# lconnect connectivity metrics

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In our package lconnect we use the Integral Index of connectivity to obtain patch importance, but several other metrics are currently available. A description of each of this metrics can be found below. For more information about each metric please see the references provided. At the end of the post an example using the function currently implemented to compute the metrics can be found. These are the landscape connectivity metrics currently provided:

### Number of components

NC – Number of components (groups of interconnected patches) in the landscape (Urban and Keitt, 2001). Patches in the same component are considered to be accessible, while patches in different components are not. Highly connected landscapes have less components. Threshold dependent, i.e., maximum distance for two patches to be considered connected. Can be interpreted as the maximum dispersal distance for a certain species.

### Number of links

LNK – Number of links connecting the patches. The landscape is interpreted as binary, which means that the habitat patches are either connected or not (Pascual-Hortal and Saura, 2006). Higher LNK implies higher connectivity. Threshold dependent.

### Size of the largest component

SLC – Area of the largest group of interconnected patches (Pascual- Hortal and Saura, 2006). Threshold dependent.

### Mean size of components

MSC – Mean area of interconnected patches (Pascual-Hortal and Saura, 2006). Threshold dependent.

### Class coincidence probability

CCP – Class coincidence probability. It is defined as the probability that two randomly chosen points within the habitat belong to the same component (or cluster). Ranges between 0 and 1 (Pascual-Hortal and Saura 2006). Higher CCP implies higher connectivity. Threshold dependent.

### Landscape coincidence probability

LCP – Landscape coincidence probability. It is defined as the probability that two randomly chosen points in the landscape (whether in an habitat patch or not) belong to the same habitat component (or cluster). Ranges between 0 and 1 (Pascual-Hortal and Saura 2006). Threshold dependent.

### Characteristic path length

CPL – Characteristic path length. Mean of all the shortest paths between the habitat patches (Minor and Urban, 2008). The shorter the CPL value the more connected the patches are. Threshold dependent.

### Expected cluster size

ECS – Expected component (or cluster) size. Mean cluster size of the clusters weighted by area. (O’Brien et al., 2006 and Fall et al, 2007). This represents the size of the component in which a randomly located point in an habitat patch would reside. Although it is informative regarding the area of the component, it does not provide any ecologically meaningful information regarding the total area of habitat. As an example: ECS increases with less isolated small components or patches, although the total habitat decreases (Laita et al. 2011). Threshold dependent.

### Area-weighted flux

AWF – Area-weighted Flux. Evaluates the flow, weighted by area, between all pairs of patches (Bunn et al. 2000 and Urban and Keitt 2001). The probability of dispersal between two patches, was computed using pij=exp(-k * dij), where k is a constant making pij (the dispersal probability between patches) 50% at half the dispersal distance defined by the user. Although k, as was implemented, is dependent on the dispersal distance, AWF is a probabilistic index and not directly dependent on the threshold.

### Integral index of connectivity

IIC – Integral index of connectivity. Index developed specifically for landscapes by Pascual-Hortal and Saura (2006). It is based on habitat availability and on a binary connection model (as opposed to a probabilistic). It ranges from 0 to 1 (higher values indicating more connectivity). Threshold dependent.

The implementation of the metrics is done by the function con_metric(), the workhorse of this package. A boundary for the landscape can be provided by the user, if not, a convex hull is computed around the patches and used as landscape boundary:

# Install package first from github. See previous post for instructions library(lconnect) # The package provides an example landscape that can acessed by this path vec_path <- system.file("extdata/vec_projected.shp", package = "lconnect")

At this point only shapefiles are allowed and the first column atribute must contain the habitat class. Can be numeric or character, and the values representing habitat patches must be provided. The minimum distance should be provided if the metric to be calculated uses it. If not provided only a few metrics can be calculated. Methods in the plot function were implemented for visualization, please refer to previous post for examples.

# Upload landscape landscape <- upload_land(vec_path, bound_path = NULL, habitat = 1, max_dist = 500)

The previous function generates a “lconnect” object that can now be used to compute metrics. In this example all the metrics available are computed.

con_metric(landscape, metric = c("NC", "LNK", "SLC", "MSC", "CCP", "LCP", "CPL", "ECS", "AWF","IIC")) ## values ## NC 1.600000e+01 ## LNK 2.400000e+01 ## SLC 1.871012e+07 ## MSC 2.252755e+06 ## CCP 3.255600e-01 ## LCP 1.413000e-02 ## CPL 1.811320e+00 ## ECS 1.173444e+07 ## AWF 4.390062e+13 ## IIC 9.620000e-03

### References

Bunn, A. G., Urban, D. L., and Keitt, T. H. (2000). Landscape connectivity: a conservation application of graph theory. Journal of Environmental Management, 59(4): 265-278.

Fall, A., Fortin, M. J., Manseau, M., and O’ Brien, D. (2007). Spatial graphs: principles and applications for habitat connectivity. Ecosystems, 10(3): 448-461.

Laita, A., Kotiaho, J.S., Monkkonen, M. (2011). Graph-theoretic connectivity measures: what do they tell us about connectivity? Landscape Ecology, 26: 951-967.

Minor, E. S., and Urban, D. L. (2008). A Graph-Theory Framework for Evaluating Landscape Connectivity and Conservation Planning. Conservation Biology, 22(2): 297-307.

O’Brien, D., Manseau, M., Fall, A., and Fortin, M. J. (2006). Testing the importance of spatial configuration of winter habitat for woodland caribou: an application of graph theory. Biological Conservation, 130(1): 70-83.

Pascual-Hortal, L., and Saura, S. (2006). Comparison and development of new graph-based landscape connectivity indices: towards the priorization of habitat patches and corridors for conservation. Landscape Ecology, 21(7): 959-967.

Urban, D., and Keitt, T. (2001). Landscape connectivity: a graph-theoretic perspective. Ecology, 82(5): 1205-1218.

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