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Spatiotemporal dynamics of surface water networks across a global biodiversity hotspot - Implications for conservation

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The concept of habitat networks represents an important tool for landscape conservation and management at regional scales. Previous studies simulated degradation of temporally fixed networks but few quantified the change in network connectivity from disintegration of key features that undergo naturally occurring spatiotemporal dynamics. This is particularly of concern for aquatic systems, which typically show high natural spatiotemporal variability. Here we focused on the Swan Coastal Plain, a bioregion that encompasses a global biodiversity hotspot in Australia with over 1500 water bodies of high biodiversity. Using graph theory, we conducted a temporal analysis of water body connectivity over 13 years of variable climate. We derived large networks of surface water bodies using Landsat data (1999–2011). We generated an ensemble of 278 potential networks at three dispersal distances approximating the maximum dispersal distance of different water dependent organisms. We assessed network connectivity through several network topology metrics and quantified the resilience of the network topology during wet and dry phases. We identified 'stepping stone' water bodies across time and compared our networks with theoretical network models with known properties. Results showed a highly dynamic seasonal pattern of variability in network topology metrics. A decline in connectivity over the 13 years was noted with potential negative consequences for species with limited dispersal capacity. The networks described here resemble theoretical scale-free models, also known as 'rich get richer' algorithm. The 'stepping stone' water bodies are located in the area around the Peel-Harvey Estuary, a Ramsar listed site, and some are located in a national park. Our results describe a powerful approach that can be implemented when assessing the connectivity for a particular organism with known dispersal distance. The approach of identifying the surface water bodies that act as 'stepping stone' over time may help prioritize surface water bodies that are essential for maintaining regional scale connectivity.
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Spatiotemporal dynamics of surface water
networks across a global biodiversity
hotspotimplications for conservation
Mirela G Tulbure
1
, Stuart Kininmonth
2
and Mark Broich
1
1
Centre for Ecosystem Science, School of Biological, Earth & Environmental Sciences, University of New
South Wales, Sydney, NSW 2052, Australia
2
Stockholm Resilience Centre, Stockholm University, Sweden
E-mail: Mirela.Tulbure@unsw.edu.au,stuart.kininmonth@stockholmresilience.su.se and Mark.
Broich@unsw.edu.au
Received 5 January 2014
Accepted for publication 26 September 2014
Published 14 November 2014
Abstract
The concept of habitat networks represents an important tool for landscape conservation and
management at regional scales. Previous studies simulated degradation of temporally xed
networks but few quantied the change in network connectivity from disintegration of key
features that undergo naturally occurring spatiotemporal dynamics. This is particularly of
concern for aquatic systems, which typically show high natural spatiotemporal variability. Here
we focused on the Swan Coastal Plain, a bioregion that encompasses a global biodiversity
hotspot in Australia with over 1500 water bodies of high biodiversity. Using graph theory, we
conducted a temporal analysis of water body connectivity over 13 years of variable climate. We
derived large networks of surface water bodies using Landsat data (19992011). We generated
an ensemble of 278 potential networks at three dispersal distances approximating the maximum
dispersal distance of different water dependent organisms. We assessed network connectivity
through several network topology metrics and quantied the resilience of the network topology
during wet and dry phases. We identied stepping stonewater bodies across time and
compared our networks with theoretical network models with known properties. Results showed
a highly dynamic seasonal pattern of variability in network topology metrics. A decline in
connectivity over the 13 years was noted with potential negative consequences for species with
limited dispersal capacity. The networks described here resemble theoretical scale-free models,
also known as rich get richeralgorithm. The stepping stonewater bodies are located in the
area around the Peel-Harvey Estuary, a Ramsar listed site, and some are located in a national
park. Our results describe a powerful approach that can be implemented when assessing the
connectivity for a particular organism with known dispersal distance. The approach of
identifying the surface water bodies that act as stepping stoneover time may help prioritize
surface water bodies that are essential for maintaining regional scale connectivity.
Keywords: surface water dynamics, spatiotemporal dynamics of surface water networks,
complex networks, graph theory, remote sensing, Landsat, conservation
Introduction
Aquatic systems, and their biota, are some of the most
threatened ecosystems in the world (Saunders et al 2002, Nel
et al 2009) since they are affected by changes in climate and
anthropogenic factors (e.g., land use change in the
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catchment). These factors not only increase direct stress on
surface water habitat but also affect dispersal opportunities for
water dependent organisms as neighbouring water bodies
degenerate. Moreover, most water dependent organisms,
dened here as vertebrates (e.g., amphibians or waterbirds)
that either live in water bodies or are dependent on water
bodies for critical periods during their life stages, live in
metapopulations and travel between water bodies to maintain
sustainable and resilient populations. Thus adaptations to
climate change at regional and landscape scales require
measures that facilitate species dispersal such as preserving or
enhancing landscape features essential for species
connectivity.
Graph theory, a branch of mathematics useful for
describing how objects are connected in space (e.g., social
networks, World Wide Web, road networks), is a powerful
approach for assessing connectivity (Urban and Keitt 2001,
Calabrese and Fagan 2004, Minor and Urban 2008) with
valuable applications in ecology, social sciences, and physical
systems (Strogatz 2001, Borgatti et al 2009, Olesen
et al 2011). Networks in ecology are based on graph theory
and are comprised of a set of nodes (vertices), which can have
properties such as location and size, and the relationships
between these nodes, represented via edges. Given their
capacity for describing conservation and management sys-
tems at regional scales, networks have become powerful tools
in spatial ecology (Bunn et al 2000, Urban and Keitt 2001,
Fagan 2002). Spatial graphs have been successfully applied in
terrestrial ecology (Urban et al 2009) and more recently in
marine conservation (Treml et al 2008). Wetland connectivity
has also been a focus for graph theory but limited to few
small-scale snapshots in time (Fortuna et al 2006,
Wright 2010).
Most studies assumed a xed network structure through
time, which is particularly of concern for aquatic systems that
typically show high natural variability in space and time
(Puckridge et al 1988). For example, variability in the node
set is likely to have substantial implications for the size and
density of the resulting network and subsequently on the
behaviour and properties of networks. Failing to consider the
temporal dynamics in a network can lead to spurious results
for the system under investigation (Butts 2009). Acknowl-
edging the importance of representing the high spatiotemporal
dynamics in network structure, previous studies have mod-
elled the response of habitat networks to removal of habitat
patches either randomly (Urban and Keitt 2001) or based on
anticipated changes such as wetland drying (Fortuna
et al 2006), or as snapshots in time of how wetland networks
change during a drought, deluge or an average rainfall year
(Wright 2010). Yet, the actual dynamics across space and
time using time series data of surface water body networks
can only be accomplished by employing seasonally con-
tinuous time series of surface water bodies derived from
remote sensing data and linking these with network analysis
(Wright 2010). There has been little progress in under-
standing the actual effects of loss of habitat using time-series
of remotely sensed data as connectivity networks change in
space and time. Here we determined past patterns of surface
water body connectivity integrating graph theory with a 13
year seasonally-continuous time series of remotely sensed
surface water bodies.
Patterns of connectivity are assessed through knowledge
of network topology and associated metrics and how these
change over time (e.g., number of edges, number of clusters,
average path length, table 1). Importantly this provides insight
into emergent network properties, such as the spread of
information and network resilience and vulnerability to
Table 1. Description of network connectivity metrics computed for seasonally continuous network time series on the Swan Coastal Plain
from 1999 to 2011.
Metrics used in the
connectivity analysis Denition Ecological meaning Citation
Number of edges Total number of edges in a network given
the search radius
Connectivity among habitats (Newman 2003)
Number of clusters Counts the numbers of disconnected sub-
graphs
Potential discrete populations (Newman 2003)
Average minimum path
length
Average number of edges in the shortest
path between all pairs in a
graph averaged over possible between-
vertex connexions
How quick creatures can disperse across
the entire system
(Montoya and
Sole 2002)
Diameter Longest minimum path length that exists
between any nodes in a network
The number of dispersal events to reach
any part of the system.
(Montoya and
Sole 2002)
Transitivity/clustering
coefcient
How clustered nodes are Average local resilience based on a sup-
porting triangular linkage structure
Montoya and
Sole 2002
Average betweenness
centralitynodes
Average proportion of shortest paths going
through a vertex
Calculates shortest paths and based on a
count of the paths passing through each
node a proportion is calculated. This
can represent stepping stonesif the
assumption that those animals chose
the shortest path is accepted.
(Newman 2003)
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Environ. Res. Lett. 9(2014) 114012 M G Tulbure et al
disturbances (Melián and Bascompte 2002). Based on
topology, several types of networks can be identied. These
networks include planar, regular, random and complex (e.g.,
small-world and scale-free). For planar networks, no edges
cross or intersect and have long average path length and low
clustering coefcient (Minor and Urban 2008). This would be
applicable to a dispersing organism that moves only small
distances to neighbouring habitats. Random networks have a
bell-shaped degree distribution highlighting that most nodes
have a similar number of edges, with an absence of network
hubs. Most real worldnetworks are not represented by
random congurations. One common network type is a
power-law or scale-free distribution, where edges connect
based on preferential attachment also known as the rich get
richeralgorithm. The resultant network has the majority of
nodes having a minimal number of links and a few nodes
having a very high number of links (Newman 2003). These
networks have short path lengths and are resilient to random
attack but vulnerable to targeted attack of the hubs. Examples
of systems that can be modelled with this network cong-
uration include the World Wide Web, the citation network
and wetlands of the prairie pothole in North America
(Wright 2010). A small-world network is similar to a scale-
free distribution but it is highly clustered, has more shortcuts
and shorter average path lengths (Watts and Strogatz 1998).
Examples of these congurations include neural networks,
evolving networks and the Great Barrier Reef (Kininmonth
et al 2010). Comparing existing networks with simulated
network models of known topology and properties is impor-
tant because it provides insight into regional and emergent
network properties and allows us to make inferences about
habitat connectivity and thus conservation strategies.
Besides assessing the temporal dynamics in connectivity
and the resemblance with theoretical network models,
changes in network topology metrics following structural
disturbance allows us to quantify network resilience.
Knowledge of network resilience provides understanding of
how landscape connectivity might change as a function of
an attackto the network (e.g., small surface water body
removal as they dry out due to a warmer climate). At the
landscape scale, network models are useful for linking
species movement among habitat patches (Keitt 2003) and
quantifying the survival of metapopulations under habitat
loss by identifying stepping stonepatches (Urban and
Keitt 2001, Keitt 2003). Stepping stonepatches act as
connectivity bottlenecksenabling access to multiple habi-
tats because of their position in the landscape. Because
stepping stonewater bodies are critical linkages in surface
water networks, identifying them across space and time
provides important information for prioritizing surface water
bodies in need of conservation.
Here we focused on a global biodiversity hotspot in
Western Australia and conducted a temporal analysis of water
body connectivity over 13 years of variable climate using
graph theory. Specic objectives addressed in this research
were to:
(1) Assess changes in connectivity over time and examine
the impact of climate variability in this system using a
range of network topology metrics.
(2) Assess the resilience of the surface water networks by
quantifying the impact of removing nodes on network
topology according to four different strategies (remov-
ing smallest, random, least and most connected nodes)
during a wet and a dry time phase.
(3) Identify stepping stonesurface water bodies across
space and time.
(4) Compare with other constructed networks and assess
whether networks are similar to constructed random,
scale-free or small-world networks.
Methods
Study site and data used
Our study site was the Swan Coastal Plain (SCP), a
36000 km
2
area that encompasses one of the 25 global
biodiversity hotspots (sensu Myers), dened as biogeo-
graphic regions that contain at least 0.5% or 1500 of the
world's 300 000 endemics plant species and have lost 70%
or more of their primary vegetation (Myers et al 2000). The
SCP has over 1500 wetlands that retain signicant biodi-
versity values with several listed as protected wetlands of
international importance under the Ramsar convention while
others are recognized as nature reserves and wetlands of
national importance (Davis and Froend 1999). However,
more than 70% of the wetlands have been lost since Eur-
opean settlement and the SCP is an area affected by recent
drying climate and rapid urban development and ground
water abstraction. The SCP shows high seasonal and inter-
annual variability in surface water dynamics (Tulbure and
Broich 2013a), with winter lling and summer drawdown
(Townley et al 1993).
We used the seasonally continuous Landsat archive to
derive an ensemble of 278 potential surface water body net-
works for the SCP. The data covered a period spanning 13
years when the SCP experienced one of the driest years on
record (Bureau of Meteorology 2011), representing a unique
opportunity to study how the networks change during extreme
climatic events. Surface water dynamics data have been
developed using the Landsat TM and ETM+ imagery for the
SCP from 1999 to 2011 (Tulbure and Broich 2013a). The
overall classication accuracy of surface water bodies was
96% (with 89% producers accuracy and 93% users accu-
racy) and yielded 278 surface water time steps, each corre-
sponding with a Landsat acquisition over the study area. The
data are freely available (Tulbure and Broich 2013b) and an
animation of the dynamics is available at the following link:
http://www.mirela-tulbure.com/surface-water-dynamics/.
Tulbure and Broich (2013a) showed that the number,
total area and size of water bodies have considerable intra and
interannual variation with highest values in winter and lowest
values in the Southern hemisphere summer. To reduce the
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Environ. Res. Lett. 9(2014) 114012 M G Tulbure et al
analytical artifacts in the surface water data, the 900 m
2
water
bodies (single Landsat pixel water bodies with no neigh-
bouring water pixel) were removed. We computed the area of
each water body polygon for every time step. We assigned a
unique identier to temporally overlapping polygons. For
each water body, we rst determined the maximum extent
during the 278 time steps and assigned it a unique identier.
Any overlapping polygons across the time series were
assigned the same identier to ensure that in years when water
bodies shrink or split into smaller water bodies they were
identied and tracked in subsequent analyses as part of a
seasonally larger water body.
The dispersal ability of water dependent biota is highly
variable and results in diverse temporal and spatial patterns of
connectivity (Morris 2012). Landscape connectivity is species
specic and varies across scales. Rather than focusing on one
particular organism, here we focused on how the landscape
scale connectivity of the entire biogeoregion changes from the
perspective of a range of water-dependent organisms with
different dispersal distances, aiming to generalize the results.
To create potential networks we used three example dispersal
distances (500 m, 1000 m and 2000 m) approximating a wide
range of water dependent species (Smith and Green 2005).
Dispersal distances considered here approximate dispersal of
amphibian species and turtles as well as waterbirds during
breeding and moulting when they need close proximity to
water bodies (Roe and Georges 2007, Morris 2012). Pairwise
distances between water bodies were computed as Euclidian
distances between the nearest edges under the assumption that
the habitat matrix is homogeneous (Urban and Keitt 2001).
The edge weights, representing a cost of movement, were
simplied to be directly proportional to dispersal distances.
The network was assembled based on unique water bodies as
nodes.
Climate data
We used monthly spatially explicit climate data from the
Australian Water Availability Project (Raupach
et al 2009,2011). For climate variables we selected pre-
cipitation and maximum, minimum and average temperature
in the same months as the image acquisition. To investigate
lag time effects we also used the climate variables in the
previous month, including the average of the previous two,
three and four months from the image acquisition date. We
conducted cross-correlations between the number of water
bodies against climate variables and picked a precipitation
and a temperature variable based on the highest linear cor-
relation values. Next section provides methodology specic
to each of the four objectives.
(1) Connectivity over time
For connectivity analysis we used the igraph package
(Csardi and Nepusz 2006) in the statistical R software (R
Development Core Team 2012) to compute several network
topology metrics (Newman 2003). Network topology metrics
included number of edges (links between water bodies),
average path lengths of a graph, transitivity (graph-wide
average clustering coefcient) and diameter (Urban and
Keitt 2001, Urban et al 2009) and are summarized in table 1.
For a more in depth description of network topology metrics
readers are referred to Newman (2003).
We used MannKendal statistics to assess the temporal
trend of network topology metrics over the 13-year time
series. We rst assessed whether the autocorrelation in each
data series was signicant using the acf function in the
Kendall package (McLeod 2011). If there was a signicant
autocorrelation in the data set we used the MannKendall
modied trend test for serially correlated data in the fume
package (Group 2012) and noted the p-value for signicance.
(2) Network resilience
We tested how the network topology responds to loss of
nodes and contrasted the network response to node removal
during a wet (July 2005) and a dry time step (December 2010)
at a dispersal distance of 2000 m. These two time steps were
chosen to correspond to one of the wettest and driest times
steps with the highest and lowest number of nodes, respec-
tively. Using these contrasting wet and dry time steps, we
removed nodes (water bodies) in 1% increments from 1 to
30% based on four different strategies. The four strategies
included the removal of nodes based on size (based on cal-
culated area), random selection, least connected (lowest
degree) and highest connected. We considered the impact of
these removals on several topology metrics which included
number of edges, number of clusters, diameter relative to
number of nodes, average path length relative to number of
nodes and transitivity.
(3) Stepping stonewater bodies
To assess which surface water bodies acted as stepping
stoneover time and at three maximum dispersal distances we
computed average betweenness centrality per uniquewater
body per time step (denition of unique below). The analysis
was complicated by the seasonal dynamics with wet winters
and dry summers as well as the drying trend between 1999
and 2013. During the wet winter, water bodies expand and
several small water bodies can merge into a larger water body.
Conversely, during the summer certain larger water bodies
disintegrate into multiple smaller ones, some of which persist
to the next wet season while others dry up and subsequently
rell during the next wet season. In order to identify stepping
stonenodes in the network, small water bodies that merge
into a larger water body were treated as a single water body.
For this purpose we used a uniqueidentier (based on the
maximum extent of the water body) to track and treat as
uniquewater bodies that broke up, overlapped and reunited
over time. After computing betweenness per uniquewater
body per time step, we then took the average betweenness of
each unique water body for the entire time series. This
allowed us to rank water bodies based on their betweenness
centrality over the time series.
(4) Comparison with other networks
We compared our 278 surface water networks with four
theoretical networks (random, scale-free and two small-world
networks) using the same number of nodes and when possible
the same average degree with our surface water body net-
works. The theoretical networks included (1) the random
ErdosRenyi network, which uses the same number of nodes
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Environ. Res. Lett. 9(2014) 114012 M G Tulbure et al
and edges, adding edges chosen uniformly randomly from all
the possible edges (Erdős and Rényi 1959); (2) the scale-free
BarabasiAlbert model, whereby one vertex is added at each
time and edges are then created to link nodes following
preferential attachment based on degree distribution (Barabási
and Albert 1999); (3) the WattsStrogatz small-world model,
where rst a regular lattice is created and then edges rewired
uniformly with a specied probability (Watts and Stro-
gatz 1998); (4) small-world forest renetwork, which
resembles a forest re spreading by igniting trees close by,
and where nodes are added sequentially and edges are created
based on existing conguration (Leskovec et al 2007).
At each of our 278 time steps across 13 years, we
computed the average path length and the clustering coef-
cient of our networks as they are indicators of network type
and compared them with the average path lengths and clus-
tering coefcient of the four constructed networks.
Results
(1) Temporal variability in connectivity
Topology metrics of surface water networks at different
maximum dispersal distances varied by an order of magni-
tude. All network topology metrics computed (e.g., number of
edges, number of clusters, diameter and average path length
as well as global transitivity) showed a highly dynamic sea-
sonal variability (gure 1). A signicant decline over time can
be noted at all three dispersal distances (p< 0.001) for the
number of edges (gure 1(a)) and number of clusters
(gure 1(b)). It is important to note that the lowest number of
clusters (CI =110) was in 2010, which was an unusually dry
year, after which the range of seasonal variability was
reduced. The average path length and diameter relative to
number of nodes showed seasonal variability and an
increasing trend over time at all three distances (gures 1(c)
and (d)). This suggests that dispersing through these networks
would take more energy if the drying trend continues. The
clustering coefcient stayed relatively similar over time at
1000 m and 500 m dispersal distances but slightly increased at
2000m (gure 1(e)).
Average precipitation in the previous two months to
image acquisition explained the highest proportion (70%) of
variability in number of nodes and had a positive relationship
with number of nodes (F-statistic = 626.3, df = 272,
p< 0.001). Maximum temperature in the previous month
explained the highest proportion (65%) of variability in
number of nodes and the relationship with number of nodes
was negative (F-statistic = 501.9, df = 272, p< 0.001).
(2) Network resilience
We removed nodes from the network during two con-
trasting (wet and dry) time steps at a dispersal distance of
2000 m and based on four different strategies (smallest, ran-
dom, least and most connected nodes) and recorded the
impact on several network topology metrics (number of edges
and clusters, diameter relative to number of nodes, average
path length relative to number of nodes and transitivity). The
overall trends in network topology metrics as a response to
node removal were similar between the dry and wet time
steps. During the dry time step, the total number of nodes
removed varied between 6 and 193 nodes which corre-
sponded to 1% and 30% respectively from a network with
644 nodes. The wet time step investigated here was among
the time steps with the highest number of water bodies
(N= 3147) and the number of nodes removed representing 1
and 30% of the nodes varied between 31 and 994,
respectively.
The total number of edges in the observed networks
decreased over time for all four removal strategies, however
as expected, it decreased fastest when removing the highly
connected nodes (measured by the degree) and lowest when
removing the least connected nodes, while the smallest area
and random removal showed more similar results
(gure 2(a)). The number of clusters showed a slight decrease
when removing the smallest nodes and when removing nodes
randomly (gure 2(b), gures 3(b) and (c)). In contrast, the
number of clusters increased when removing the most con-
nected nodes and decreased when removing the least con-
nected nodes (gure 2(b)). The diameter and average path
length, normalized over the network size, increased over time
for both wet and dry time steps for all node removal strategies
with the exception of the highly connected node removal
which initially increased up to 10% node removal and then
decrease until 30% node removal for the dry time step
(gures 2(c) Dry and 2(d) Dry). For the wet time step, the
diameter and average path length normalized over the net-
work size increased up to 20% and then decreased after that
(gures 2(c) and (d) Wet panel). Transitivity or the clustering
coefcient remained similar for all except the highly con-
nected node removal strategy which showed an increase in the
clustering coefcient (gure 2(e)). Despite the fact that the
overall trends in network topology metrics as a response to
node removal were similar between the dry and wet time
steps, the original networks were different during dry and wet
phases (gure 3(a)). Networks during dry and wet time steps
were also visually different under the four different removal
strategies (gures 3(b)(e)).
(3) Stepping stonewater bodies
We computed average betweenness centrality over the 13
year period for each water body at three dispersal distances to
assess which water bodies act consistently as stepping stone
and whether they are functionally similar at different dispersal
distances. At all three dispersal distances water bodies with
high betweenness centrality were located in the area sur-
rounding the Peel-Harvey Estuary, primarely South and West
of the estuary. At 2000 m the water bodies with the highest
betweeneess centrality included the large lakes South of the
Peel, such as Preston Lake, Lake Clifton, Lake Newnham,
Lakes Hayward, Yalgorup, Martins Tank Lake as well as
Black Swan Lake (gure 4(a)). Several of these lakes were
important as stepping stones at a 1000 m dispersal distance
with the exeption of Lake Preston and Martins Tank Lake and
Lakes Yalgorup and Hayward (gure 4(b)). At 500 m the
water bodies with highest betweenness centrality included
smaller water bodies (gure 4(c)) located primarely East of
the Peel-Harvey.
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Environ. Res. Lett. 9(2014) 114012 M G Tulbure et al
(4) Comparison with theoretical networks
To assess which theoretical network model they
resemble the most, we compared differences in clustering
coefcient and average path length between the time-series
of SCP surface-water networks with existing random, scale-
free and small-world models at three distances. The surface
water networks derived in this work had similar clustering
coefcient to the forest re small-world network at 2000 m
but a lower clustering coefcient than the small-world
WattsStrogartz networks and had similar average path
lengths to the small-world WattsStrogartz networks
(gure 5(a)). The networks were more clustered than the
random network and scale-free network (gure 5(a)), sug-
gesting that at 2000 m the networks are closest to a small-
world network. At both 1000 m and 500 m the networks
were less clustered than the small-world networks and more
similar to the scale-free networks. The network had longer
average path lengths at 1000 m than the scale-free network
(gure 5(b)) and showed more temporal variability in both
the average path lengths and clustering coefcient than the
scale-free at 500 m (gure 5(c)).
Discussion
Our work quantied dynamics in landscape connectivity
through the integration of a seasonally continuous time-series
of surface water bodies derived using the entire USGS
Landsat archive over the study area from 1999 until 2011 and
an ensemble of potential networks derived using
graph theory. We focused on an area that encompasses one of
the worlds 25 global biodiversity hotspots, where the
majority of surface water bodies have been lost (Horwitz
et al 2008, Froend and Sommer 2010). We identied and
quantied changes in landscape connectivity as the rainfall
patterns vary across extended ranges of time of over a decade
leading to high dynamics in water body extent, numbers and
subsequently network connectivity metrics.
Figure 1. Graph theory metrics for the Swan Coastal Plain from 1999 to 2011 (278 time steps) at three different dispersal distances 2000 m
(left columns; red), 1000 m (middle column; green) and 500 m (right hand column; blue) over time (x-axis shows the 278 time steps).
Connectivity metrics include (a) number of edges, (b) number of clusters, (c) relative average path length (average path length divided by the
number of nodes), (d) relative diameter (diameter divided by the number of nodes), and (e) transitivity. P-values are < 0.001 except for the
last two graphs where P-values = 0.65 and represent signicance of the temporal trend line (see method for explanation).
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Environ. Res. Lett. 9(2014) 114012 M G Tulbure et al
Figure 2. Changes in the graph theory metrics ((a) number of edges, (b) number of clusters, (c) diameter relative to number of nodes, (d)
average path length relative to the number of nodes and (e) transitivity) for surface water bodies on the Swan Coastal Plain in a dry phase
(December 2010, left panels) and during a wet phase (July 2005, right panels) when removing nodes based on four different strategies at a
dispersal distance of 2000 m. The four removal strategies were smallest nodes removed rst (red line), random removal (green), least
connected nodes (blue line) and most connected nodes (black line) and removed nodes in increments of 1% from 1 to 30% nodes in a
network.
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Environ. Res. Lett. 9(2014) 114012 M G Tulbure et al
We computed several network topology indices for the
SCP surface water body networks to characterize changes in
connectivity from 1999 to 2011. Results suggest that since
1999 the surface water networks, at the three examined dis-
persal distances, have increased in diameter and average path
length. Whereas other connectivity metrics suggest that over
time there were fewer clusters of connected water bodies and
fewer links between water bodies. As groups of surface water
bodies are a more meaningful unit of management and con-
servation than individual lakes (Johnson et al 2010), these
results point to the fact that the connectivity has signicantly
decreased since 1999 until 2011, with potentially negative
consequences for species that have limited disperal capacity
(e.g., amphibians). An aquatic organism would have fewer
opportunities for dispersal events (implying the need for more
time and effort) to connect to the spatially distributed
individuals of the same species. Long term implications for
metapopulation viability are likely given this decadal trend of
decreasing connectivity. We assessed the impact of climate
variability on network topology metrics and found that
average precipitation in the previous two months explained
approximately two third of the variability in number of nodes.
Future work should use downscaled global climate models to
forecast changes in surface water structure under various
climate change scenarios and help prioritize surface water
bodies in need of conservation for maintaining regional scale
connectivity for different groups of organisms.
We assessed the resilience of the network by quantifying
the impact of node removal on several network topology
metrics. Assuming that the smallest water bodies would dry
out rst in a drier climate and given that the size of water
bodies and depth are correlated (Halse et al 1993), we
removed nodes according to four different strategies includ-
ing removing smallest, randomly, least and most connected
nodes. Removing these smaller water bodies resulted in sig-
nicant changes to the network conguration. As expected,
when removing these small surface water nodes, the number
of edges was reduced and the networks become longer as
shown by greater diameter and longer average path length,
thus increasing the number of steps an organism would need
to traverse the network. The fact that the diameter decreased
after a certain percentage of node removal for the highest
connected node removal strategy suggests that the networks
become disconnected to the degree that the majority of nodes
are not part of the core network anymore. Despite the fact that
the removal of nodes triggered similar patterns in network
topology response for both dry and wet phases, the resulting
networks were quite different (gures 3(a) and (b)). The
removal of the smallest area nodes and randomly selected
nodes disconnected a similar set of nodes. These were the
ones located in the Southern part of the network (results not
displayed). Conversely, during the wet phase the dis-
connected nodes were further North, suggesting that the
function of the dispersal networks will be highly dependent
on whether loss of habitat occurs during a dry or a wet phase
as the impact of loss differs between wet and dry phases. The
fact that the graph clustering coefcient remained similar for
all except the highly connected node removal strategy sug-
gests that the removal of the highly connected water body
nodes left a fragmented and sparsely connected network. In
dry years the number of water bodies was substantially
reduced and they were sparsely distributed and disconnected
across the SCP.
We identied individual stepping-stonewater bodies
that are disproportionally high in importance in preserving the
ability of organisms to traverse the fragmented landscape by
computing betweenness centrality. Nodes that play a critical
role as shortcuts have high betweenness centrality and act as
mechanisms to link persistent habitat together and permit the
utilization by animals of the landscape despite the high
variability in environmental conditions. Here we identied
water bodies of high betweeness centrality across seasons and
over 13 years including drought and deluge years, and
spanning three dispersal distances. The fact that all water
Figure 3. Examples of networks for a dry phase (December 2010,
left hand size) and during a wet phase (July 2005, right hand size) at
a dispersal distance of 2000 m for the original network (a) and after
removing 30% of the nodes according to four different strategies that
remove the smallest nodes rst (b), randomly (c), least connected (d)
and most connected (e) nodes rst.
8
Environ. Res. Lett. 9(2014) 114012 M G Tulbure et al
bodies that act as stepping stoneare located around the Peel-
Harvey area suggests the importance of the area to the system
connectivity. The Peel-Harvey is a Ramsar listed site for its
importance as waterbird area and based on our results we
suggest that the lakes of high betweeness centrality identied
around the Harvey Estuary should be considered for addi-
tional protection. Some of these lakes are located in the
Yalgorup National Park. These results can be used for future
conservation of the landscape, by targeting these water bodies
as priority habitats for conservation.
We assessed what theoretical network models our sur-
face water networks resemble at the three dispersal distances
and found that the surface water networks on the SCP are
small-world networks at 2000 m but closer to scale-free
networks at 1000 m and 500 m. This suggests that there are
a few water bodies that act as hubs whereas the majority of
them have only a few connexions. For the wetlands repre-
sented here, the continued protection of the surface water
network hubs (e.g., Ramsar sites, natural parks) will likely
maintain the landscape health. In particular the prevention of
disease spread and invasive species and other disturbances
require the networks to be in good health. The types of
networks found on the SCP are resistant to random attacks
such as random node removal, but not resistant to targeted
removals based on connectivity, emphasizing the need to
identify and protect the surface water bodies that act as
network hubs. This conrms that the topology of the net-
work is important as it affects the resilience of the network
when being disturbed.
One caveat should be noted. As with most research
investigating spatial networks at landscape scales, the net-
works presented here are based on the indirect assumption
regarding movement rather than observed movement
(Fletcher et al 2011). However, this approach represents a
cost-effective way of assessing connectivity (Calabrese and
Fagan 2004, Urban et al 2009, Fletcher et al 2011) for eco-
logical and conservation biology networks when movement
data and cost surfaces are not available. Here we picked three
distances that represent different groups of organisms rather
than a specic species, but the same analysis can be con-
ducted for a different species of interest especially if actual
movement data is collected and cost distances can be incor-
porated. Fletcher et al (2011) found that compared with social
network models, landscape connectivity metrics based on
Figure 4. Stepping stonewater bodies (orange contours) with highest betweeness centrality at (a) 2000 m; (b)1000 m and (c) 500 m
overlayed on a Landsat 7 ETM+ image mosaic displayed as red band 7 (20902350 nm), green band 4 (770900 nm), blue band 2
(520600 nm) available from the United States Geological Survey (http://glovis.usgs.gov/).
Figure 5. Comparison of surface water networks on the SCP with
alternative models such as random (R), scale free (SF) and small-
world (SW) networks for key metrics including average minimum
path length (y-axis) and clustering coefcient/transitivity (x-axis) at
(a) 2000 m; (b) 1000 m and (c) 500 m.
9
Environ. Res. Lett. 9(2014) 114012 M G Tulbure et al
maximum distance constructions can overpredict connectivity
and provide high estimates of metapopulation lifetime in
landscape networks. While the metrics presented in this
research represent potential connectivity, they show in
relative terms how the connectivity has changed over time
with both interannual changes in wet and dry years as well as
intraannual changes.
Our work has direct implications for conservation plan-
ning and represents a way of identifying stepping stone
water bodies in a biodiversity hotspot that is subject to water
abstraction, urban development and climate change. Future
work should predict how connectivity may be affected by
future climate change with particular emphasis on the
alteration of habitat and barriers to dispersal. Climate change
and anthropogenic activity (urban development and ground
water abstraction) on the SCP will likely result in decreased
availability of surface water, with the expected outcome being
a reduction in water levels and size of water bodies as well as
losing smaller or temporary surface water bodies (Nielsen and
Brock 2009). This can negatively impact the aquatic biota by
decreasing available habitat and increasing distance among
suitable habitats (Davis and Froend 1999). The network
approach utilized to analyse the wetlands in the SCP high-
lights the functional character of this dynamic yet fragile
ecosystem.
Quantifying the spatiotemporal dynamics in network
structure of surface water bodies represents a powerful tool
for assessing potential survival of species that are dependent
on surface water bodies and their regional connectivity. Most
studies of this type focused on static landscapes, with few
studies including a modelled dynamic (Fortuna et al 2006).
Furthermore, little advancement has been made in quantifying
the actual effects of loss of habitats for networks that also
undergo natural change across seasons and years
(Wright 2010), but this spatial and temporal dynamics of
aquatic networks can now be represented as time-series of
systematically acquired and characterized remotely sensed
data (e.g., Landsat, MODIS).
Acknowledgements
Tulbure was funded through an Australian Research Council
Discovery Early Career Researcher Award (DE140101608).
This research was partially supported by UNSW FRGP
funding to Tulbure. SK was partially supported by Mistra
through a core grant to the Stockholm Resilience Centre, a
cross-faculty research centre at Stockholm University, and the
Strategic Research Programme EkoKlim at Stockholm
University.
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Ecological Network Analysis (ENA) capability has led to develop a set of indicators. Ecological Network Indicators (ENIs) investigates a range of subject in different context “e.g. Graph theory”, which is the origin of variety of questions such as following: What is the geographical distribution of studies and their relationship with each other? On what fields these studies are focused? What graph-based index or indexes have been used in the studies of ecological networks? What are the most widely used indexes in ecological studies? Accordingly, this study is to investigate the related literature between 2014 and 2019 in the framework of graph theory. To answer the mentioned question, we conducted systematic literature review. To find as many potentially eligible articles as possible, the search was performed multiple times using diverse related keywords. We identified 456 related records. After the screening process, 114 articles were left as the basis of further analysis. The results indicate that ENA applied mainly in China, USA, France. ENIs is studied more frequently among plants and mammals. We identified about 58 ENIs. But the Probability of Connectivity (PC), Integral index of connectivity (IIC) have been consistently used in most studies. Also, these two indices are used in combination with others ENIs. The outcomes show researchers introduce new indexes every year. The increasing trend of introducing new indicators shows the usability and applicability ENIs. But so far, PC, IIC, and LCP seem to be the most credible graph-based indexes for use in ecological network research. The overall results imply that graph theory as base of ecological network is developing, presents new indicators and opening new dimensions in the study and analysis of connections and communications in ecological networks. It has adequate flexibility to answer questions that may arise in the future in the field of ecological network analysis.
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The presence or absence of 61 waterbird species on 95 wetlands in south-western Australia was related to six wetland characteristics: salinity, emergent vegetation, water depth, pH, phosphorus level and wetland size. More species were associated with salinity and vegetation than with other wetland characteristics. There were more positive associations with brackish than with fresh or saline wetlands and few species occurred in hypersaline wetlands. Trees or shrubs and sedges were the vegetation with which most species were associated; few species were recorded on completely open wetlands or those with only samphire. The 95 wetlands were classified into five groups on the basis of waterbird use. All wetland characteristics differed between groups but larger differences occurred in salinity, vegetation and water depth. The wetland group that supported most species also supported the highest numbers of waterbirds and most breeding species.
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Ecological processes in large rivers are controlled by their flow variability. However, it is difficult to find measures of hydrological variability that characterize groups of rivers and can also be used to generate hypotheses about their ecology. Multivariate analyses of the hydrographs of 52 rivers worldwide revealed distinctive patterns of flow variability that were often correlated with climate. For example, there were groups of rivers that corresponded broadly with ‘tropical’ and ‘dryland’ climates. However, some rivers from continental climates occupy both extremes of this range, illustrating the limitations of simple classification. Individual rivers and groups of rivers may also have different hydrographic ‘signatures’, and attempts to combine measures of hydrological variability into indices mask biologically significant information. This paper identifies 11 relatively independent measures of hydrological variability that help categorize river types and are each associated with aspects of fish biology. Ways are suggested by which the Flood Pulse Concept can be expanded to encompass hydrological variability and accommodate differences among groups of rivers from different climatic regions. Such recognition of the complex role of hydrological variability enhances the value of the concept for river conservation, management and restoration.
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The wetland complex is the functional ecological unit of the prairie pothole region (PPR) of central North America. Diverse complexes of wetlands contribute high spatial and temporal environmental heterogeneity, productivity, and biodiversity to these glaciated prairie landscapes. Climate- warming simulations using the new model WETLANDSCAPE (WLS) project major reductions in water volume, shortening of hydroperiods, and less-dynamic vegetation for prairie wetland complexes. The WLS model portrays the future PPR as a much less resilient ecosystem: The western PPR will be too dry and the eastern PPR will have too few functional wetlands and nesting habitat to support historic levels of waterfowl and other wetland-dependent species. Maintaining ecosystem goods and services at current levels in a warmer climate will be a major challenge for the conservation community.
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Ecologists are familiar with two data structures commonly used to represent landscapes. Vector-based maps delineate land cover types as polygons, while raster lattices represent the landscape as a grid. Here we adopt a third lattice data structure, the graph. A graph represents a landscape as a set of nodes (e.g., habitat patches) connected to some degree by edges that join pairs of nodes functionally (e.g., via dispersal). Graph theory is well developed in other fields, including geography (transportation networks, routing applications, siting problems) and computer science (circuitry and network optimization). We present an overview of basic elements of graph theory as it might be applied to issues of connectivity in heterogeneous landscapes, focusing especially on applications of metapopulation theory in conservation biology. We develop a general set of analyses using a hypothetical landscape mosaic of habitat patches in a nonhabitat matrix. Our results suggest that a simple graph construct, the minimum spanning tree, can serve as a powerful guide to decisions about the relative importance of individual patches to overall landscape connectivity. We then apply this approach to an actual conservation scenario involving the threatened Mexican Spotted Owl (Strix occidentalis lucida). Simulations with an incidence-function metapopulation model suggest that population persistence can be maintained despite substantial losses of habitat area, so long as the minimum spanning tree is protected. We believe that graph theory has considerable promise for applications concerned with connectivity and ecological flows in general. Because the theory is already well developed in other disciplines, it might be brought to bear immediately on pressing ecological applications in conservation biology and landscape ecology.
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Neither linear nor two-dimensional frameworks may be the most appropriate for fish and other species constrained to disperse within river-creek systems. In particular, the hierarchical, dendritic structures of riverine networks are not well captured by existing spatial models. Here I use a simple geometric model and metapopulation modeling to make three points concerning the ecological consequences of dendritic landscapes. First, connectivity patterns of river-creek networks differ from linear landscapes, and these differences in connectivity can either enhance or reduce metapopulation persistence compared to linear systems, depending on the details of dispersal. Second, habitat fragmentation in dendritic landscapes has different (and arguably more severe) consequences on fragment size than in either linear or two-dimensional systems, resulting in both smaller fragments and higher variance in fragment size. Third, dendritic landscapes can induce striking mismatches between the geometry of dispersal and the geometry of disturbance, and as is the case for arid-lands fishes, such mismatches can be important for population persistence.
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Connectivity is an important but inconsistently defined concept in spatial ecology and conservation biology. Theoreticians from various subdisciplines of ecology argue over its definition and measurement, but no consensus has yet emerged. Despite this disagreement, measuring connectivity is an integral part of many resource management plans. A more practical approach to understanding the many connectivity metrics is needed. Instead of focusing on theoretical issues surrounding the concept of connectivity, we describe a data-dependent framework for classifying these metrics. This framework illustrates the data requirements, spatial scales, and information yields of a range of different connectivity measures. By highlighting the costs and benefits associated with using alternative metrics, this framework allows practitioners to make more informed decisions concerning connectivity measurement.
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Detailed information on the spatiotemporal dynamic in surface water bodies is important for quantifying the effects of a drying climate, increased water abstraction and rapid urbanization on wetlands. The Swan Coastal Plain (SCP) with over 1500 wetlands is a global biodiversity hotspot located in the southwest of Western Australia, where more than 70% of the wetlands have been lost since European settlement. SCP is located in an area affected by recent climate change that also experiences rapid urban development and ground water abstraction. Landsat TM and ETM+ imagery from 1999 to 2011 has been used to automatically derive a spatially and temporally explicit time-series of surface water body extent on the SCP. A mapping method based on the Landsat data and a decision tree classification algorithm is described. Two generic classifiers were derived for the Landsat 5 and Landsat 7 data. Several landscape metrics were computed to summarize the intra and interannual patterns of surface water dynamic. Top of the atmosphere (TOA) reflectance of band 5 followed by TOA reflectance of bands 4 and 3 were the explanatory variables most important for mapping surface water bodies. Accuracy assessment yielded an overall classification accuracy of 96%, with 89% producer’s accuracy and 93% user’s accuracy of surface water bodies. The number, mean size, and total area of water bodies showed high seasonal variability with highest numbers in winter and lowest numbers in summer. The number of water bodies in winter increased until 2005 after which a decline can be noted. The lowest numbers occurred in 2010 which coincided with one of the years with the lowest rainfall in the area. Understanding the spatiotemporal dynamic of surface water bodies on the SCP constitutes the basis for understanding the effect of rainfall, water abstraction and urban development on water bodies in a spatially explicit way.