# The probability of connectivity metric (PC) The probability of

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```The probability of connectivity metric (PC)
PC is a graph-based habitat availability metric that quantifies functional connectivity
Definition:
probability that two points randomly placed within the landscape fall into habitat
areas that are reachable from each other (interconnected) given a set of n habitat
patches and the links (direct connections) among them.
Useful as a relative metric in order to evaluate the importance of landscape
elements or changes.
The probability of connectivity metric (PC)
Applicability:
prioritization and ranking of landscape elements (patches and links) by their
contribution to overall habitat connectivity.
dPCk: percentage of variation (decrease) in PC caused by the removal of
each individual element from the landscape
- dPCk: importance of element k for the maintenance of overall habitat availability in the landscape.
- PC: metric value in the original intact landscape, when each of the original elements, including k,
is present.
- PCremove,k: the metric value after the removal of k (computed by setting ak=0 and pij=0 when
either i=k or j=k).
dPCk and ΔPCk are affected only by PCnum and not by the denominator, since AL only depends
on the extent of the study area and remains constant after removing any element.
Useful as a relative metric in order to evaluate the importance of landscape elements or changes.
The probability of connectivity metric (PC)
Partitioning dPCk into three different fractions
Intrapatch connectivity for patch k, corresponding to ai*aj when i=j=k (ak2), or the
available habitat area (or some other relevant patch attribute) provided by the patch k
itself, as related to the habitat availability concept.
how well is connected patch k to other patches
Area-weighted dispersal flux through the connections of patch k to or from all of the
other patches in the landscape. It depends both on the attribute (e.g. area) of patch k
and on its position within the landscape network.
Sum of
for each pair of patches for which either i=k or j=k and i≠j.
The probability of connectivity metric (PC)
Partitioning dPCk into three different fractions
how important is patch k for maintaining connectivity between other patches
Contribution of patch (or link) k to the connectivity between other habitat patches, as a
connecting element or stepping stone between them. A certain patch or link k will
contribute to dPCconnector,k only when it is part of the best (maximum product probability)
path for dispersal between two other patches i and j.
Part of the sum
for each pair of patches i and j in which i≠k, j≠k and k is
part of the maximum probability path between them (pij*).
The probability of connectivity metric (PC)
Equivalent Connectivity EC(PC)
(ECA = Equivalent Connected Area)
√
Useful for quantifying changes in landscape connectivity and comparing them with the
changes in the amount of habitat in the landscape.
ECA when the patch attribute is area. EC (Equivalent Connectivity) in the more general
case of any attribute different from area.
In the case of using area-weighted habitat quality as attribute of nodes (quality ranging
between 0 and 1), EC corresponds to the sum of area (hectares) of habitat of the
maximum quality, 2EC to the sum of area of habitat with a quality of 0.5, and so on.
By calculating the area-weighted mean habitat quality for all the patches in the habitat
network it is possible to obtain the value of total area with that average quality that
corresponds to the EC of the current landscape.
Consideraciones para el ejercicio
1) Cambiar configuraci&oacute;n regional (punto por coma como separador decimal).
2) Crear campos nuevos en la capa de h&aacute;bitat.
ID: integer
AWquality: float
3) Conefor Inputs:
- usar como input los dos campos creados
- calcular archivo de distancias borde-borde y archivo de nodos
4) Conefor:
- calcular PC (usar archivos de conexiones y nodos generados por Conefor Inputs)
- fijar la distancia mediana de dispersi&oacute;n de la especie utilizando los valores “Distance =
5000 (m), corresponds to probability = 0.5”
- seleccionar el c&aacute;lculo de deltas, vars y EC