analysis were investigated. The regional-scale analysis provided an assessment of
changes on the overall connectivity throughout the study area. The local-scale
analysis provided a finer assessment by identifying the most severely affected
patches and corridors, i.e., those that experienced the largest changes in local
connectivity or that removed by the infrastructure.
The identification of the best locations for potential wildlife crossings was based
on a cumulative method developed by Foltête et al. (2014) and Girardet et al.
(2016). The method consisted of testing each graph link crossed by the HSR line
and to validate the one maximizing the global connectivity of the tree frog network.
In the first step, all links cut by the HSR line were removed and the global connectivity was calculated. Then, an iterative process added each link and computed
again connectivity. After testing all links individually, the one that produced the
biggest increase in the connectivity was validated. The process was repeated until
the desired number of new crossings was reached by integrating changes in the
graph topology induced by the addition of previous crossings.
For all analysis, connectivity was quantifying by the Probability of Connectivity
(PC) developed by Saura and Pascual-Hortal (2007). The PC index is a global
metric given by the expression:
PC ¼
X n
i¼1
X n
j¼1
a i a j p
Ã
ij
!,
A
2
where a i and a j are the capacities of the patches i and j, p
Ã
ij is the maximum
probability of all potential paths between patches i and j, and A is the total area
under study. The maximum p
Ã
ij is obtained from p ij which is determined by an
exponential function such that:
p ij ¼ expðÀad ij Þ
where d ij is the least-cost distance between these patches and a (0 < a < 1)
expresses the intensity of the decrease of the dispersal probabilities resulting from
this exponential function (Foltête et al. 2012a).
From the global metric PC, a patch-based metric was derived, the PC flux (Foltête
et al. 2014), which is the contribution of each patch to the global PC index. For a
given patch j, PC flux(j) is given by:
PC fluxðjÞ ¼
X n
i¼1
a i a j p
Ã
ij
!,
A
2
where a i and a j are the capacities of the patches i and j, p
Ã
ij is the maximum
probability of all potential paths between patches i and j, and A is the total area
under study.
13 Evaluating and Mitigating the Impact of a High-Speed Railway …
221
changes on the overall connectivity throughout the study area. The local-scale
analysis provided a finer assessment by identifying the most severely affected
patches and corridors, i.e., those that experienced the largest changes in local
connectivity or that removed by the infrastructure.
The identification of the best locations for potential wildlife crossings was based
on a cumulative method developed by Foltête et al. (2014) and Girardet et al.
(2016). The method consisted of testing each graph link crossed by the HSR line
and to validate the one maximizing the global connectivity of the tree frog network.
In the first step, all links cut by the HSR line were removed and the global connectivity was calculated. Then, an iterative process added each link and computed
again connectivity. After testing all links individually, the one that produced the
biggest increase in the connectivity was validated. The process was repeated until
the desired number of new crossings was reached by integrating changes in the
graph topology induced by the addition of previous crossings.
For all analysis, connectivity was quantifying by the Probability of Connectivity
(PC) developed by Saura and Pascual-Hortal (2007). The PC index is a global
metric given by the expression:
PC ¼
X n
i¼1
X n
j¼1
a i a j p
Ã
ij
!,
A
2
where a i and a j are the capacities of the patches i and j, p
Ã
ij is the maximum
probability of all potential paths between patches i and j, and A is the total area
under study. The maximum p
Ã
ij is obtained from p ij which is determined by an
exponential function such that:
p ij ¼ expðÀad ij Þ
where d ij is the least-cost distance between these patches and a (0 < a < 1)
expresses the intensity of the decrease of the dispersal probabilities resulting from
this exponential function (Foltête et al. 2012a).
From the global metric PC, a patch-based metric was derived, the PC flux (Foltête
et al. 2014), which is the contribution of each patch to the global PC index. For a
given patch j, PC flux(j) is given by:
PC fluxðjÞ ¼
X n
i¼1
a i a j p
Ã
ij
!,
A
2
where a i and a j are the capacities of the patches i and j, p
Ã
ij is the maximum
probability of all potential paths between patches i and j, and A is the total area
under study.
13 Evaluating and Mitigating the Impact of a High-Speed Railway …
221