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Keywords:

  • Connectivity;
  • conservation planning;
  • site prioritization;
  • river conservation;
  • marine conservation;
  • larval dispersal;
  • Marxan;
  • Great Barrier Reef;
  • Snowy River

Abstract

  1. Top of page
  2. Abstract
  3. Introduction
  4. Formulation of asymmetric connectivity problem in Marxan
  5. Case studies for implementation of asymmetric connectivity in Marxan
  6. Discussion
  7. Acknowledgments
  8. References
  9. Supporting Information

Real patterns of ecological connectivity are seldom explicitly or systematically accounted for systematic conservation planning, in part because commonly used decision support systems can only capture simplistic notions of connectivity. Conventionally, the surrogates used to represent connectivity in conservation plans have assumed the connection between two sites to be symmetric in strength. In reality, ecological linkages between sites are rarely symmetric and often strongly asymmetric. Here, we develop a novel formulation that enabled us to incorporate asymmetric connectivity into the conservation decision support system Marxan. We illustrate this approach using hypothetical examples of a river catchment and a group of reefs, and then apply it to case studies in the Snowy River catchment and Great Barrier Reef, Australia. We show that incorporating asymmetric ecological connectivity in systematic reserve design leads to solutions that more effectively capture connectivity patterns, relative to either ignoring connectivity or assuming symmetric connectivity.


Introduction

  1. Top of page
  2. Abstract
  3. Introduction
  4. Formulation of asymmetric connectivity problem in Marxan
  5. Case studies for implementation of asymmetric connectivity in Marxan
  6. Discussion
  7. Acknowledgments
  8. References
  9. Supporting Information

The movement of organisms between habitat areas is often vital for population persistence and is essential for maintaining the ecological integrity of many ecosystems (Beger et al. 2010). This movement, or connectivity, is often quantified by the probability that individuals (adults, juveniles, or larvae) successfully move from a source site to some distant site (Cowen et al. 2006; Vuilleumier & Possingham 2006; Martin et al. 2007; Treml et al. 2008). Metapopulation theory predicts that better connected sites have higher population densities and greater persistence, all other factors being equal (Hanski 1998; Moilanen et al. 2008), yet connectivity is rarely explicitly accounted for in systematic site prioritization for conservation (Wilson et al. 2009). Ecological connectivity has been represented in conservation planning through surrogate data, for example, the length of a corridor (Ball et al. 2009), the geographic distance between habitat patches (Nicholson & Ovaskainen 2009), site adjacency (Ball et al. 2009), or a simplified dispersal kernel (Fagan & Lutscher 2006). These approaches typically assume that the strength of this relationship is equal in both directions (Mumby 2006). In reality, most ecological connections are highly asymmetric (Vuilleumier & Possingham 2006). Unfortunately, current conservation decision support systems have so far been limited in their ability to account for these important asymmetries.

Systematic decision support systems provide objective driven, repeatable, and efficient solutions to the prioritization of sites for conservation and natural resource management (Wilson et al. 2009). The use of a decision support system traditionally involves setting conservation targets for the protection of ecological features (usually species or habitats). Increasingly, the focus of conservation science is moving from static pattern-based targets toward the protection of processes that support the persistence and functioning of ecosystems and their biodiversity (Meir et al. 2004; Possingham et al. 2005). Integrating ecological connectivity into planning is a research and innovation priority in conservation science, aiming to enhance the adequacy of conservation solutions (Beier et al. 2008; Moilanen et al. 2008; Beger et al. 2010). For example, connectivity of dispersing larvae is viewed as a crucial factor in ensuring the long-term viability of populations in marine reserve networks (Gaines et al. 2003; McCook et al. 2009; White et al. 2010). Similarly, linkages for migrating fishes in rivers (Fausch et al. 2002) or connections between migratory bird sites (Martin et al. 2007) are essential for the persistence of these species. Although several approaches to incorporating symmetrical or linear connectivity in systematic conservation planning have been proposed (Gerber et al. 2005; Pyke 2005; Moilanen et al. 2008; McCook et al. 2009), only one has explicitly incorporated the directional properties of connectivity. Moilanen et al. (2008) developed a method in the software Zonation that considers upstream and downstream connectivity in river systems.

To address the generally inadequate consideration of ecological connectivity in conservation planning, we formulated and implemented an explicit method for incorporating asymmetric connectivity in the software program Marxan (http://www.uq.edu.au/marxan, Ball et al. 2009). We demonstrate how including asymmetric ecological connectivity influences the selection of conservation sites, with two theoretical and two real-world examples.

Formulation of asymmetric connectivity problem in Marxan

  1. Top of page
  2. Abstract
  3. Introduction
  4. Formulation of asymmetric connectivity problem in Marxan
  5. Case studies for implementation of asymmetric connectivity in Marxan
  6. Discussion
  7. Acknowledgments
  8. References
  9. Supporting Information

Connectivity can be represented in Marxan by including a connectivity cost between planning units (Wilson et al. 2009), where the magnitude of the connectivity cost indicates the strength of the process between all ecologically connected sites, whether adjacent or distant (Figure 1A and B). This can be interpreted as the added importance or value of conserving both sites if one is already protected (Beger et al. 2010). The connection cost in the algorithm's objective function promotes the selection of sites that produce a more connected conservation network (Wilson et al. 2009). Where connectivity is asymmetric, explicit directionality is required, for example, from planning unit 1 to 4, but not in the opposite direction (Figure 1C).

image

Figure 1. Schematic diagram showing (A) adjacent planning units connected through their boundaries where ecological connectivity is implied through shared boundaries, (B) symmetric connectivity between nonadjacent planning units, (C) asymmetric connectivity across nonadjacent planning units.

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The difference between symmetric and asymmetric connectivity in Marxan is controlled by the connectivity value matrix (cv, Equation (1)), which can be either symmetric (typical implementation) or asymmetric, as illustrated here. The importance of connectivity relative to other elements in a conservation planning problem (e.g., cost or biodiversity representation) is quantified by the connectivity strength modifier parameter (CSM, Equation (1)). Mathematically, the CSM is a generalization of the boundary length modifier used to assign the importance of reducing the physical boundary length of a reserve system relative to its cost (McDonnell et al. 2002). A connectivity penalty applies if the source site in a connected pair is in the reserve network but the destination site is not. A zero value for CSM means there is no preference for connectivity, and an increasing value for CSM results in an increasing emphasis on connectivity. When a nonzero value for CSM is used, the software seeks to reduce the connectivity penalty by minimizing the sum of missing connections in the design of the reserve system (Equation (1)). As with the boundary length modifier, the value of CSM scales with the number and costs of planning sites and needs to be determined for each project.

With these definitions, the conservation planning problem solved by Marxan now becomes minimize the sum of the total cost of selected sites, plus the sum of the missing asymmetric connections across selected sites, subject to the target tj for every feature being met

  • image(1)
  • image(2)

where there are m planning units with costs ci and j= 1, … n conservation features with the amounts ai,j present in the planning units, i. The first term of Equation (1) represents the basic reserve selection problem with xi indicating if a site is selected or not (Wilson et al. 2009). The second term is the sum of missed connections of the reserve system configuration, with the CSM parameter controlling the overall relative importance of connectivity in the objective function, and cvi,j is the connectivity penalty value associated with having planning unit i selected and planning unit j not selected, but not necessarily vice versa. These objectives, a weighted combination of costs and missing connections (Equation (1)), are minimized subject to all conservation features meeting their targets tj (Equation (2)).

Case studies for implementation of asymmetric connectivity in Marxan

  1. Top of page
  2. Abstract
  3. Introduction
  4. Formulation of asymmetric connectivity problem in Marxan
  5. Case studies for implementation of asymmetric connectivity in Marxan
  6. Discussion
  7. Acknowledgments
  8. References
  9. Supporting Information

Rivers

Hypothetical river system Selecting sites for protection in the lower reaches of a river without protecting upstream sites is risky because upstream influences may compromise the integrity of downstream conservation features. Hence, if planning unit i is upstream of planning unit j, we require cvij > 0 so that there is a cost of choosing planning unit j and not i, but not vice versa. We demonstrate the effect of including asymmetric connectivity rules in a hypothetical river represented by 10 adjacent planning units, with five of the planning units containing a single conservation feature, each separated by an empty unit (Figure 2A). To represent the decreasing influence of upstream planning units, we choose connectivity values that decline with increasing upstream distance, as widely accepted for nutrient and sediment transport (Newham et al. 2004) and pollutants (Phillips 1988) (Appendix S1). Each planning unit is connected to upstream planning units with connectivity values cv equal to the inverse number of steps between them (Figure 2A). With a target of three occurrences of the conservation feature, three sites with features were selected (Figure 2B and C) without asymmetric connectivity (or CSM= 0). When the importance of connectivity was increased (CSM > 0), the three selected sites with features were clumped in a cohesive upstream protected area network (Figure 2B and C, CSM= 3). The results illustrate the effect of adding asymmetric (upstream) connectivity values into the spatial prioritization—in this case only upstream conservation features are targeted. In many real-world scenarios, trade-offs between contrasting processes will have to be considered (e.g., sediment transport vs. diadromous fish life cycles).

image

Figure 2. Hypothetical river with 10 planning units, where (A) black indicates the presence of the conservation feature, with arrows showing relative connectivity (decreasing with distance) with connectivity weightings, (B) best reserve configuration solutions, and (C) selection frequency at CSM= 0 and CSM= 3.

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Snowy River catchment, Australia. We applied the asymmetric connectivity algorithm to the Snowy River catchment in Victoria, Australia. Data available for this catchment included modeled distributions for 400 macro-invertebrate taxa, converted into occurrence data by assuming the species are present when the modeled probability is greater than 0.5, and absent otherwise (Wilson et al. 2005; Linke et al. 2008). We set a target of two occurrences for each of the macro-invertebrate taxa in Marxan. The connectivity between upstream and downstream planning units was calculated from a catchment routing network delineated from a 90 m digital elevation model in ArcHydro, and the connectivity value between a downstream unit i and an upstream unit j, cvij, was the reciprocal of the number of steps to reach unit j from unit i. The asymmetric connectivity rules improved the efficiency of solutions compared to previous solutions for the Snowy River catchment (Linke et al. 2008). These original schemes for riverine planning assumed protection of the entire upstream catchment (Figure 3A)—if a planning unit was needed, the entire area upstream needed to be selected, no matter how large. This is unlikely to be implemented as very large tracts of river would need to be protected. When this system was parameterized with asymmetric connectivity (as aforementioned) and a moderate CSM (Figure 3B), more realistic solutions were found balancing the relative benefits and costs of upstream connectedness and protecting conservation features. When the relative emphasis on upstream connectivity was high (CSM= 5), a similar solution to Linke et al. (2008) was found (Figure 3A). Modifying the CSM allowed us to explore solutions that vary the importance of connections. Avoiding the automatic inclusion of all headwaters while retaining important upstream connectivity is important for the social acceptability (fewer potential reserve sites mean fewer potential for conflict with users) and likely improves the ecological adequacy of proposed conservation solutions. Without implementing the asymmetric (upstream) connectivity, this balanced solution would not be possible.

image

Figure 3. Invertebrate upstream protected areas in the Snowy River at (A) CSM= 5, (B) CSM= 1.4, and (C) CSM= 1.2.

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Reefs

In marine conservation planning, the benefit of incorporating dispersal connectivity is widely acknowledged (Gaines et al. 2003; Sale et al. 2005; McCook et al. 2009), yet never explicitly implemented (Shanks et al. 2003). As connectivity information becomes increasingly available through both empirical and modeling studies (Jones et al. 2009), it is foreseeable that conservation planners may soon have access to marine connectivity estimates for designing conservation area networks.

Hypothetical reef system We created a hypothetical seascape containing 25 reefs distributed across a grid, in which alternating reefs contain a target feature. A connectivity matrix between each pair of reefs in each direction was parameterized as the larval dispersal among reefs to represent main flows, cross connections, and reverse flows (Figure 4A). With this seascape, we analyzed outcomes of 1,000 Marxan runs with the target of protecting eight reefs with the conservation feature (32% of target) across five CSM values from 0 (no connectivity) to 3 (high emphasis on connectivity) for scenarios incorporating asymmetric or symmetric connectivity. For the symmetric scenario, directionality was removed by selecting a single connectivity value for each pair of reefs (i.e., cvi,j=cvj,i). We evaluated the solutions in their ability to capture highly connected reefs by assessing connectedness of reefs with closeness centrality calculated with the software Pajek (Batagelj & Mrvar 2003), a graph-theoretic measure that describes the position of a site within a network (Newman 2001, Figure 4B). A site with high closeness centrality has strong connections to most other sites.

image

Figure 4. Hypothetical 25-reef seascape with (A) alternating reefs containing target habitat (gray) with the ecological connectivity direction and strength indicated by arrows and thickness, and (B) relative centrality (sensu Newman 2001) of reefs in the network (darkest color denotes highest relative centrality).

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As expected, there was evidence that the conservation priority of reefs changed with the incorporation of connectivity, confirming the influence of asymmetric connectivity on the prioritization of marine reserves. When no consideration was given to connectivity (CSM= 0), sites were selected at random from the planning units containing the feature (Figure 5, Column 1). For scenarios incorporating connectivity, the mean centrality of selected reefs increased with increasing CSM (Figure 6). In addition, at higher CSM values highly connected, nonfeature reefs were also frequently chosen (Figures 5, 6). As in the river case study, increasing the emphasis on connectivity decreased the variety of solutions produced by Marxan in the 1,000 runs (Figure 5). By incorporating the direction of connectivity between sites, the asymmetric connectivity formulation resulted in connected networks with far fewer planning units than under the symmetric formulations (Figure 5). For the asymmetric connectivity scenarios, highly central sites that contained the planning feature were frequently ignored when the emphasis on connectivity was low (e.g., CSM= 0.5), because the planning unit cost was high relative to the penalty paid for the diminished connectivity (Figure 6). When the emphasis on finding well-connected solutions was increased, the trade-off tipped in favor of including sites with high closeness centrality (Figure 6A). Sites containing the target habitat but with low centrality were frequently included in solutions when the emphasis on connectivity was low. With increasing emphasis on connectivity, these low centrality sites were avoided in favor of sites with higher centrality.

image

Figure 5. Comparison of varying CSM in a typical (best) solution and selection frequency for Marxan scenarios considering (A) symmetrical connectivity and (B) asymmetrical connectivity. Note that when CSM= 0 connectivity has no influence upon the solutions created by Marxan.

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image

Figure 6. The relative selection frequency of planning units for different CSM scenarios and reef centrality categories. Centrality categories range from low to high centrality and were determined by placing centrality values in five equal sized bins. The relative selection frequency of a planning unit is its selection frequency when connectivity is considered minus its selection frequency when connectivity is ignored. Results are presented for the combination of (A) symmetric connectivity and (B) asymmetric connectivity, both separately for planning units with and without conservation feature. When CSM is zero, about 60% of the planning units with the conservation feature and none of the ones without are selected.

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Under the symmetric connectivity formulation, there was little differentiation of sites based on their centrality. With increasing emphasis on connectivity, almost all sites were selected with higher frequency in the 1,000 runs, increasing the overall size of the resulting reserve network (Figure 6B). Sites without features were rarely selected in scenarios with low emphasis on connectivity, but as this increased, sites without feature were often included in the solution if they had high centrality (Figure 6A and B).

Great Barrier Reef, Australia. We combined a connectivity model and a metapopulation model to approximate long-term connectivity for coral trout, Plectropomus leopardus (Lacepède, 1802) in Australia's Great Barrier Reef Central Section. The connectivity model for the 20-year period from 1977 to 1996 included 321 reefs (James et al. 2002), based on a release of 1,000 propagules per 1 km of reef crest, larval release at night, a 7-day precompetent period, and no behavioral traits. For each pair of reefs, this model described the proportion of larvae from the source reef arriving at the downstream reef. Because realized connectivity represents how many larvae actually settle on the receiving reef, we applied a species-specific Beverton-Holt metapopulation model for P. leopardus, which incorporated growth and death functions, age classes and the proportional connectivity values to describe larval supply (Bode et al. 2008). The metapopulation model was run for 500 years, with randomly alternating connectivity matrices for all modeled years of the connectivity model. The resulting connectivity strengths between pairs of sites served as the connectivity matrix cvij for Marxan scenarios. The planning units for Marxan also contained the conservation features bathymetry and bioregions with targets set to 20% (Fernandes et al. 2005). We identified the frequency with which reefs were selected for scenarios with 1,000 runs with both symmetrical and asymmetrical connectivity importance ranging from a CSM= 0 to CSM= 1,000 (Figure 7). We compared the selection frequency of reefs with their closeness centrality to assess how a changing emphasis on connectivity caused changes in conservation priority of reefs. Selection frequency differed substantially between symmetric and asymmetric connectivity scenarios. Symmetric connectivity scenarios prioritized highly connected reefs only with high CSM, which then were ineffective because they selected most reefs, regardless of their centrality (Figure 7A). In the asymmetric scenarios, highly connected reefs were prioritized from CSMs of 15 and higher (Figure 7B). High CSM (e.g., above CSM= 100) caused Marxan to select almost all reefs at each run, leading to unrealistically high costs of portfolios. The correlation analysis between centrality and selection frequency as demonstrated in our example identified CSM values that allowed Marxan to consider connectivity, but also provide relatively efficient portfolios. Of particular interest are those reefs that become more or less frequently selected depending upon the assumptions of the nature of connectivity and that would be missed without connectivity data.

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Figure 7. Centrality (connectedness) and selection frequency (also called reef conservation priority) of coral reefs in the Central Great Barrier Reef for different CSM values (indicated above each reef map) for (A) symmetric connectivity and (B) asymmetric connectivity. Reefs with the highest selection frequency are red and Spearman correlations (ρ and type I error probability) between centrality and selection frequency are noted.

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Discussion

  1. Top of page
  2. Abstract
  3. Introduction
  4. Formulation of asymmetric connectivity problem in Marxan
  5. Case studies for implementation of asymmetric connectivity in Marxan
  6. Discussion
  7. Acknowledgments
  8. References
  9. Supporting Information

Connectivity within ecological systems is rarely symmetric, be it migration routes (Pyke 2005), individual movement, (Stevens et al. 2000) or larval dispersal (Cowen et al. 2006; Treml et al. 2008). Here, we have described a method for recognizing the asymmetry of ecological connections in the widely used conservation prioritization software Marxan. With this tool, ecological linkages among sites can be incorporated into systematic conservation planning, greatly enhancing the capacity to develop conservation solutions that address complex ecological requirements.

Good estimates of ecological connectivity from modeled and empirical studies are increasingly available (Almany et al. 2007; Treml et al. 2008). As managers include these connectivity estimates into conservation planning, they must evaluate and consider the limitations and strength of these datasets in relation to their conservation objectives. A major challenge for conservation planners in the future will be to decide how much emphasis to place on ecological connectivity for conservation solutions. Improving connectivity in reserve networks may come at the expense of risk spreading (McCook et al. 2009), overall cost (McDonnell et al. 2002), and possibly ecological representation (Game et al. 2008), thus creating a trade-off between connectivity objectives and other conservation targets (Hodgson et al. 2009). Similarly, a well-connected system for one species will not necessarily be well connected for another. Within the asymmetric connectivity formulation described here, the emphasis on connectivity is determined by the CSM. As our examples demonstrate, there often is a CSM value at which connectivity objectives are achieved (e.g., there is a high correlation between the centrality and selection frequency of selected sites, Figure 7B), while still achieving realistic outcomes for other conservation objectives (Figures 3B, 7). The most appropriate weighting on connectivity will differ among projects and should be determined by a sensitivity analysis as demonstrated in Figure 7. Low CSM will not achieve connectivity objectives, but very high CSM will lead to expensive solutions with many more sites than needed to just meet biodiversity objectives. Planners need to evaluate trade-offs between their connectivity and other objectives (such as representation and risk spreading) to reach an efficient and defendable solution.

In addition, increasing the overall ecological connectivity of a reserve network is not necessarily beneficial for all organisms (Simberloff & Cox 1987). For example, the protection of a dispersal corridor for a species of conservation concern may inadvertently also maintain the connectivity of invasive species. The development of models that accurately capture these processes is difficult, but incorporating the beneficial or harmful aspects of connectivity is important. Although an in-depth review of this duality in connectivity is beyond the scope of this article, realizing it exists is critical. Whether beneficial or detrimental, the methodology presented here can adequately accommodate the complex and asymmetric estimates.

Acknowledgments

  1. Top of page
  2. Abstract
  3. Introduction
  4. Formulation of asymmetric connectivity problem in Marxan
  5. Case studies for implementation of asymmetric connectivity in Marxan
  6. Discussion
  7. Acknowledgments
  8. References
  9. Supporting Information

This article was inspired by a workshop funded by the Commonwealth Research Facility for Applied Environmental Decision Analysis. MB and HPP were funded by ARC grants and The Nature Conservancy. SL was funded by an eWater CRC fellowship. ET was funded by a World Wildlife Fund Fuller Fellowship and an ARC grant. Thanks for M. Bode for help with GBR modeling. We also appreciated the constructive comments of the editors and three anonymous reviewers.

References

  1. Top of page
  2. Abstract
  3. Introduction
  4. Formulation of asymmetric connectivity problem in Marxan
  5. Case studies for implementation of asymmetric connectivity in Marxan
  6. Discussion
  7. Acknowledgments
  8. References
  9. Supporting Information
  • Almany, G.R., Berumen M.L., Thorrold S.R., Planes S., Jones G.P. (2007) Local replenishment of coral reef fish populations in a marine reserve. Science 316, 742744.
  • Ball, I.R., Possingham H.P., Watts M. (2009) Marxan and relatives: software for spatial conservation prioritisation. Pages 185195 in A. Moilanen, K.A. Wilson, H.P. Possingham, editors. Spatial conservation prioritisation: quantitative methods and computational tools . Oxford University Press, Oxford , UK .
  • Batagelj, V., Mrvar A. (2003) Pajek - analysis and visualization of large networks. Pages 77103 in M. Jünger, P. Mutzel, editors. Graph drawing software. Springer, Berlin .
  • Beger, M., Grantham H., Pressey R.L. (2010) Conservation planning for connectivity across marine, freshwater, and terrestrial realms. Biol Conserv 143, 565575.
  • Beier, P., Majka D.R., Spencer W.D. (2008) Forks in the road: choices in procedures for designing wildland linkages. Conserv Biol 22, 836851.
  • Bode, M., Burrage K., Possingham H.P. (2008) Using complex network metrics to predict the persistence of metapopulations with asymmetric connectivity patterns. Ecol Model 214, 201209.
  • Cowen, R.K., Paris C.B., Srinivasan A. (2006) Scaling of connectivity in marine populations. Science 311, 522527.
  • Fagan, W.F., Lutscher F. (2006) Average dispersal success: linking home range, dispersal, and metapopulation dynamics to reserve design. Ecol Appl 16, 820828.
  • Fausch, K.D., Torgersen C.E., Baxter C.V., Li H.W. (2002) Landscapes to riverscapes: bridging the gap between research and conservation of stream fishes. Bioscience 52, 483498.
  • Fernandes, L., Day J., Lewis A. et al . (2005) Establishing representative no-take areas in the Great Barrier Reef: large-scale implementation of theory on marine protected areas. Conserv Biol 19, 17331744.
  • Gaines, S.D., Gaylord B., Largier J.L. (2003) Avoiding current oversights in marine reserve design. Ecol Appl 13, S32S46.
  • Game, E.T., Watts M.E., Wooldridge S., Possingham H.P. (2008) Planning for persistence in marine reserves: a question of catastrophic importance. Ecol Appl 18, 670680.
  • Gerber, L.R., Heppell S.S., Ballantyne F., Sala E. (2005) The role of dispersal and demography in determining the efficacy of marine reserves. Can J Fish Aquat Sci 62, 863871.
  • Hanski I. (1998) Metapopulation dynamics. Nature 396, 4149.
  • Hodgson, J.A., Thomas C.D., Wintle B.A., Moilanen A. (2009) Climate change, connectivity and conservation decision making: back to basics. J Appl Ecol 46, 964969.
  • James, M.K., Armsworth P.R., Mason L.B., Bode L. (2002) The structure of reef fish metapopulations: modelling larval dispersal and retention patterns. Proc R Soc Lond S B Biol Sci 269, 20792086.
  • Jones, G.P., Almany G.R., Russ G.R. et al . (2009) Larval retention and connectivity among populations of corals and reef fishes: history, advances and challenges. Proceedings of the Workshop on Connectivity and Resilience Sustaining Coral Reefs during the coming Century Townsville , Australia , 307325.
  • Linke, S., Norris R.H., Pressey R.L. (2008) Irreplaceability of river networks: towards catchment-based conservation planning. J Appl Ecol 45, 14861495.
  • Martin, T.G., Chade's I., Arcese P., Marra P.P., Possingham H.P., Norris D.R. (2007) Optimal conservation of migratory species. PLoS One 2, e751. doi:10.1371/journal.pone.0000751.
  • McCook, L.J., Almany G.R., Berumen M.L. et al . (2009) The challenge of incorporating connectivity science into coral reef management now: principles and practice. Coral Reefs 28, 353366.
  • McDonnell, M., Possingham H.P., Ball I.R., Cousins E. (2002) Mathematical methods for spatially cohesive reserve design. Environ Model Assess 7, 107114.
  • Meir, E., Andelman S., Possingham H.P. (2004) Does conservation planning matter in a dynamic and uncertain world Ecol Lett 7, 615622.
  • Moilanen, A., Leathwick J., Elith J. (2008) A method for spatial freshwater conservation prioritization. Freshw Biol 53, 577592.
  • Mumby, P.J. (2006) Connectivity of reef fish between mangroves and coral reefs: algorithms for the design of marine reserves at seascape scales. Biol Conserv 128, 215222.
  • Newham, L.T.H., Letcher R.A., Jakeman A.J., Kobayashi T. (2004) A framework for integrated hydrologic, sediment and nutrient export modelling for catchment-scale management. Environ Model Softw 19, 10291038.
  • Newman, M.E.J. (2001) Scientific collaboration networks. Part II. Shortest paths, weighted networks, and centrality. Phys Rev E 64, 016132-1016132-7.
  • Nicholson, E., Ovaskainen O. (2009) Conservation prioritization using metapopulation models. Pages 110121 in A. Moilanen, K.A. Wilson, H.P. Possingham, editors. Spatial conservation prioritisation: quantitative methods and computational tools . Oxford University Press, Oxford , UK .
  • Phillips, J.D. (1988) Nonpoint source pollution and spatial aspects of risk assessment. Ann Assoc Am Geogr 78, 611623.
  • Possingham, H.P., Franklin J., Wilson K.A., Regan T.J. (2005) The roles of spatial heterogeneity and ecological processes in conservation planning. Pages 389406 in G.M. Lovett, C.G. Jones, M.G. Turner, K.C.Weathers, editors. Ecosystem function in heterogeneous landscapes . Springer-Verlag, New York .
  • Pyke, C.R. (2005) Assessing suitability for conservation action: prioritizing interpond linkages for the California tiger salamander. Conserv Biol 19, 492503.
  • Sale, P.F., Cowen R.K., Danilowicz B.S. et al . (2005) Critical science gaps impede use of no-take fishery reserves. Trends Ecol Evol 20, 7480.
  • Shanks, A.L., Grantham B.A., Carr M.H. (2003) Propagule dispersal distance and the size and spacing of marine reserves. Ecol Appl 13, S159S169.
  • Simberloff, D., Cox J. (1987) Consequences and costs of conservation corridors. Conserv Biol 1, 6371.
  • Stevens, J.D., West G.J., McLoughlin K.J. (2000) Movements, recapture patterns, and factors affecting the return rate of carcharhinid and other sharks tagged off northern Australia. Mar Freshw Res 51, 127141.
  • Treml, E.A., Halpin P.N., Urban D.L., Pratson L.F. (2008) Modeling population connectivity by ocean currents, a graph-theoretic approach for marine conservation. Landsc Ecol 23, 1936.
  • Vuilleumier, S., Possingham H.P. (2006) Does colonization asymmetry matter in metapopulations Proc R Soc B Biol Sci 273, 16371642.
  • White, J.W., Botsford L.W., Hastings A., Largier J.L. (2010) Population persistence in marine reserve networks: incorporating spatial heterogeneities in larval dispersal. Mar Ecol Prog Ser 398, 4967.
  • Wilson, K.A., Cabeza M., Klein C.J. (2009) Fundamental concepts of spatial conservation prioritization. Pages 1627 in A. Moilanen, K.A. Wilson, H.P. Possingham, editors. Spatial conservation prioritisation: quantitative methods and computational tools . Oxford University Press, Oxford , UK .
  • Wilson, K.A., Westphal M.I., Possingham H.P., Elith J. (2005) Sensitivity of conservation planning to uncertainty associated with predicted species distribution data. Biol Conserv 122, 99112.

Supporting Information

  1. Top of page
  2. Abstract
  3. Introduction
  4. Formulation of asymmetric connectivity problem in Marxan
  5. Case studies for implementation of asymmetric connectivity in Marxan
  6. Discussion
  7. Acknowledgments
  8. References
  9. Supporting Information

Appendix S1. Penalty file setup for a river example. If planning unit 10 needs to be protected, the penalty for not protecting unit 9 equals 1. (1/distance). The penalty for not protecting unit 8 = ½.

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Please note: Wiley Blackwell is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.