ND {bipartite}R Documentation

Normalised degree, betweenness and closeness centrality

Description

Calculates normalised degrees, and two measures of centrality, betweenness and closeness. These two are based on one-mode representations of the network and invoke functions from sna.

Usage

ND(web, normalised=TRUE)
BC(web, rescale=TRUE, ...)
CC(web, cmode="suminvdir", rescale=TRUE, ...)

Arguments

web A matrix with lower trophic level species as rows, higher trophic level species as columns and number of interactions as entries.
normalised Shall the degrees be normalised? If so (default), the degree for a species is divided by the number of potential partners-1 (see, e.g., Martín González et al. 2009).
rescale If TRUE (default), centrality scores are rescaled such that they sum to 1.
cmode String indicating the type of betweenness centrality being computed (directed or undirected geodesics, or a variant form - see help for closeness in sna for details). The default, "suminvdir", uses a formula that can also be applied to disconnected (=compartmented) graphs. Other cmodes cannot.
... Options passed on to betweenness and closeness, respectively.

Details

These functions are convinience functions to enable easy reproduction of the type of analyses by Martín González et al. (2009). BC and CC are wrappers calling two functions from sna, which uses one-mode, rather than bipartite data.

Value

A list with two entries, ``lower'' and ``higher'', which contain a named vector of normalised degrees, betweenness centrality and closeness centrality, respectively. The lower-entry contains the lower trophic level species, the higher analogously the higher trophic level species.

Note

Experimental. Should work most of the time, but not necessarily always. Also, on trials with the same data as those of Martín González et al. (2009), numerical values differed slightly. Whether this is due to rounding errors, different non-linear least square fits in JMP and R or whatever I cannot tell. See example for my attempt to reproduce their values for the network ``Azores'' (aka olesen2002flores).

Author(s)

Carsten F. Dormann carsten.dormann@ufz.de

References

Martín Gonzáles, A.M., Dalsgaard, B. and Olesen, J.M. 2009. Centrality measures and the importance of generalist species in pollination networks. Ecological Complexity, in press (doi:10.1016/j.ecocom.2009.03.008)

See Also

centralization, betweenness and closeness in sna; specieslevel which calls them

Examples

## example:
data(olesen2002flores)
(ndi <- ND(olesen2002flores))
(cci <- CC(olesen2002flores))
(bci <- BC(olesen2002flores))

cor.test(bci[[1]], ndi[[1]], method="spear") # 0.779
cor.test(cci[[1]], ndi[[1]], method="spear") # 0.826

cor.test(bci[[2]], ndi[[2]], method="spear") # 0.992
cor.test(cci[[2]], ndi[[2]], method="spear") # 0.919

## PLANTS:
bc <- bci[[1]]
cc <- cci[[1]]
nd <- ndi[[1]]
# CC:
summary(nls(cc ~ a*nd+b, start=list(a=1,b=1))) # lower RSE
summary(nls(cc ~ c*nd^d, start=list(c=0.02,d=2))) 
# BC:
summary(nls(bc ~ a*nd+b, start=list(a=1,b=1)))
summary(nls(bc ~ c*nd^d, start=list(c=0.02,d=2))) # lower RSE

## ANIMALS:
bc <- bci[[2]]
cc <- cci[[2]]
nd <- ndi[[2]]
# CC:
summary(nls(cc ~ a*nd+b, start=list(a=1,b=1))) 
summary(nls(cc ~ c*nd^d, start=list(c=0.2,d=2))) # lower RSE
# BC:
summary(nls(bc ~ a*nd+b, start=list(a=1,b=1)))
summary(nls(bc ~ c*nd^d, start=list(c=0.2,d=2))) # lower RSE

[Package bipartite version 1.06 Index]