making graph theory operational for landscape ecological assessments planning and design

8/11/2019 Making Graph Theory Operational for Landscape Ecological Assessments Planning and Design

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Landscape and Urban Planning 95 (2010) 181191

Contents lists available atScienceDirect

Landscape and Urban Planning

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / l a n d u r b p l a n

Making graph theory operational for landscape ecological assessments,planning, and design

Andreas Zetterberg, Ulla M. Mrtberg, Berit Balfors

Environmental Management and Assessment Research Group, Department of Land and Water Resources Engineering, Royal Institute of Technology,

Teknikringen 76, SE-100 44 Stockholm, Sweden

a r t i c l e i n f o

Article history:

Received 16 January 2009Received in revised form 21 January 2010

Accepted 21 January 2010

Available online 1 March 2010

Keywords:

Least-cost modeling

Functional connectivity

Environmental planning

European common toad

Metapatch

Spatial redundancy

a b s t r a c t

Graph theoryand network analysis havebecome established as promisingways to efficiently exploreand

analyzelandscapeor habitatconnectivity. However, littleattentionhas been paid to makingthesegraph-

theoretic approaches operational within landscape ecological assessments, planning, and design. In this

paper, a set of both theoretical and practical methodological developments are presented to address

this issue. In highly fragmented landscapes, many species are restricted to moving among small, scat-

tered patches of different resources, instead of one, large patch. A life-cycle based approach is therefore

introduced,in whicha metapatch is constructed,spanningover theseresources, scattered acrossthe land-

scape. The importance of spatially explicit and geographically defined representations of the network in

urban and regional planning and design is stressed, and appropriate, context-dependent visualizations

of these are suggested based on experience from real-world planning cases. The study moves beyond

the issue of conservation of currently important structures, and seeks to identify suitable redesigns

of the landscape to improve its socialecological qualities, or increase resilience. By introducing both

a system-centric and a site-centric analysis, two conflicting perspectives can be addressed. The first

answers the question what can I do for the network, and the second, what can the network do for

me. A methodfor typicalplanningstrategies within each of these perspectivesis presented.To illustrate

the basic principles of the proposed methods, an ecological study on the European common toad (Bufo

bufo) in Stockholm, Sweden is presented, using the betweenness centrality index to capture importantstepping-stone structures.

2010 Elsevier B.V. All rights reserved.

1. Introduction

Land use change represents the primary driving force in the loss

of biodiversity world wide, and negative effects reach far beyond

the directly impacted areas (Vitousek et al., 1997). To preserve and

develop biodiversity and other ecosystem services, planning and

management activities must recognize the dynamics and complex

interactions within socialecologicalsystems,where physicalplan-

ning activities are an integral part, and the physical landscape is

the common point of reference. Network analysis and graph the-

oryprovidepowerful tools andmethodsfor theanalysis of complexsystems. The network is often represented by a graph, G(N,L), con-

sisting of a set of nodes, N(G) and a set of links, L(G). The linkl ijconnects nodes i andj. When using this model in landscape ecolog-

ical applications, a node typically represents a habitat patch and a

link typically represents dispersal.

Recently several papers have explored graph-based models of

specieshabitat interactions from a landscape perspective (for a

Corresponding author.

E-mail address:[email protected](A. Zetterberg).

review, see Urban et al., 2009). Many of these feature analysis

and visualization techniques useful in landscape ecological assess-

ments, planning, and design. Graph theory can be used as an

initial, heuristic framework for management, driven in an iterative

and exploratory manner, and with very little data requirements

(Bunn et al., 2000; Calabrese and Fagan, 2004).It does not require

long-term population data, making it an important tool for rapid

landscape-scale assessments (Urban and Keitt, 2001),but graph

theory is at the same time dynamic,allowingadditional knowledge

to be incorporated. Despite itssimplicity,a graph model based only

on habitat and dispersal distance, has been shown to make predic-tions very similar to a spatially explicit population model (SEPM),

which had nine additional life-history and behavioral parameters

(Minor and Urban, 2007).

Another attractive property of network analysis is itslong tradi-

tion, welldeveloped andtested tools, as wellas efficient algorithms,

used in a wide variety of disciplines (e.g. Ahuja et al., 1993),many

of which are used in planning. Several graph-theoretic metrics

related to classical network analysis problems, such as maximum

flow, connectivity, and shortest paths, have been developed over

decades, andBunn et al. (2000)as well asUrban and Keitt (2001)

haveproposedecological interpretations for someof these. Someof

0169-2046/$ see front matter 2010 Elsevier B.V. All rights reserved.

doi:10.1016/j.landurbplan.2010.01.002
http://www.sciencedirect.com/science/journal/01692046http://www.elsevier.com/locate/landurbplanmailto:[email protected]://localhost/var/www/apps/conversion/tmp/scratch_9/dx.doi.org/10.1016/j.landurbplan.2010.01.002http://localhost/var/www/apps/conversion/tmp/scratch_9/dx.doi.org/10.1016/j.landurbplan.2010.01.002mailto:[email protected]://www.elsevier.com/locate/landurbplanhttp://www.sciencedirect.com/science/journal/01692046


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A. Zetterberg et al. / Landscape and Urban Planning95 (2010) 181191 183

such a wayas to achieve the planningobjectives. The followingcri-

teria are based on the results from seven real-world planningcases

involving stakeholders from many disciplines (Zetterberg, 2009).

In order to be successfully operational within planning, design,

or assessment activities, the graph-based approaches need to be

spatially explicit, and geographically defined. Another important

aspect is the ability to deploy these theoretic concepts in a case-

dependentcontextand daily workingenvironment already in place

by planners and designers. The operational maps of the network

should therefore be implemented in such a way that they can be

used seamlessly with other maps, tools andconstructs used within

the planning and design process, which is often achieved using a

GIS. As an example, a mapping of each site together with a quick

overview of potential impacts and concerns has been shown to

be an important communicative tool between different types of

stakeholders (Theobald et al., 2000).

Graph models of networks can be presented in many different

ways dependingon thecontext(Fig.1). A simple visualization tech-

nique used within landscape ecology is to present geographically

explicit graphs, showing the full extent of the linked patches on

top of a map (e.g.Bodin and Norberg, 2007; Fall et al., 2007; Keitt

et al., 1997; OBrien et al., 2006; Urban and Keitt, 2001; Uy and

Nakagoshi, 2007; van Langevelde, 2000; Zhang and Wang, 2006).

This corresponds toFig. 1b.However, the extent of the area corresponding to the links,

such as the migration or juvenile dispersal zones, must also be

considered (Fig. 1c). This is just as important from the mapping

perspective as the geographic extent of the patches. In addition,

there are of course several other plausible mapping possibilities

and the users engaged in planning, assessments or design activi-

ties need tobe able toswitch between differentvisualizations ofthe

graph dependingon the context andsituation. The ability to visual-

ize differentaspects of thenetwork using a varying degree of detail

depending on the context and scale, as for example when zooming

between a regional overview and a detailed local perspective, is

a crucial part of making the graph-based approaches operational,

placing the local planning and design in a regional network con-

text. One interesting approach has been presented byTheobald et

al. (2006) where several different visual and geographically defined

representations of nodes, links, patches, and linkages can be mixed.

Several of these visual representations are adopted and used in

this paper and suggestions on when to use which representation

are presented throughout the case study. The tools used to create

the different representations span from standard software through

third-party software to our own developments and are presented

in their respective methods section.

2.3. Study area and geospatial data

An ecological study was performed within the county of Stock-

holm, the capital of Sweden (Fig. 2a), using the European common

toad (Bufobufo) asa focalspecies.First, a regionalstudyof thewhole

county was performed (Fig. 2b), after which a local study (Fig. 2c),

followed by a more detailed study (Fig.2d), both withinthe munic-

ipality of Stockholm, were carried out. The regional study aimed

at finding important ecological structures through the region. The

local studyillustrated examples of finding areaswith improvement

potential both from a system-centric, and site-centric perspec-

tive. The detailed study showed how to liberate this improvement

potential through the construction of three new spawning ponds.

Fig. 2. Study areas. (a) The location of the study area for the regional study, encompassing Stockholm County. (b) The entire study area in detail and points out the location

of (c), showing the study area for finding improvement potential in the municipality of Stockholm. (d) The study area for designing a link through the National Urban Park.


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184 A. Zetterberg et al. / Landscape and Urban Planning95 (2010) 181191

The geospatial data used as input for modeling were GSD-

Landcover and GSD-Propertymap (National Landsurvey of Sweden,

2006), a biotope map (Lfvenhaft et al., 2002; Stockholm

Municipality, 1999),and a vegetation map (Sollentuna kommun,

1993). GSD-Landcover contains about 60 landcover and vegetation

classes andis based on Multispectral satellitedatafrom Landsat TM

with 30 m30 m geometric resolution. The biotope map and the

vegetation map are based on interpretation of aerial photographs,

and together with the GSD-Property map, they were used to com-

plement GSD-Landcover with smaller waterbodies and wetlands.

The biotope maphas previously been used to assess the amphibian

distribution in Stockholm Municipality (Lfvenhaft et al., 2004).

2.4. A life-cycle based approach and the metapatch concept

In highly fragmented landscapes, such as urbanizing regions,

many species are restricted to moving among small, scattered

patches of different resources instead of one, large, contiguous

habitat patch. In these cases, the traditional approach of construct-

ing a patch by selecting contiguous cells of some land use class

will fail. If instead modeling the accessibilityof different resources

needed, a habitat patch can be constructed that spans over scat-

tered resources and includes the regions needed to move between

them. Such a patch is in this sense a metapatchresembling theideaof smaller sub-populations forming a metapopulation.

Another seldom emphasized fact is that the size and type of a

patch vary with the temporal scale. Theobald (2006)argues that

the functional definitionof a patch depends on the movement type

considered, and that these occur at a range of temporal scales. For

example, for a certain organism with temporal dynamics similar to

human, themovementtype on a dailybasis could typicallybe forag-

ing,and the patches reflectingthe correspondingtime framewould

therefore contain foraging resources. On a yearly basis, the move-

ment types could typically be natal dispersal and genetic exchange,

and the patch types would be home-range patches (either annual

or lifetime). On a centurial basis, the relation could typically be

long-term genetic exchange and the patches would correspond

to (meta-) population patches. The same reasoning can be usedfor the traditional matrix and corridor concepts; as the temporal

scale increases and the patches change type, parts of what was

previously considered matrix or connectivity zone are successively

incorporated intothe patch, andnew connectivityzones are formed

reflecting the processes relevant at the new time scale ( Fig. 3).

In order to generalize this view and devise a method more suit-

able for fragmented landscapes, a life-cycle based approach and

the general metapatch were introduced. Metapatches and links

need to be defined with respect to a temporal scale related to a

specified partof the life-cycle. Thesewere hereconstructedby find-

ing contiguous areas containing all resourceswithin reach, needed

throughout this selected part of the life-cycle. In this study, the

metapatches were set to represent annual home-ranges, contain-

ing all the resources needed throughout the year (e.g. spawning,foraging, overwintering), including the migration zones between

these resources. The links and corresponding connectivity zones

were accordingly set to represent juvenile dispersal.

2.5. Cost-distance modeling of the common European toad (Bufo

bufo)

Cost-distance analysis (for details, see for exampleAdriaensen

et al., 2003)was used to define the annual home-range patches

according to our life-cycle based approach. This enabled the con-

struction of a metapatch to be based on the accessible necessary

life-cycle resources scattered across the landscape. The migra-

tion zones between the resources were automatically integrated

into the patches. For the analysis, ArcGIS cost-distance was used

Fig. 3. Schematic overview of how clusters of patches and links gradually build

up larger metapatches, connected by new links as the temporal domain increases.

Clusters of resourcepatches and linksmake up home-range patches, whichare con-

nected by dispersal links. On a longer time scale, these home-range clusters make

up (meta-)population patches, connected by genetic links.

(ESRI, 2006).This tool needs two GIS-layers, a source and a friction

layer, as input. In the proposed method, the source layer contains

patches of the resourcesin the landscape, and the frictionlayercon-

tains the different costs of movement across each raster cell. The

annual home-range patches were based around potential breeding

sites, and the source layer was therefore constructed by selecting,

from the geospatial datasets, all pixels corresponding with suit-

able parts of lakes, ponds, or wetlands (Table 1).A range for each

input parameter was found through semi-structured interviews

with four experts inNovember2005. Anassessmentof these ranges

was conductedby the authors in anattempt to find a representative

parameter set.

The outputis an accessibility map, containing the total least-cost

to move from each cell to its closest source across the friction sur-

face. By setting the friction for optimal habitat to 1, the least-cost

throughoptimal habitat is equalto the Euclideandistance along the

same path. The geographic extents (i.e. the borders) of the annual

home-range patches werefinally found by setting a thresholdvalue

for the maximum effective distance from a resource, in effect cor-

responding to a probability threshold of reaching that far within a

year. The probability of migrating a certain distance from a source

is often modeled using a negative exponential decay kernel (e.g.Bunn et al., 2000; Urban and Keitt, 2001):

pij =e(dij),

where pij is the probability of migrating from point i to point j,

dij, is the distance from point i to j, and is a species-specific

parameter. The parameter assessment suggested = 2.30103,

corresponding to 90.0% of the individuals migrating a distance

less than 1 km, and 99.0% less than 2km within the annual home-

range patch. The probability threshold for the metapatches was

selected to cover 90% of the annual migration events, correspond-

ingto an effectivedistance of 1 km.Any metapatchesnot containing

all the required resources, in this case, reproduction sites, sum-

mer habitat and winter habitat (Table 1),within reach (i.e. within


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Table 1

Parameter values for the different kinds of vegetation classes found through expert solicitation.

Biotope Resource Friction

(S) summer habitat

(W) winter habitat

(R) reproduction habitat

Forest

(deciduous, mixed, coniferous)

S, W 25

Wetland

(smaller open, semi-open, wooded)

S, W, R 1

Larger water bodies 2

Open grassland

(natural or cultivated)

S, W 25

Semi-open land

(gardens, sparsely developed land w

trees/bushes)

S, W 15

No or sparse vegetation 1050

the effective distance and therefore within its boundaries) were

eliminated.

Juvenile dispersal was also modeled using cost-distance meth-

ods. Male toads are sexually mature in their 3rd year (Hemelaar,

1983),and therefore the probability of effective juvenile dispersal

distances was modeled in the same way as the annual migrationdistance, only this time using = 7.67104, corresponding to a

three times longer distance than the annual migration distance (to

be reached within 3 years). Potential dispersal zones were mod-

eledusing theConditionalMinimumTransitCost (CMTC) (Pinto and

Keitt, 2009), where the CMTC of eachraster cell is the effective dis-

tance between two given patches along the least-cost path passing

through that particular cell. This was done using ArcGIS least-cost

corridor(ESRI, 2006), which uses twocost-distancerasters as input,

one for each of the two patches between which the corridor is to

be found. The output is a raster showing, for each cell, the CMTC

between the two sources used to form the input rasters. By using

the threshold level for juvenile dispersal given above, a potential

dispersalzone is found between thetwo patches, containing all the

cells along all least-cost paths shorter than the threshold distance.

2.6. Finding important structures within the network

After havingfound the annual home-range patches and the dis-

persal links between these, graph theory was used to filter out

importantstructures within the network,i.e. which of these patches

and links could be considered more important from a certain per-

spective. For the purposes of this study, the chosen perspective of

importance was finding stepping-stones through the highly frag-

mented and urbanized parts of the landscape that are critical for

keeping the network connected. These stepping-stones are typi-

cally not important for example as major sources of recruitment,

but rather for the long-term genetic flow through barriers such

as built-up areas, infrastructure, or large water bodies. Without

these stepping-stones, the network would fall apart into at least

two smaller components instead of one larger component.

The betweenness centrality index (Freeman, 1979) has been

proposed as a suitable measure of stepping-stone importance

(Bodin and Norberg, 2007; Minor and Urban, 2007).For a graph,G = (N,L), the betweenness centrality CB(n) of node n is calculated

as:

CB(n) =

i /=n /=j N

i /=j

ij(n)

ij

whereij is the total number of least-cost paths from node i to j,

andij(n) is the number of least-cost paths fromitojthat actually

pass through node n. Hence,the index fornode n corresponds to the

proportion of all possible least-cost paths of the network that are

routed through noden.

In order to find important stepping-stone structures through

the network, betweenness centrality was therefore calculated, and

the corresponding important landscape structure was visualizedby emphasizingthe resulting importantpatchesin the maps. These

were found using ArcGISnatural breaks(ESRI, 2006), which creates

data classes according to clusters by maximizing their differences.

The classes are ranked, and when increasing the number of desired

classes, additional break points do not affect the previously found,

higher ranked break points. The top two classes filtered out less

than 1% of the patches while still forming a connected structure

through the bottleneck in the center, and were therefore selected

as important (Fig. 5).

2.7. Exploring the improvement potential from two perspectives

In order to move from an assessment of the current situation

and illustrate how to look for improvement potential, two differentperspectives, the site-centric and system-centric, were introduced.

The site-centric perspective focuses on finding parts of the sys-

tem that can be modified to improve the situation at a particular

geographic site, while the system-centric perspective focuses on

finding parts that canimprovesome studied property forthe entire

system. These perspectives can often be conflicting and trade-offs

between them need to be considered.

A method for finding improvement potential from each of these

twoperspectivesispresentedbelowandin Fig.4. The system-centric

perspective, aimedat finding areas withthe potentialfor improving

the resilience of the important internal structure of thenetworkby

increasing its spatial redundancy. The increase in resiliencewas not

based on a comparison between quantifiedmeasures, butrather on

the argument that increasing the link (or node) redundancy in thenetwork makes the network more resilient to the removal of links

(or nodes) (Janssen et al., 2006).

First the important structure needs to be identified. In the case

study, this was made up of the nodes with high betweenness

centrality and their interconnecting links as previously explained.

Regions within this structure with little redundancy (i.e. important

regions but with very few alternative routes through the network)

were consideredcritical. The criticalregionsfacing highthreats (e.g.

urbanizing areas), received the highest priority (Fig. 4a) in which

improvement potential should be looked for.

The attention then turned to the existing non-important struc-

ture in this high-priority region. The non-important structure

contains nodes and links that could be considered as poten-

tial building-blocks. Areas where redundancy could effectively


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Fig. 4. Schematic overview of the methods for finding improvement potential. (a) System-centric perspective. Regionallyimportant nodes (solid) are presented together

with theother nodes,the building-blocks (hollow).A vulnerablearea with lowredundancy is indicated andan area suitable forcreatingredundancy is found.(b) Site-centric

perspective. Three locally important nodes (solid), with differentnetwork-related properties, are shown: (i) well-connected,(ii) isolated,(iii) exposed (due to the single link).

Areas with improvement potential for the latter two are highlighted.

be created by restoring nodes or links were considered to have

improvement potential from the system-centric perspective.

The site-centric perspective aimed at finding areas with the

potential of mitigating the exposure or isolation oflocally impor-

tant sites. A generalization of the concept of exposure (Jenelius et

al., 2006)is that a site is exposed if small changes in the network

have large consequences for the local site, which can ultimately

become isolated. For this analysis, important sites, not withrespect

to the system but rather for some other reason such as high recre-ational values, were identified (Fig. 4b). Among these sites, those

highly exposed or isolated from the network were identified. In

the case study, a highly exposed site was simply a site with one or

very few links. Areas in the network where the exposure or isola-

tion could be mitigated, for example by restoring a link or adding

redundancy, were considered to have improvement potential from

the site-centric perspective.

A suitable representationof the network corresponding to Fig.4

was created using the third-party ArcGIS tool FunnConn (Theobald

et al., 2006).By using the previously created home-range patches

and the friction values as input and setting the thresholds for dis-

persal previously given, this tool can create an attractive visual

representationof thenetworkthat we suggestis suitableat thispar-

ticular scale. This representation shows the patches together with

simplifiedmultiplelinkages(Theobald, 2006; Theobald et al., 2006)

between these (Fig. 6). The linkages are simple representations

showing the approximate locations of the different connectivity

zones between the patches.

3. Results

3.1. Cost-distance analysis

Aggregation of the pixels selected as suitable for reproduction

resulted in 22 428 potential reproduction patches within the study

area of whichmanywere incorporatedintothe same annualhome-

range patches during cost-distance analysis. The cost-distance

analysis resulted in 1361 separate annual home-range patches

(Fig.5a) and4372links with an effectivedistance belowthe thresh-

old level of 6 km, covering 99.0% of the potential dispersal events.

3.2. Finding important structures within the network

The betweenness centrality index managed to clearly highlight

the important small stepping-stones connecting the northern with

the southern parts of the county. Two threshold levels, 1.74102

(class 2) and 8.38102

(class 1), were found using ArcGIS naturalbreaks(ESRI, 2006). The99 outof all1361 metapatches correspond-

ingto a value within anyof these classes wereconsideredimportant

with respect to this index, since theremoval of anyof these patches

would significantly increase the average least-cost dispersal dis-

tance between tworandomly chosen nodes of the network (Fig. 5b).

Twomajor structures emerged within thestudyarea:a stronger

western path, with several small but critical stepping-stones

through parts of the municipality of Stockholm, and a weaker east-

ern path through parts of the Stockholm archipelago. The patches

witha value belowthese thresholds werenot considered regionally

important with respect to betweenness centrality, and therefore

only visualized inFig. 5a.

3.3. Identification of improvement potential

In the regional study, the graph was based on 22 428 potential

reproduction sites, which is too many to be effectively visualized

as any of the graph examples in Fig. 1, and the visualizations in

Fig. 5were therefore considered more appropriate. When zoom-

ing in, however, and studying the role of the part of the network

situated within Stockholm Municipality (Fig. 2c), fewer nodes and

links need to be visualized. This opens up for an intermediate and

moredetailed representation(Fig. 6, similar to Fig.1b), showingthe

same information asFig. 5,but in addition the links are shown. All

patches and links are included in this representation to show the

potential building-blocks (striped) of the network, and at the same

time the regionally important patches withrespect to betweenness

centrality (both class 1 and class 2) are highlighted (solid).


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Fig. 5. All of the 1361 patches are shown to the left (a), and the patches considered important (class 1 and class 2) with respect to betweenness centrality are shown to the

right (b). These small stepping-stone patches run through, and on either side of the city of Stockholm.

This patch-link representation gives insights into the relations

between the local network structure and the regionally important

structure; it matches the method presented inFig. 4, and can be

used to find parts of the network with improvement potential both

from a system-centric, and a site-centric perspective.Fig. 6shows

examples of both these perspectives. Restoringarea (b) would have

virtually no effect on the rest of the network but rather enable

a stronger influx of propagules into the site itself, which is con-

sidered locally important due to its accessibility, biodiversity, and

recreational values for the inhabitants of Stockholm Municipality.

3.4. Connecting the National Urban Park

In order to find the spatial extent of an area in which a new link

could be created into the southern part of the National Urban Park,

the least-cost corridor tool (ESRI, 2006)was run between the two

involved patches. By relaxing the threshold for the CMTC (which

would normally correspond to the maximum juvenile dispersal

distance), a potential restoration zone emerged (Fig. 7).This area

was studied in detail with the aim of adding new ponds, and for

this the potential restoration zone was visualized in a GIS together

withother contextually importantinformation,such as the biotope

map, topography, an orthophoto, property boundaries, and a city

map for local reference. Three new ponds were considered to be

sufficient to direct the flow of amphibians through the area and to

restore the connection, and within this new connection there was

sufficient summer and winter habitat. Fig. 7shows the suggested

locations for these three newponds, andalso illustrates the impor-

tance of visualizing thisin a spatiallyexplicitmanner, togetherwith

relevant GIS-data.

The effect of the redesign was evaluated by re-running the cost-

distance analysis for the new network containing the new ponds,

andtheir correspondinglinks usingthesethree newsources (Fig.8).

The longest of the least-cost effective distances between the two

initial home-range patches decreased dramatically from 9702m

to 1096 m (effective), improving the probability of dispersal for

a propagule through the link. As a result of the additional three

breeding ponds, the productive area, and thus the potential net

production, also increased. The combined effect of the increased

dispersal probability and potential net production is a significantpotential increase of the dispersal flux in the region. The potential

influx to the previously isolated area therefore increased.

4. Discussion

4.1. Operational aspects

One of the major advantages of the network approach was the

abilitytozoominandoutbetweenalocalareaandtheentireregion,

while efficiently incorporating important system properties into

the respective planning context at each scale. Knowledge from the

network analysis in combination with the corresponding spatial

extents of the nodes and links, can thus provide input to both the


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Fig. 6. Patch-link representation of a network revealing the relationship between important patches, other available building-block patches and improvement potential

gaps. Solid patches are regionally important with respect to betweenness centrality (fromFig. 5b). Striped patches are those with lower betweenness centrality (potential

building-blocks). Twoexamplesitesare highlighted.Site(a) in theupper left corner hasthe potentialof restoringa link toimprove resilience of theregional network through

increased spatial redundancy. Site (b), has the potential of connecting the locally important, but isolated southern part of the National Urban Park, to the rest of the network

in the north.

regional and the local planning process, such as when developingcomprehensive plans. Understanding which nodes and links are

important, or even critical, and their spatial extents, facilitates the

identification of areas with high ecological values that are in need

of protection, as well as areas with low ecological and social val-

ues that could have an improvement potential. For example, there

may be a potential for improving the ecological properties such as

connectivity or resilience in some cases, and social properties such

as housing or transportation in others.

Results from seven real-world planning and assessment cases,

involving different kinds of stakeholders (Zetterberg, 2009),

demonstrate the need to be able to move from the overall systems

analysis leveldown to the planningand assessmentmaps, under-

standing notonly how the overall systemis affected, butalso where

critical areas are situated. It is also valuable to understand why cer-tain impacts arise,and the geographic extentof critical regions. The

results also call for the inclusion of an assessment of the improve-

ment potential in addition to the assessment of the currentsituation,

and finally how to design the landscape so as to mitigate negative

impacts, or evenimprove desirable properties. The ability to switch

to a close-up of network, showing itsspatial extent, andin the same

GIS add other important information such as topography, property

boundaries, roads, and vegetation turned out to be a major quality

in the process of landscape design.

4.2. Betweenness centrality

The betweenness centrality index (Freeman, 1979)managed to

clearly highlight the importance of the smaller stepping-stones.

This result is in agreement withBodin and Norberg (2007)statingthat this index manages to emphasize areas thought to be impor-

tant to the connectivity of the network even when the risk for

habitat isolation is low.Minor and Urban (2007)also showed that

betweenness centrality could be used to identify stepping-stone

patches that were not easily identified with an SEPM.

An ecological interpretation of betweenness centrality is that

it could indicate areas with long-term genetic variety. The index

identifiesthe patches routing the highest proportionof the shortest

effective dispersal paths within the network. Since the algorithm

is influenced by all patches, including those that are far from

each other and thus probably more genetically different, patches

with the highest betweenness (Fig. 5b) may indicate the geneti-

cally most diverse paths through the network. These paths could

therefore be regarded as important for biodiversity at the geneticlevel, and should then be considered in impact assessments, such

as Environmental Impact Assessment and Strategic Environmental

Assessment.

When increasing the number of patches within a region, the

relative importance of each of these decreases. Hence, an impor-

tant region with many alternative patches (i.e. high redundancy)

may not be identified as important until all but a few patches are

removed. This may result in difficulties finding or designing regions

that are important and redundant at the same time.

The example in this paper has only dealt with importance with

respect to stepping-stone quality, using betweenness centrality.

However, even though most of the patches of Fig. 5a are not

important with respect to betweenness, several of them are most

probably important in other aspects, such as major sources for


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Fig. 7. An area suitable for redesigning the network was found by calculating a potential dispersal zone (striped area) between two existing but unconnected annual

home-range patches, and presenting this area together with other important information for the design, such as topography and buildings.

Fig. 8. The effect of the redesign is illustrated by showing the new home-range patches (striped patches), formed around each of the three new ponds, and the new links

(dashed lines) between the patches. Note that two new links were found between the southernmost of the new patches and the two original patches in the very south.


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recruitment, or as redundant back-up routes building resilience.

Within the planning and design process as well as in ecological

assessments, several different aspects of the network need to be

studied. Size,quality andconnectivity are three examples of impor-

tant attributes of the patches within a network (e.g. Minor and

Urban, 2007).

4.3. Important network structures

Notwithstanding its limitations due to uncertainties, the graph

is useful as a heuristic framework requiring little data (Bunn et

al., 2000; Urban and Keitt, 2001),and critical parts of the network

can still be identified, for example using patch importance indices

found through patch removal (Keitt et al., 1997),or using central-

ity indices (Estrada and Bodin, 2008). The critical structures can

then be emphasized using a ranking of these important patches

and selecting the top ranked patches (Urban and Keitt, 2001),or

as was done in this paper, finding thresholds using natural breaks

for the index and emphasizing all patches that are more important

than the threshold level. The number of important patches can be

increased by including more classes into the natural breaks tool.

The natural breaks correspond to threshold values where theindex

changes rapidly, whichcould be used as an effective way of negoti-

ating the trade-off between protectedimportant structuresand thecorresponding area required. Similar techniques have been used to

explore trade-offs between a patchs contribution to overall con-

nectivity and its corresponding increase in protected area (Rothley

andRae,2005), or to analyze criticalthresholds in connectivitywith

respect to dispersal distance (e.g.Keitt et al., 1997).In this kind of

analysis, the critical spatial structures of the links need also to be

considered in addition to those of the patches.

4.4. Cost-distance modeling and ecology

Traditionally, the friction values in cost-distance modeling are

related to a mixture of energyexpenditure, behavioral aspects, and

mortality risks (e.g.Adriaensen et al., 2003; Joly et al., 2003; Ray et

al., 2002; Theobald, 2006).As a consequence, areas with high mor-tality are assigned a higher friction value, which in effect results

in a reduction of the accessible patch area instead of for example

a reduction of the surviving number of propagules. In this study

we therefore separated mortality risks from energy expenditure,

only acknowledging energy expenditure as being part of the effec-

tive distance. This opens up for other methods for handling the

mortality risks, such as probability-related models, which in turn

can result in both a better geographic representation of the poten-

tially accessible patch, and a separate analysis of how to mitigate

mortality risks.

As an example, roads were assigned to the class no or sparse

vegetation (Table 1)with friction values only related to energy

expenditure. Traditionally however, roads would be considered a

barrier due to high mortality and assigned extremely high frictionvalues. This would give the false impression that the potentially

accessible patch is small, bordered by a road and with no informa-

tion about mortality. In this paper, the roads are considered just as

accessible as any land with no or sparse vegetation, but deadly. In

reality, they should be considered to be population sinks. By sepa-

ratingmortality from friction, the road layer can be added on top of

the potentially accessible patch producing a map of conflict areas

in need of mitigation or monitoring.

There are also a number of problems related to the ecological

assumption of least-cost. First of all, low cost (i.e. low friction)

of the landscape for an organism does not necessarily imply that it

is the chosen route through the landscapefor that particular organ-

ism. Indeed, taking amphibians as an example, there are indications

that juveniles of some species tend to migrate towards a spe-

cific habitat, such as distant forests, even though the local friction

may be much lower in other directions (e.g. Sjgren-Gulve, 1998;

Walston and Mullin, 2008).Second, even though some indices of

connectivity take the size and often even some quality-weighted

area of the patches into account, this is usually not the case for

the links. In essence, basing the connectivity index only on some

functionof the least-cost path hasthe unwantedside effectthatthe

entire dispersal zone between two patches could be removed, leav-

ingnothing morethan a narrow region around thepath withoutthis

affectingthe value of the index. This may make an index calculated

in this way unsuitable as an indicator of connectivity, for example,

bothwithin environmental assessments, planning, and design. One

of the major challenges will be to better model the probability of

dispersal or the dispersal flux between two patches as well as the

corresponding spatial extent of the dispersal zones.

Theobald (2006)has raised parts of this issue by introducing

the concept of multiple-paths, also recognizing the problems asso-

ciated with the least-cost path. This has been further explored

by Pinto and Keitt (2009), using two different methods to find

multiple-paths. One of them, CMTC, was used in this paper to con-

struct dispersal zones. However, eventhough these methods create

multiple-paths or connectivity zones, they are still based on the

concept of the least-cost path which again may not be ecologi-

cally relevant. Another promisingapproach, basedon random walktheory, is using circuit theory which also allows the modeling of

multiple-paths between nodes (Mcrae et al., 2008).

4.5. Redundancy, resilience, and planning

Within physical planning, it is of interest to know which areas

are suitable to develop without a large negative ecological impact.

One way of achieving this is to look for redundancies in the net-

work. However, one has to keep in mind that the resilience of

the network with respect to link (or patch) removal is degraded

when removing spatial redundancy in the network (Janssen et al.,

2006).Indeed, one of the results in this paper illustrated how to

increase resilienceby finding areassuitable for creatingredundancy

in important structures. Nevertheless, a deeper understanding ofthe network structure helps to select areas where redundancy can

be increased as well as areas that are of less ecological importance

andwhere redundancy could be decreased, allowingfor other func-

tional aspects of the landscape, such as housing.

Acknowledgements

The study was financed by Formas, the Swedish Research Coun-

cil for Environment, Agricultural Sciences and Spatial Planning.

We thank Ebbe Adolfsson, Bjrn-Axel Beier, Margareta Ihse, Oskar

Kindvall, and Lars-Gran Mattsson for interesting discussions and

valuable input. We would also like to thank the reviewers for tak-

ing their time and giving constructive feedback. Finally, we would

like to thank Claes Andrn, Jon Loman, Jan Malmgren, and PerSjgren-Gulve for their valuable time and input during the expert

solicitation.

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