Ranking individual habitat patches as connectivity providers: Integrating network analysis and patch removal experiments
Introduction
Network-based modeling approaches are receiving increased interests in ecology (e.g. Bascompte, 2009, Bodin, 2009). Species interactions in food webs and plant-pollinator networks are two fields where network analysis is successfully applied (e.g. Bascompte et al., 2006, Pascual and Dunne, 2006). In landscape ecology and metapopulation studies network-based models (or graph theoretical as they are often called) are used to describe and analyze the possibilities for species movement among spatially separated patches of habitats in heterogeneous landscapes (Keitt et al., 1997, Urban and Keitt, 2001, Jordán et al., 2003, Pascual-Hortal and Saura, 2006, Bodin and Norberg, 2007, Fall et al., 2007, Estrada and Bodin, 2008, Urban et al., 2009, Saura and Rubio, 2010). Individual habitat patches are here modeled as nodes in a spatially explicit landscape-wide network, and the links between the nodes represent possibilities for movement or dispersal between them (i.e. functional connectivity, see Taylor et al., 1993).
In general, network-based models and metrics have been suggested to possess a convenient benefit to effort ratio for conservation problems that require characterization of connectivity at relatively large scales (Calabrese and Fagan, 2004). They provide a spatially explicit representation of the landscape connectivity that is still usable even when the available information is relatively scarce, as is usually the case in real-world planning applications (Calabrese and Fagan, 2004). In addition, recent studies show that some network metrics are just as good as other more complex and biologically detailed metapopulation models in terms of their ability to, for example, identify habitat patches and linkages where conservation or restoration efforts could favorably be concentrated (Minor and Urban, 2007, Visconti and Elkin, 2009). Even though many of the adaptations of network science to the analysis of ecological connectivity are quite recent, there are already numerous examples of their application for landscape conservation planning purposes (e.g. Pascual-Hortal and Saura, 2008, Phillips et al., 2008, Perotto-Baldivieso et al., 2009, Vasas et al., 2009, Fu et al., 2010, Laita et al., 2010). In addition, recent empirical studies have also demonstrated the capacity of the network approach to explain relevant ecological processes and patterns related to landscape connectivity (e.g. O’Brien et al., 2006, McRae and Beier, 2007, Neel, 2008, Andersson and Bodin, 2009).
Network-based modeling approaches currently applied in assessing and ranking habitat patch importance can, broadly, be classified into two different categories. The first category uses a two-stage process. First, a specific network metric developed to assess some aspect of the landscape's connectivity is chosen and calculated for a given landscape. Then, each individual patch (i.e. node) is removed, one at the time, and the resulting effect on the metric is recorded (e.g. Urban and Keitt, 2001, Saura and Pascual-Hortal, 2007). Patches are then ranked according to how much the connectivity metric decreased when they were removed. Hence, this category uses experiments (albeit theoretical) to assess patch importance. The second category uses properties or characteristics of the intact network to assess the importance of each and every individual patch. Here, network centrality is a key concept. Various variants of network centrality have been developed within the multidisciplinary field of network analysis (e.g. Wasserman and Faust, 1994). A common denominator for all these variants is that they assess different aspects of how influential, based on its topological position in the network, a specific node might be. Recently, a set of different centrality measures were tested and analyzed in terms of their potential in assessing individual patches’ contribution to different aspects of landscape connectivity (Estrada and Bodin, 2008).
These two categories have different benefits and limitations. The category based on experiments delivers easily interpretable answers on what would be consequence of the removal of a particular patch (i.e. the importance of a patch equals the reduction of the connectivity metric following its removal). However, this approach is implicitly based on the assumption that the organisms that used to move through a particular patch are able to find the alternative dispersal pathways throughout the reduced network of patches, and that no competition among the dispersers for the use of the fewer remnant pathways limits the movement abilities of the species in the disturbed landscape.
Measures of a node's centrality, on the other hand, assess patch importance based on the network model of the intact landscape. In effect, they are aimed to assess how much (or in what way) a particular patch is involved in the current flows of organisms in the undisturbed landscape. Hence, they do not explicitly try to capture how the flows might change as a consequence of losing a particular patch. For this reason, centrality measures do not deliver easily interpretable estimates of the connectivity loss following a patch removal.
Furthermore, none of the methods in these categories are particularly good in predicting how vulnerable the remaining landscape would be, beyond the loss of a particular patch, to further patch removals. Using experimental approaches, such assessments are inherently difficult since they require the researcher to specify a non-arbitrarily chosen patch removal sequence beforehand. In contrast, assessments of patch importance using centrality measures do not require the researcher to specify a specific patch removal sequence. However, the centrality assessments are based on the intact network, and they will inevitably lose relevance as more and more patches are removed from the undisturbed landscape.
The discussion above shows that it would be desirable to (where relevant) bridge these different categories in such a way that their pros are preserved while their different cons are suppressed. Also, there is a need for new methods and metrics that help to assess the increases in landscape vulnerability following the removal of a certain patch. In this paper, we contribute to such development by undertaking integrated analytical investigations of the recently proposed habitat availability (reachability) metrics probability of connectivity (PC) (Saura and Pascual-Hortal, 2007) and integral index of connectivity (IIC) (Pascual-Hortal and Saura, 2006), and the network centrality metric betweenness centrality (BC) (Freeman, 1977, Bodin and Norberg, 2007). The change in the PC and IIC metrics following experimental removals of individual patches can be partitioned in three different fractions which are relevant in assessing the different ways a habitat patch can contribute to habitat connectivity and availability in the landscape. In particular, one of these three fractions (the connector fraction described further down) evaluates a patch's contribution to connectivity between other patches by acting as a intermediate stepping stone patch (Saura and Rubio, 2010). As related to this fraction, BC measures how much a specific node sits between all other pairs of nodes in a network, i.e. it captures how many pairs of nodes are connected through that specific node (Freeman, 1977). A particular patch with a high score on BC may then experience comparative large flows of individuals that come not only from nearby patches, but also from patches which could be located quite far away in the landscape (Bodin and Norberg, 2007).
Based on the analyses of the PC, IIC and BC metrics, we suggest some extensions of the BC metric in order to more clearly link these metrics together in a common modeling framework. We show how this framework can be used to identify critical patches upholding dispersal processes in a fragmented landscape and to assess the distinctive contributions of individual habitat patches to connectivity. These analytical developments are tested and evaluated using data from two real-world landscapes in Madagascar and Catalonia (NE Spain). Based on these results, we suggest a procedure that could be used to rank patch importance. We conclude by discussing the scope of application and ecological relevance of each of these metrics in assessing various aspects of landscape connectivity.
Section snippets
The habitat availability metrics PC and IIC
PC is defined as the probability that two points randomly placed within the landscape fall into habitat areas that are reachable from each other (see Table 1 for further details), and is given by (Saura and Pascual-Hortal, 2007):where n is the number of habitat patches existing in the landscape, each with an habitat area ai (ai could instead represent some other relevant patch attribute such as habitat quality, although we, for the sake of simplicity, here only use it
Results
We started by varying the distance thresholds D, for both study areas, to estimate at which dispersal distances the intermediate connecting patches are most important for overall habitat connectivity and availability in the landscape as measured using dIICconnectork and dPCconnectork (Fig. 2A and B). The maximum contribution of dIICconnectork (as shown in Fig. 2) was considerably higher (peaks at about 40% and 35% for the Madagascar and Catalonian cases respectively) and was found at a lower
An integrated modeling framework for PC, IIC and the generalized betweenness centrality
As shown by the analytical evaluation of these conceptually different metrics, it is clear that they are capturing different aspects of a patch's contribution to the connectivity of the landscape (Table 1). Furthermore, the evaluation also shows how these conceptually different metrics are analytically related to each other. This provided for an integration of the two conceptual different approaches typically applied when assessing patch importance using a network-based approach (i.e. patch
Acknowledgements
The first author acknowledges support from the Swedish Research Council for Environment, Agricultural Sciences and Spatial Planning (Formas), and the Foundation for Strategic Environmental Research (Mistra). The second author has received financial support from the Spanish Ministry of Science and Innovation and European FEDER funds through DECOFOR (AGL2009-07140/FOR) and MONTES-CONSOLIDER (CSD2008-00040) projects.
References (39)
- et al.
Landscape connectivity: a conservation application of graph theory
J. Environ. Manage.
(2000) - et al.
Woodland key habitats evaluated as part of a functional reserve network
Biol. Conserv.
(2010) Patch connectivity and genetic diversity conservation in the federally endangered and narrowly endemic plant species Astragalus albens (Fabaceae)
Biol. Conserv.
(2008)- et al.
Testing the importance of spatial configuration of winter habitat for woodland caribou: an application of graph theory
Biol. Conserv.
(2006) - et al.
A new habitat availability index to integrate connectivity in landscape conservation planning: comparison with existing indices and application to a case study
Landsc. Urban Plan.
(2007) - et al.
Conefor Sensinode 2.2: a software package for quantifying the importance of habitat patches for landscape connectivity
Environ. Modell. Software
(2009) - et al.
Practical tool for landscape planning? An empirical investigation of network based models of habitat fragmentation
Ecography
(2009) - Bascompte, J., 2009. Ecological systems. In: Meyers, R.A. (Ed.), Encyclopedia of Complexity and System Science....
- et al.
Asymmetric coevolutionary networks facilitate biodiversity maintenance
Science
(2006) - Bodin, Ö., 2009. Ecological topology and networks. In: Meyers, R.A. (Ed.), Encyclopedia of Complexity and Systems...
A network approach for analyzing spatially structured populations in fragmented landscape
Landsc. Ecol.
The value of small size: loss of forest patches and ecological thresholds in southern Madagascar
Ecol. Appl.
A comparison-shopper's guide to connectivity metrics
Front. Ecol. Environ.
Using network centrality measures to manage landscape connectivity
Ecol. Appl.
Spatial graphs: principles and applications for habitat connectivity
Ecosystem
A set of measures of centrality based on betweenness
Sociometry
A practical model of metapopulation dynamics
J. Anim. Ecol.
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