concerns space (Gurrutxaga, Lozano, & del Barrio, 2010; Theobald et al., 2000): where can one act most effectively in the field in order to maintain biodiversity? This generic question can be subdivided into three specific questions for the different approaches to ecological network planning discussed here: (1) Where are the most vulnerable landscape patches for a given habitat or a given species? Assuming that such patches have to be protected and monitored so as to preserve functional linkages in the current ecological network, this question is one of prioritisation, i.e. of identifying the zones to be protected first (Rubio & Saura, 2012; Urban, 2002). (2) In which locations is it appropriate to modify the ecological network, for example by implementing or restoring certain elements, so as to enhance landscape connectivity, i.e. to improve the functional relationships and the resilience of a ˜ given species? (McRae, Hall, Beier, & Theobald, 2012; Nunez et al., 2013). Such a question also concerns the design of corridors in the adaptation strategies in response to climate change (Beier, 2012). (3) Where are wildlife species likely to be disturbed by a change in existing land cover? How can the level of disturbance in such areas be evaluated? Such questions about environmental impact assessment arise when a specific development is planned and when one needs to anticipate its impact on biodiversity. All these issues facing land-use planners are problematic because ecological networks are spatial patterns that do not necessarily correspond to spatially explicit elements in the landscape. Consequently, answering the questions above involves a methodological approach specifically designed for modelling ecological networks and functional connectivity. Landscape ecologists quantify connectivity by various methods such as individual-based movement models (Grimm & Railsback, 2005), least-cost analysis (Adriaensen et al., 2003), circuit theory (McRae, Dickson, Keitt, & Shah, 2008; McRae et al., 2012), centrality analyses (Rudnick et al., 2012) or landscape graphs (Urban & Keitt, 2001). Calabrese and Fagan (2004) have reported that these methods differ in their capacity to characterise the ecological processes and in the amount of input data and adjustments they require. Graph-theoretical methods provide an interesting compromise for both those criteria. The great advantage of landscape graphs over other possible ways of modelling functional connectivity is that they can easily be applied on a broad spatial scale. Experiments have shown that landscape graphs can provide similar results to individual simulations (Lookingbill, Gardner, Ferrari, & Keller, 2010; Minor & Urban, 2007), confirming their capacity to represent ecological processes. This useful compromise between methodological simplicity and ecological relevance makes landscape graphs suitable for land planning, which is usually concerned with broad spatial scales (Urban, Minor, Treml, & Schick, 2009). A series of original works introducing graph theory to the landscape-ecology community (Bunn, Urban, & Keitt, 2000; Keitt, Urban, & Milne, 1997; Urban & Keitt, 2001) has provided a basis which has been expanded substantially in recent years. Some recent reviews of landscape graphs have covered the whole approach and the ecological issues raised by these methods (Dale & Fortin, 2010; Galpern, Manseau, & Fall, 2011; Urban et al., 2009) while others have focused on connectivity computations by listing and comparing the available metrics (Baranyi, Saura, Podani, & Jordán, 2011; Laita, Kotiaho, & Mönkkönen, 2011; Rayfield, Fortin, & Fall, 2011). Nonetheless, although many researchers (e.g. Pereira,
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Segurado, & Neves, 2011) have claimed that landscape graphs can be readily applied to land-use planning, there has not yet been any synthesis of the operational applications of these methods. Beginning with the questions above about the major needs of land-use planners, we propose an overview of the operational use of landscape graphs. The aim is to clarify the main ways of applying these methods, by moving one step beyond the qualitative and visual use of network mapping and by making use of systematic methods as much as possible. A case study from eastern France will illustrate these applications, by focusing on a pond network in a landscape much changed by human activity. 2. Methods We propose a global framework for combining the needs arising in land-use planning with applications of landscape graphs (Section 2.1). This methodological framework encompasses current research in this domain, especially the background to landscape graph construction (Section 2.2). From this foundation, we provide details about the specific implementations of landscape graphs in each type of application (Sections 2.3–2.5). A final part examines the question of the spatial scale on which landscape connectivity should be considered (2.6). 2.1. Global framework The operational goal assigned to graph-based methods involves specifying how the decision-support process might benefit from the use of landscape graphs. The questions set out above likely to be asked of land-use planners lead us to list three main purposes: prioritisation, modification of the ecological network and impact assessment. These purposes concern different fields of application and result in specific approaches which differ in their temporal dimensions. In case 1, support for prioritisation is a static approach in which the landscape is considered solely in its current state. An important point in such an application is how best to define protected areas and conservation measures. For the second purpose, the landscape graph is used as a template for designing new elements capable of modifying the functional properties of the network, which raises concrete questions about landscape management. The approach is prospective, in the sense of potential developments the analysis may suggest. Two cases are distinguished depending on the context: case 2 is about the improvement of the current ecological network whereas case 3 is a mitigation approach for a disruptive element. Then in case 4, the potential impact assessment of a given land cover change implies a diachronic approach between an initial state and a modified state of the ecological network. This type of application relates to environmental impact assessment. 2.2. Background: graph construction The common background to most graph-based approaches to ecological networks is first the definition of a landscape map, which may be either a straightforward land-cover map or the result of a more complicated combination of several factors such as land cover, slope, topographic aspect or climatic variables. On this map, a specific category is defined as the preferential habitat of one or more target species. These habitat patches are the nodes of the landscape graph and the links represent functional connections between nodes. Most of the links are generated if the cost of movement between two nodes is less than a given value, which varies with the species. The spatial metric used to measure the cost of movement may be the Euclidean distance but it is more often based on least-cost distances, allowing the user to take into account the resistance value of each landscape category and to include barrier
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effects induced by linear infrastructures. The resulting graph is used to compute connectivity metrics at different structural levels characterising either the entire network (global level), the sub-graphs (component level) or the individual elements (patch or link level) (Rayfield et al., 2011). In practice, the construction of a given graph and the use of connectivity metrics derived from this graph are based on many choices and adjustments dictated by contextual elements (Galpern et al., 2011; Urban et al., 2009). Several ecological criteria can be invoked to justify these choices. For example, the population structure of the target species may determine the relevant type of link to be defined (Urban et al., 2009). The way a species moves across the landscape has also to be considered as a guide for adjusting resistance values in least-cost computations (Zeller, McGarigal, & Whiteley, 2012). Field data describing the presence or the movements of species may also serve as a guide for selecting the relevant connectivity metrics (Foltête, Clauzel, Vuidel, & Tournant, 2012) and for validating the entire modelling approach. In addition, certain practical elements with no ecological significance may also affect choices; for example a minimum planar graph containing fewer links (Fall, Fortin, Manseau, & O’Brien, 2007) may be preferred to a complete graph simply because it is advantageous in terms of computation cost. This paper does not discuss such choices, most of which can be justified on ecological or practical grounds (Galpern et al., 2011). As the present study is focused on the operational applications of these methods, it will be assumed that a given landscape graph is set up to appropriately reflect the ecological network of the target species. In the same way, we will not compare the properties of the available connectivity metrics (that has already been done in reviews such as Rayfield et al., 2011), but we will consider a generic metric noted M in the rest of the paper when characterising connectivity at landscape scale and Mi when representing patch-level connectivity at patch i.
2.3. Graph computations to support prioritisation This section concerns case 1 described in Section 2.1. The approach explicitly answering the question of prioritisation has been proposed ever since the earliest use of landscape graphs in ecology (Bunn et al., 2000; Keitt et al., 1997). The aim is to identify the landscape graph elements that are most important for preserving the graph’s structure and that should be protected first. This type of application can be employed either for patches (node removal method) or for links (link removal method). It consists in computing a global metric and then removing each graph element in turn and calculating the rate of variation in the global metric induced by each removal. For a given connectivity metric and a graph element i, this rate is computed as: Mi = (M − M ) × 100/M where M is the initial value of the metric and M is the value of this metric resulting from the removal of the element i. This generic computation has been used in many studies including Bodin and Saura (2010); Erös, Schmera, and Schick (2011); Gurrutxaga et al. (2010); Pereira et al. (2011), Rothley and Rae (2005) and Saura, Vogt, Velásquez, Hernando, and Tejera (2011). The removal method is not the only way to identify the key elements of an ecological network. The Betweenness Centrality (BC) index may be used for the same purpose (Bodin & Norberg, 2007; Goetz, Jantz, & Jantz, 2009; Zetterberg, Mörtberg, & Balfors, 2010). This index is based on the aggregation of the least-cost paths joining all pairs of patches. Given the index’s generic definition, a uniform weight is assigned to patches and paths alike, but the weighting proposed by Bodin and Saura (2010) make it possible to take into
account the demographic capacity of the patches and the dispersal probabilities, restricting inter-patch movements to dispersal. 2.4. Computations to support the improved connectivity of the ecological network This section concerns cases 2 and 3. Just as with prioritisation, the starting point is the selection of a global connectivity metric which is expected to significantly reflect the number of individual interactions of the focal species. Landscape connectivity can be improved in either of two ways: (i) by adding habitat patches; or (ii) by adding links between patches. The two differ in that adding new patches induces the addition of new links, but not vice versa. Moreover, depending on the context of the analysis, i.e. the target species or the habitat defining the nodes, these modifications of the landscape graph may refer to different realworld actions. New habitat patches can often be added when the patches to be created are quite small, i.e. when it is both economically and administratively feasible to create them. Examples of small patches likely to be implemented include wetlands or small areas for reforestation to mitigate a landscape perturbation. Conversely, adding new links seems to be an easier matter, since this may involve creating either small developments explicitly linking two existing patches (e.g., hedgerows, underground or overhead wildlife crossing structures between two woodland patches), or scattered elements (hedgerows or small wooded patches) which modify matrix permeability and act as stepping stones. Whatever the type of element to be added, this approach has to be spatially restricted to areas where the design of new elements should a priori be feasible, both (i) administratively, unlike areas where a planned land use precludes acting on the landscape, (ii) and ecologically, to implement new landscape elements in a context that is thought suitable. As an example of ecological conditions required for the method to be applied in relevant areas, the concept of restorable habitat may be invoked to account for landscape dynamics, as in Sutherland et al. (2007). According to these authors, a restorable habitat is likely to become a suitable habitat after a given time, for example by using a model of vegetation growth and mortality. Consequently, a subpart of the study area has first to be defined by the user as a candidate area for modification of the ecological network. In all cases, landscape-graph modelling is an interesting way to support the implementation of new landscape elements so as to improve the level of functional connectivity. Zetterberg et al. (2010) have shown how to examine this issue by a visual approach. It is also possible to make a systematic search for the best locations for elements capable of increasing connectivity. This aim can be fulfilled by using the same kind of procedure as for prioritisation, as suggested in García-Feced, Saura, and Elena-Rosselló (2011). According to those authors, the patch addition method consists in calculating the relative amount of connectivity Mi that each additional patch i could contribute with respect to a global metric M: Mi = (M − M) × 100/M where M is the initial value of the metric and M is the value of this metric resulting from the addition of the element i. The same method can be used for adding new links. We propose to improve this approach to serve the same purpose, but here we use an iterative process taking into account the cumulative effect of several additional elements (i.e. patches or links). In this procedure, a global connectivity metric M is first calculated from the initial state, i.e. before adding new elements. Then a search algorithm scans all the candidate areas where no element has so far been selected and computes their respective value M (as the value of the metric resulting from the addition of all previous new
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elements) then Mi . The element involving the maximum value of Mi is finally validated. This algorithm is then repeated until the desired number of additional elements is reached by including elements already added at each step. This stepwise procedure allows the user to identify the most complementary implementations. It should be noted that if the additional elements are patches, this procedure involves investigating the changes each virtual patch may induce in the graph topology, by adding new links from this patch to existing patches at each iteration. As a result, the curve of Mi versus the number of additional elements may help to identify the best trade-off between the improvement in connectivity and the cost of building these elements. 2.5. Computations to assess the potential impact of a development on the ecological network This section concerns case 4. The question now is to estimate how a given human development potentially affects functional connectivity. The disruptive element may be an actual development or a planned development. The impact assessment is based on a diachronic analysis, by comparing two states of the same study area and by noticing how the land cover change affects certain graph properties. A global assessment of the impact can be based on a landscapelevel metric, by using the values obtained before and after the land cover change in a global rate of variation such as: M = (M − M ) × 100/M where M is the global metric computed after the land cover change. The absolute value of this rate is meaningless per se and the global assessment is only meaningful when several scenarios of land cover change are compared. This approach has been used to evaluate the potential effects of planned highway routes (Vasas, Magura, Jordán, & Tóthmérész, 2009) and of existing road networks (Fu, Liu, Degloria, Dong, & Beazley, 2010). A similar situation has been discussed in Tannier, Foltête, and Girardet (2012), where several scenarios of urban development were compared in terms of their impact on the connectivity of forest areas. The focus on a single development (or a small number of developments) modifying the land cover underscores the spatial distribution of the impact. In this perspective, the mapping of the graph elements which have been removed (i.e. the fragmentation effect) provides a first overview of the local impact on the ecological network. However, since indirect impacts such as the barrier effect may occur, structural investigation alone is insufficient and it is advisable to draw on the functional diagnosis of local connectivity metrics. The values of a given local metric may be computed for each node (or link) before and after the land cover change. The resulting pair of maps may be compared visually as in the study by Gurrutxaga, Rubio, and Saura (2011) of the impact of the highway network on forest mammals in northern Spain and southern France. As with the global impact, a rate of variation can be calculated for each local value, representing the local change in functional connectivity induced by the development project modifying the land cover: Mi = (Mi − Mi ) × 100/Mi where Mi is the value of the metric M for patch i before the development and Mi is the value computed after the land-cover change. This diachronic approach can detect indirect impacts, i.e. taking into account potential movements of species. This advantage in assessing ecological impacts is all the more obvious when the landcover change relates to the implantation of a linear infrastructure,
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which covers a narrow strip of ground but has a potential barrier effect on species movements. Girardet, Foltête, and Clauzel (2013) have illustrated how such an approach may be used in combination with a species distribution model.
2.6. The right spatial scale for measuring landscape connectivity Whatever the aim pursued through the use of landscape graphs, another basic question is the spatial scale on which landscape connectivity should be considered. Each case identified in Section 2.1 may therefore give rise to graph computations that should be in line with the spatial scale. This criterion refers specifically to the adjustment of the distance parameter for the weighted connectivity metrics. It should be noted that given the adjustment of the metric M in all the approaches previously mentioned, the connectivity measurement may pertain to different scales, from close-range to long-range, strongly influencing the results. This question relates primarily to the distinction outlined by Zetterberg et al. (2010) with respect to improvement of the network, between the ‘site-centric’ perspective, which focuses on the local issues concerning a specific site, and the ‘system-centric’ perspective, which is designed to improve the resilience of the network as a whole. This question is also linked to the temporal dimension of the ecological processes underlying connectivity measurement. As inter-populational processes (e.g. gene flows) cannot be captured by local analysis, the regional scale is a more relevant scale for addressing the question of population persistence (Galpern, Manseau, & Wilson, 2012). This explains why determining the best way to characterise longdistance connectivity is a recurrent issue when investigating the preservation of ecological networks, even if the choice of appropriate scale depends in part on the context of the application.
3. Illustration of all three approaches in a single case study 3.1. Geographical context, focal species and data preparation The study was conducted in a 750 km2 area around the town of Belfort, in the region of Franche-Comté, eastern France (Fig. 1). This region, where the altitude ranges from 300 to 900 m, is bounded to the North by the Vosges granite massif and to the South by the foothills of the Jura, a large limestone plateau. Except for the urban core, the landscape mosaic is dominated by forest (46% of total area) and farmland (34%). The study area is crossed by transport infrastructures including a motorway, several roads, railway lines and a canal connecting the Rhône to the Rhine. In 2011, a high-speed railway line (HSR Rhine-Rhône) was built in this area to better connect the Alsace region to the Rhône valley. The study deals with a pond network forming the aquatic habitat of amphibian species such as the European tree frog (Hyla arborea), the natterjack toad (Bufo calamita) or the yellow-bellied toad (Bombina variegate). Amphibians are a topical subject since several populations are declining in Western Europe and are on the IUCN Regional Red List of Threatened Species for Franche-Comté (Pinston, Craney, Pépin, Montadert, & Duquet, 2000). The loss and fragmentation of their habitat are thought to be the major causes of their decline (Cushman, 2006). Amphibians usually occupy an aquatic habitat (ponds) during the breeding and larval periods and a terrestrial habitat for the remainder of the time. The terrestrial habitat, composed of shrubs and bushes, has to be located in the vicinity of the breeding area. Dispersal allows juveniles and some adults to colonise new ponds, generally over distances of between 1000 m and 4000 m but this varies with the species (Alex Smith & Green, 2005). In this study, 1500 m was arbitrarily considered as the maximum dispersal distance to illustrate the proposed method.
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Fig. 1. Location of the study area in north-eastern France.
A landscape map in a raster layer format was constructed by combining several land-cover databases. The spatial resolution was set at 10 m so as to catch small elements such as hedgerows. The positions of forests, rivers, roads, motorways, (high-speed and standard) railway lines and buildings were provided by the French land cover database (BD Topo IGN) with 1 m accuracy. Ponds were mapped from a specific database (BD Zones Humides DREAL). The agricultural census (BD Agreste 2010) was used to distinguish between grasslands and arable land in open areas. Hedgerows, forest edges and forest core areas were dissociated by morphological spatial pattern analysis (MSPA) (Vogt et al., 2007). Finally, a landscape map composed of 13 classes was obtained. Land cover types were classified in accordance with an earlier study of the European tree frog distribution, in which ecological literature and expert opinions were used to distinguish optimal habitat category defined as the aquatic habitat, favourable elements defined as the terrestrial habitat and unfavourable elements (Foltête, Clauzel,
Vuidel & Tournant, 2012). Ponds, i.e. the optimal habitat category, were assigned a cost of 1. Favourable landscape elements such as grasslands or hedgerows were assigned a low cost value (10) and landscape elements avoided by amphibians a high cost value (100). The values of 10 and 100 were chosen based on Clauzel, Girardet, and Foltête (2013), in which an analysis of sensitivity to cost values had shown that highly contrasting values between favourable and unfavourable categories better explained the presence of the tree frog. The different approaches described in the methods section were applied using the same connectivity metric, the PC index (Probability of Connectivity) developed by Saura and Pascual-Hortal (2007) given the expression:
n n PC =
i=1
a a p∗ j=1 i j ij 2 A
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where ai and aj are the areas of the patches i and j, p∗ij is the maximum probability of movement between these patches (i.e. corresponding to the minimum cost) and A is the total area of the study zone. The PC index was adjusted by choosing the parameter ˛ in the expression pij = exp(−˛dij ). This parameter expresses the greater or lesser decline in the probability of flux (p) with distance (d). To have a probability of flux close to 1 whatever the distance between the patches, the value of ˛ was determined so that pij = 0.05 when dij = 65,000, i.e. with a long distance arbitrarily chosen to be equal to the graph diameter. This is consistent with the scenario based on the PC-infinite in the study of structural connectivity by Saura et al. (2011). Here we chose to characterise long-distance connectivity to illustrate the methods with regard to the overall network, in keeping with the ‘system-centric’ perspective described by Zetterberg et al. (2010). Starting from the state before the implementation of the HSR Rhine-Rhône, the first task was to guide the prioritisation of the ponds so as to best preserve overall connectivity. In this case, the PC index was applied by using the patch-removal method to provide a local dPC value for each patch (see Section 2.3). The second task was to identify the best locations for enhancing connectivity by excavating new ponds, following the stepwise procedure described in Section 2.4. A 400 m-resolution grid was defined to identify candidate ponds (at the centre of a cell) without other spatial restrictions. The stepwise procedure consists in (1) selecting the first new pond among the 4456 candidates maximising the global PC index, (2) selecting the second new pond which, combined with the first one, maximises the global PC index, and so on until 10 new ponds were identified. The third task was to mitigate as far as possible the barrier effect of the Rhine-Rhône HSR line. The 35 links cut by the HSR and likely to be reactivated by the implementation of wildlife crossings were considered as candidates in the same stepwise procedure as before. The link maximising the global PC index was ranked first, the second link maximising the PC index when added to the previous one was ranked second, and so on. The final task was to assess and map the potential impact of the HSR on local connectivity (see Section 2.5). The patch-based metric PCflux , i.e. the local contribution of each patch to the global PC index, was computed to compare the local connectivity before and after construction of the HSR. For a given patch j, PCflux (j) is given by:
n
PCflux (j) =
a a p∗ i=1 i j ij A2
where ai and aj are the area of the patches i and j, p∗ij is the maximum probability of movement between these patches (i.e. corresponding to the minimum cost) and A is the total area of the study zone. The construction of the graph and all computations were performed using Graphab 1.1 software (Foltête, Clauzel, & Vuidel, 2012). 3.2. Results A graph was constructed by considering all the inter-patch links (i.e. complete graph as defined in Fall et al., 2007), and by removing the links exceeding the maximum dispersal distance. This graph ultimately contained 2321 patches and 4947 links. Using the prioritisation approach, the dPC was computed for each patch, yielding Fig. 2. The map reveals that the high connectivity values are located in certain nodes of the main component of the network. These nodes reflect a strong centrality position in the graph and some act as cut nodes. Conversely, the disconnected parts of the network, i.e. the small subgraphs, have low dPC values. The automatic search for 10 new pond sites was applied by testing candidates on a 400 m-resolution grid. Fig. 3 shows the locations
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successively identified for these ponds and the curve of the global PC index as new elements are added to the network. The first four ponds are located near a boundary between two components. The rank of these ponds is obviously correlated with the importance of the components that they reconnect. The fifth pond added does not reconnect two components but it reinforces the connectivity provided by a single cut node. The curve of the increase in connectivity provided by the new ponds shows that the first five new ponds contribute an increase of about 10%, followed by a smaller increase for the other ponds. Working with the map including the HSR, the links cut by this linear infrastructure were investigated. The stepwise search for the first 10 links whose reconnection maximises the PC index yielded Fig. 4. All except the final link contribute to reconnecting the main component of the initial network which was cut by the HSR. The progression of the PC index value as links are added reveals that the first new link, which reconnects the most important component to the main network, contributes a huge increase of about 22%. The increase is very low for the next three links, which reconnect smaller components. The PC index value does not increase any further after the fourth new link, meaning that only the first four links added, and especially the first one, improve connectivity. From the computation of PCflux before and after the construction of the HSR, the variation in connectivity induced by this infrastructure could be mapped for each patch (Fig. 5). The map indicates that the potential impact is globally greater in the vicinity of the HSR. However, the network configuration also plays an important role in the spatial distribution, since the impact is more pronounced when a part of the network becomes isolated from the major part of the initial component. This is specifically the case in the southeast of the study area where the impact leads to a reduction in the PCflux from 40% to 100%. In each component the impact decreases with distance from the HSR with respect to the number of available connected nodes.
4. Discussion The framework proposed in this paper has been designed to clarify the way in which landscape graphs may be used in land-use planning. As a first point, we propose to underline the main characteristics explaining their value for land planning. Globally, landscape graphs are part of a large set of methods designed to assess functional connectivity (Calabrese & Fagan, 2004). As the capacity of a given method to serve as a guide for planning and conservation decision-making depends on the trade-off between its data requirements and its realism, landscape graphs occupy a middle ground of sorts (Calabrese & Fagan, 2004) between spatial pattern indices (providing a poor representation of connectivity) and metapopulation models (being more data-intensive). Since it has been shown that visualisation is all-important when it comes to transferring methods to managers and decision-makers (Theobald et al., 2000), another advantage of landscape graphs is that they can be displayed as maps, allowing users to interpret the spatial configuration of the network intuitively (Bergsten & Zetterberg, 2013). From this point of view, pathways derived from least-cost modelling might be thought as efficient a method as landscape graphs for mapping ecological networks, as for example in Beier, Spencer, Baldwin, and McRae (2013). However landscape graphs incorporate least-costs into an object-oriented definition of landscape that goes beyond the simple representation by supplying a framework within which to quantify connectivity at several levels and by providing the opportunity to prioritise action on the ground.
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Fig. 2. Map of dPC for support to prioritisation of the pond network. Values are classified using the Jenks natural breaks method. Dark-coloured nodes have high connectivity values, reflecting a strong centrality position in the graph. Grey nodes have low connectivity values.
Fig. 3. Location of ten new ponds maximising connectivity using a stepwise procedure. The curve shows the rate of variation of the initial PC value resulting from the addition of each new patch.
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Fig. 4. Location of ten wildlife crossings for the Rhine-Rhône HSR maximising connectivity. The curve shows the rate of variation of the initial PC value resulting from the addition of each new link.
Fig. 5. Map of the variation of the PCflux value to assess the impact of the Rhine-Rhône HSR on the pond network. Values are classified using the equal interval method. Dark colours represent a marked decrease in connectivity after implementation of the infrastructure.
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Conversely, the computation cost of network analysis may place a limit on the use of landscape graphs in the context of a desktop configuration. This is specifically the case when using highresolution data (Moilanen, 2011) to capture landscape elements that are relevant to individual movements. For a high-resolution application, computation costs have been compared for several computing set-ups in Foltête, Clauzel, and Vuidel (2012), showing the value of parallelisation in software development. With the spread of multicore configurations, it could be argued that the computation time will become compatible with desktop configurations when using parallelised tools like Graphab 1.1. (Foltête, Clauzel, & Vuidel, 2012). This paper has proposed an overview of the operational use of landscape graphs in land-use planning. In the formal presentation, we have shown how three main issues (conservation planning, landscape management and environmental impact assessment) pertain to specific applications derived from the same methodological foundation, and how these applications induce a specific time dimension in the analysis (static, prospective, diachronic). This classification into main types of application may guide users in selecting the procedures likely to be relevant for their own purposes. By investigating the studies dealing with planning issues and based on landscape graph methods, it appears that the prioritisation approach has given rise to plentiful research, ranging from methodological contributions (Bodin & Saura, 2010; Rubio & Saura, 2012; Urban & Keitt, 2001) to operational applications, and focusing, for example, on the diagnosis of a habitat network (Crouzeilles, Lorini, & Viveiros Grelle, 2013; Pascual-Hortal & Saura, 2006, 2008; Pereira et al., 2011; Ribeiro et al., 2011; Saura et al., 2011; Shanthala Devi, Murthy, Debnath, & Jha, 2013) or on the design of protected areas (Rothley & Rae, 2005). It can be surmised that the use of landscape graphs to support prioritisation probably fulfils a very common need in conservation biology. However, one of the reasons for this preferential usage could be the ease with which landscape graphs can be applied for this purpose. Since such an approach is based on a single landscape map, the input data are easy to prepare. This observation is consistent with the outcome of a survey conducted by Bergsten and Zetterberg (2013) in which land-use planners ranked three potential uses of network analysis, and the preferred use was to find patches that were critical for landscape connectivity. Our contribution seeks to emphasise the value of landscape graphs as a decision-support tool for the implementation of landscape elements likely to improve the functional efficiency of the network needs to be promoted. Experiments to this end have recently been conducted, especially the study by Zetterberg et al. (2010), in which those authors have visually identified potential stepping stones from the mapping of a betweenness centrality index. In Benedek, Nagy, Rácz, Jordán, and Varga (2011), the potential benefit of the improvement of a single link has been evaluated, but without comparison with the potential contribution of other links which are likely to be improved. However, since landscape graphs are structures providing the advantage of facilitating computations, as opposed to continuous landscape-based approaches, we wish to stress the promising use of these tools for the automatic identification of locations that optimise connectivity. In Bergsten and Zetterberg (2013), the land-use planners interviewed emphasised that they lacked systematic methods for assessing connectivity at the regional level. In this perspective, García-Feced et al. (2011) have shown how the ‘patch addition method’ can be used to rank potential additional patches. The cumulative approach applied in this paper tries to go beyond this, by providing successive combinations of additional patches or links. Such a cumulative procedure may meet the needs of decision makers by associating the elements to be implemented
in the field with their economic cost. This is valuable when considering mitigation measures for transport infrastructures (Weber & Allen, 2010). In environmental impact assessment, landscape graphs can also be useful for including indicators of broad-scale connectivity in prospective analyses aimed at mapping the potential effects of a given development on target species or ecosystems. Very few studies have so far used landscape graphs in such a perspective, although it simply involves setting up a diachronic pair of landscape maps on which a single element (e.g., motorway, array of residential buildings) has been added between the first and the second map. Most recent contributions seek to assess the global impact of several scenarios (Fu et al., 2010; Tannier et al., 2012; Vasas et al., 2009), which is a convenient way of comparing them. By calculating rates of variation of local connectivity metrics, the assessment of the local impacts of a high-speed railway proposed in Girardet et al. (2013), applied in a real case in Clauzel et al. (2013) and illustrated in this paper demonstrates the value of diachronic analysis for investigating the spatial distribution of ecological impacts. It is not as easy to compare several spatial distributions of potential impacts (i.e. derived from several scenarios) as it is to assess global impacts, but conversely, the location of the area potentially subjected to disturbances may be used to conduct conservation actions as with prioritisation. For this approach dealing with the evaluation of potential impacts, it should be noted that the use of landscape graphs is restricted to the investigation of a specific change in land cover. When multiple land cover changes occur in the case of a long-term analysis, the definition of habitat patches and links may be modified between the two states with the result that the diachronic study might prove more difficult to apply at node level and should be investigated throughout the study zone with the support of spatial generalisation of the connectivity metrics. This paper has focused specifically on the different ways of implementing landscape graphs, but has not addressed the question of consistency between connectivity metrics and type of application. However, the choice of a given metric is still problematic for the user, since the sheer range of possibilities may be somewhat confusing. This underscores the need for a synthesis of the compatibility of connectivity metrics with the main purposes listed in the present study and with the spatial scale of the ecological process which the metrics are to represent. The illustration proposed here was based on the PC index following several tests. From these tests comparing the connectivity metrics available in Graphab 1.1 (Foltête, Clauzel, & Vuidel, 2012), we argue that the issues of regional-scale connectivity should guide prospective users’ choice towards metrics capable of capturing the effects of connectivity on long-distance fluxes. This logically makes the family of centrality indices very valuable, especially when the least-cost paths are not restricted by their length, as in Zetterberg et al. (2010). This is also consistent with one of the findings in the study by Saura et al. (2011), suggesting the relevance of the PC-infinite for species that are able to disperse over large distances. However, another criterion to bear in mind is the bias induced by the use of single least-cost paths between all pairs of nodes. In the results of dPC and PC as they are currently generated in standard applications, this bias is characterised by an unrealistic concentration of fluxes along the most recurrent least-cost paths.
5. Conclusion The applications of landscape graphs to support decisions in land-use planning can be subdivided into three main approaches: (i) prioritisation, (ii) modification of the ecological network and (iii) impact assessment. These approaches correspond to different ways of implementing landscape graphs. Because (i) support for
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