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togetherness <- function(web, normalise=TRUE, FUN=mean, ...){
# calculates the T-score="togetherness" for all pollinator species; the T-score represents
# the average number of specis pair identical co-occurrences and co-absences.
# (Stone & Roberts 1992)
# J*(N-J-(A-J)-(B-J)) = J*(N-A-B+J)
# for each species pair, we count the number of island pairs of the pattern (0,0,1,1) or (1,1,0,0,)
# ... to be passed on to FUN (If a species occurs on all sites, then its distance
# Carsten F. Dormann, Jan. 2008
# didn't find a simple way to calculate the upper limit for togetherness.
web <- web>0 # this whole concept works only on binary data!
D <- designdist(t(web), method="J*(P-A-B+J)", terms="minimum", name="togetherness")
# The minimum value for Ds is 0, for the special case were all species use the
# hosts exactly co-occurringly.
# The maximum value possible for each species is simply the product of number of
# 0s and 1s, so the maximum of a species pair is the minimum of each species maximum.
if (normalise){
maxD <- designdist(t(web), method="min(max(A*(P-A)), max(B*(P-B)))", terms="minimum")
D <- D/maxD
}
FUN(D, ...)
}
# example:
#m <- matrix(c(1,0,0, 1,1,0, 1,1,0, 0,1,1, 0,0,1), 5,3,TRUE)
#togetherness(m, normalise=FALSE)
#togetherness(m, normalise=TRUE)
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