Jordán, F. 2003. Quantifying landscape connectivity: key patches
and key corridors. In: Tiezzi, E., Brebbia, C. A. and Usó, J.-L.
(eds.), Ecosystems and Sustainable Development IV, WIT Press,
Southampton, pp. 883-892.
Quantifying landscape connectivity: key
patches and key corridors
Ferenc Jordán
Department of Plant Taxonomy and Ecology, Eötvös University,
Budapest, Hungary
Abstract
The problems of habitat loss and fragmentation call for understanding how do
ecological landscapes serve the needs of inhabiting metapopulations. Questions of
extreme importance are (1) how connected are landscape graphs in nature, (2)
how to measure this connectivity mathematically, and (3) how do the spatial
elements of the landscape contribute to the maintenance of connectivity. I
propose a landscape graph analysis where the positional importance of individual
habitat patches (nodes) and ecological corridors (links) is quantified. This refers
to the role of these spatial elements in maintaining landscape connectivity, i.e.
how will the landscape graph be damaged after losing its patch or corridor in
question. Our approach takes into account both structure and function; functional
aspects are expressed by the assessed quality of patches and corridors. I illustrate
this approach on a case study and, within the limits of our theory, I set
conservation priorities. In other words, I determine which patch’s lost is the worst
and which patch’s lost is the least wrong. However this analysis has a single
species in focus, I believe that, if adequate species are targeted (keystones,
flagships, umbrellas, etc…), the value of single-species approaches may be high.
I emphasize that (1) the use of spatial elements can be assessed only in a
landscape context, (2) functional aspects must complement pure structural
descriptions, and (3) quantitativity is a primary property of effective conservation
methods.
1 Introduction
The loss and fragmentation of natural habitats raises the problem whether local
populations in small habitat fragments become perfectly isolated or remain
connected to others. Small, isolated, local populations face a high risk of
extinction, because of genetic, demographic and stochastic reasons. Migration
and the resulting gene flow between habitat fragments may well be the only key
for survival in the case of a number of species [1]. If corridors connect habitat
patches and individuals can migrate through the network of these landscape
elements, metapopulation dynamics emerges [2]. The efficiency of migration
(and gene flow) depends on the topology of landscape elements (i.e. corridors and
patches, cf. Pickett and Cadenasso [3]) and their topographical properties (e.g.
corridor length). One of the major attributes of landscape graphs is their
connectivity but presently there is no consensus on how to measure it (moreover,
certain measures produce the contraintuitive artefact that fragmentation increases
connectivity). Further, there is no good approach to how to evaluate the
importance of individual landscape elements in maintaining landscape
connectivity (against fragmentation). I support the view that the value of either
habitat patches or ecological corridors can be assessed only within a network
context (cf. van der Sluis and Chardon [4]): a patch described by not very good
parameters (e.g. fertility, humidity, local population size) still can be a key habitat
fragment if its positionality within the whole landscape graph is extremely
important for maintaining migration patterns. However I only target to analyse
the landscape structure of a single species, and I acknowledge the limitations of
such results, I also hope that using these methods for analysing focal species (e.g.
umbrella, flagship, or keystone species) might be of outstanding importance [5].
Here, my aim is to present a considerably small-scale case study for
illustrating the use of some graph properties referring to landscape connectivity,
to construct a combined importance index for individual spatial elements and to
set conservation priorities, within the limits of this approach.
2 Area and the focal species
The seriously endangered, brachypterous bush-cricket Pholidoptera
transsylvanica inhabits only tall-grass semi-dry swards. Its predatory behaviour
and high mobility ensures that individuals migrate easily between certain patches
of this habitat type, if permeable corridors exist between them. The network-like
habitat structure of P. transsylvanica is characteristic for the species. The
metapopulation inhabiting the Aggtelek Karst region of NE-Hungary is perfectly
isolated from the two other Hungarian metapopulations [6, 7], so, individuals live
in a well-defined network of suitable habitats.
3 Methods of analysis
3.1 Landscape graph construction
First, the habitat structure of P. transsylvanica was determined, based on field
observations (cca in a 40 years interval) and recently detected acoustic signals of
stridulating males. Three independent observers proposed nearly exactly the same
landscape graph, and, however mark-recapture techniques do not work for this
species, a reliable consensus graph has emerged (Figure 1). This contains 11
habitat patches (coded by N, for graph nodes) and 13 corridors (coded by L, for
graph links). The names of patches are as follows: (1) "Huszas töbör", (2) "Kis
tisztások", (3) "Szilicei kaszálók", (4) "U-alakú töbör", (5) "Nagy-Nyilas", (6)
"Mogyorós-rét és tisztás", (7) "Árvalányhajas", (8) "Dénes töbör", (9) "Nagyoldal
mögötti tisztások", (10) "Gyertyánsarjas", (11) "Lófej-forrás alatti tisztás".
6
4
5
3
7
1
8
10
2
11
9
Figure 1: The weighted, semi-quantitative landscape graph of the studied
Pholidoptera transsylvanica metapopulation. Nodes represent
habitat patches; the radius is proportional to local population size
quantified by {1, 2, 3, 4}. Links represent ecological corridors.
Here, thicker lines show more permeable corridors (quantified by
{1, 2, 3, 4}). Patch names (1-11) are given in text.
A semi-quantitative estimation on the quality of these spatial elements were
also given. Both patch-quality (understood as local population size) and corridorquality (understood as permeability) were quantified by integers from 1 to 4: „4”
marks easily permeated corridors and large local populations. „1” marks hardly
but still permeable corridors and small local populations. I refer to these semiquantitative weights by „topography”.
3.2 Landscape graph analysis
Global indices describing the whole network and local indices describing a graph
point or link and its neighbourhood are analysed. Both basic topological and
topographical network properties are studied (topography now means weights on
nodes and links). Figure 2 illustrates some basic considerations formalized below.
The number of neighbours of the ith node is its degree (Di). For example, the
patch N3 has four neighbours (N2, N4, N5, N10), thus, DN3 = 4. For links, let
degree mean the average degree of their endpoints: DL2,3 = (DN2 + DN3) / 2 = 2 + 4
/ 2 = 3. A spatial elements of higher degree can be considered more important: its
loss affects more seriously the connectivity of the landscape graph (i.e. it has a
larger role in maintaining connectivity).
a
b
c
d
e
f
Figure 2: Six hypothetical landscape graphs illustrate how certain local indices
may reflect positional importance. The habitat patch represented by
the full circle is always in focus. Evidently, it is in more important
position (1) in "b" than in "a", because it is connected to more
neighbour patches (Db = 4 > Da = 2); (2) in "d" than in "c", because its
neighbours are less connected to each other (CCd = 0 < CCc = 0.66);
and (3) in "f" than in "e", because it is in a less periferial position
(measured by topological distance, df = 1 < de = 1.71). Further
explanation in text.
The clustering coefficient of the ith node (CCi) refers to how the neighbours of
i are connected to each other: it gives the ratio of actual to possible links between
these nodes in the graph. For example, node N10 has four neighbours (N3, N5,
N7, N11) and only two links exist between these nodes, however the maximum
number of links between four nodes equals six. Thus, CCN10 = 2/6 = 1/3. I note
that it would be reasonable not to consider crossing links that cannot be drawn in
two dimensions but this causes no serious failure in case of such small webs. If
the clustering coefficient is smaller, the neighbours are more separated when i is
deleted, thus, its importance is higher. For corridors, CCLX,Y is the average of
CCNX and CCNY.
The topological distance dX,Y between two nodes X and Y of a graph is the
minimal number of links connecting the two nodes. For example, the distance
between nodes N7 and N9 is d7,9 = 2 (we also can go from N7 to N9 through a
four-steps route including N6, but this is not a minimal route, i.e. this is not their
distance). The average distance of node i in a graph (di) is its distance from a
randomly selected node of the graph. For example, the distance of node N5 from
others is: dN1,N5 = 3, dN2,N5 = 2, dN3,N5 = 1, dN4,N5 = 2, dN6,N5 = 1, dN7,N5 = 1, dN8,N5 =
2, dN9,N5 = 3, dN10,N5 = 1, and dN11,N5 = 2, thus dN5 = 1.8. Let the topographical
distance of node i (dtgri) be a similar measure but when weights on links are
considered: the length of a link does not necessarily equal 1 but five minus its
weight {1, 2, 3, 4}. A highly permeable corridor („4”) can be considered just like
being closer (d = 5 - 4 = 1), while a hardly permeable one („1”) behaves like a
longer pathway (d = 5 - 1 = 4). So, the topographical distance of N5 from others
is: dtgrN1,N5 = 5, dtgrN2,N5 = 2, dtgrN3,N5 = 1, dtgrN4,N5 = 4, dtgrN6,N5 = 4, dtgrN7,N5 = 2,
dtgrN8,N5 = 3, dtgrN9,N5 = 6, dtgrN10,N5 = 2, and dtgrN11,N5 = 4, thus dtgrN5 = 3.3. For the
more peripherial node N9, this is dtgrN9 = 7.4. Losing central patches (low dtgr) is
more disadvantageous for connectivity. Again, for links, distance values equal the
average of that of their endpoints.
In the intact network, the sum of local population size values equals 23. If
certain spatial elements are deleted, the network will be separated to two or more
components. One can calculate the sums of local population size values for the
discrete components and it is of interest for conservationists how large is the
remaining largest connected metapopulation. After deleting the ith node, the value
of „maximal connected local population sizes” will be marked by LPSmaxconn(i).
For example, if N3 is deleted, we will have three components: {N4}, {N1, N2},
and {N5, N6, N7, N8, N9, N10, N11}, with LPSconn values: 2, 4, and 15,
respectively. So, LPSmaxconn(N3) = 15. This quantity can be calculated also for links.
If LPSmaxconn is small for a spatial element, its loss is a serious damage for the
whole metapopulation.
3.3 A combined importance index
For each patch and corridor, each calculated network index is given in Table 1.
According to different measures of positional importance, the ranks of spatial
elements differ. For example, D = 4 indicates three patches of highest
importance: N3, N5, and N10. Based on CC, N3 seems to be more important to
save, but dtgr suggests N5 to be of higher importance. LPS helps decision, because
it strongly indicates N3. These indices refer to different local and global
properties of the network, and their use is context-dependent (i.e., if the minimal
viable population size is approached, the emphasis is on saving as many
individuals as one can, so LPS is a more adequate index).
A combined index was constructed in order to reflect both pure topology and
the quality of patches and corridors. Let the importance of the ith element of the
landscape be:
Ii 
Di  CCi
,
max
d  LPS conn
(i )
tgr
i
(1)
where the above introduced indices are combined according to their
interrelationships. Since it has weighted components, it reflects functionality
better [8, 9, 10], than some other landscape graph indices (for some more
structural indices, see O’Neill et al. [11] and [12, 13, 14]). Based on this
combined importance index, I give the „final” rank of landscape elements
according to maintaining the connectivity of this P. transsylvanica
metapopulation (Table 2).
Table 1: Four network indices of the elements of the landscape graph shown in
Figure 1. The degree (Di), clustering coefficient (CCi), and
topographical distance (dtgri) of the ith element (patch, N, and corridor,
L) are given, as well as the maximal connected local population size
value after deleting i (LPSmaxconn(i)). CC cannot be calculated for nodes
with D = 1 and links where any of the two endpoints have D = 1. Note
that different indices suggest different importance ranks. A landscape
element is considered more important in maintaining connectivity if Di
is higher, while CCi , dtgri , and LPSmaxconn(i) are lower.
i
Di
CCi
dtgri
LPSmaxconn(i)
N1
N2
N3
N4
N5
N6
N7
N8
N9
N10
N11
1
2
4
1
4
2
3
3
1
4
1
0
0,17
0,33
0
0,33
0
0,33
-
7
4,3
3,6
6,3
3,3
6,2
4,2
4,7
7,4
4,7
6,5
20
19
15
21
21
19
22
18
20
20
22
L1/2
L2/3
L3/4
L3/5
L3/10
L5/10
L5/6
L5/7
L10/7
L10/11
L6/8
L7/8
L8/9
1,5
3
2,5
4
4
4
3
3,5
3,5
2,5
2,5
3
2
0,085
0,255
0,255
0,33
0,17
0,33
0,33
0
0,17
-
5,65
3,95
4,95
3,45
4,15
4
4,75
3,75
4,45
5,6
5,45
4,45
6,05
20
19
21
23
23
23
23
23
23
22
23
23
20
4 Results and conclusions
Based on our importance index, and within the limits of this approach, I suggest
that the patch N3 („Szilicei kaszálók”) is of highest conservation value, at least
for this seriously endangered species. Losing patch N11 („Lófej forrás alatti
tisztás”) would cause the least damage to the metapopulation. Corridors,
according to this analysis, are of less extreme importance. The most (L3,5) and
least (L1,2) important ones differ less in importance. Of course, it must be noted
that other approaches may suggest different elements to be of high conservation
value – now I focused on positionality within the network.
Table 2: The combined importance index (Ii) of the ith element of the landscape
graph (patch, N, or corridor, L). The importance rank is given. Large
values of I indicate spatial elements whose loss is more
disadvantageous for landscape connectivity.
i
N3
N5
N10
L3-5
L3-10
L5-10
N8
L2-3
L5-7
L7-10
L7-8
L5-6
N7
L3-4
L6-8
N2
L10-11
N6
L8-9
L1-2
N1
N4
N9
N11
I (i)
0,2059
0,151
0,1486
0,1416
0,1379
0,1359
0,1322
0,127
0,1185
0,1154
0,1031
0,102
0,1019
0,089
0,0879
0,0858
0,0837
0,0794
0,0695
0,0511
0,03
0,0297
0,0296
0,0284
The value of this approach is its combined nature (function and structure,
global and local properties) and quantitativity. Priorities based on this viewpoint
can be set by numbers, however it is clear that conservation decisions should not
be based on this single approach. It is emphasized again that the use and
importance of spatial elements can only be reasonably and realistically quantified
in a network context. I hope that in the future this and similar approaches might
contribute to decision support techniques. Conservation problems are extremely
complex ones, and there is no reason to find a single fruitful approach, thus, this
quantified network perspective can only be one out of many possibly useful
considerations. For example, optimal landscape design needs considerations on
the effects on added (not removed) spatial elements (see [15]).
As gene flow in metapopulations acts against inbreeding depression and the
local extinction / recolonisation dynamics is a natural part of many species’
ecology (cf. Spiller and Schoener [16]), studying the migration patterns of
individuals within ecological landscapes is of basic scientific interest and seems
to be one of the few remaining tools for conserving biodiversity.
Acknowledgements
Professor Zoltán Varga, István Rácz, and Kirill M. Orci are acknowledged for
providing field data and their help in drawing the graph. I am especially grateful
to András Báldi for excellent discussions. My research was supported by grants
of the Hungarian Scientific Research Fund (OTKA F 035092, T 037726 and D
042189), and by a Bolyai Research Fellowship of the Hungarian Academy of
Sciences. The main part of this project was made in Collegium Budapest,
Institute for Advanced Study.
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