vegdist {vegan} | R Documentation |
The function computes dissimilarity indices that are useful for or popular with community ecologists. Gower, BrayCurtis, Jaccard and Kulczynski indices are good in detecting underlying ecological gradients (Faith et al. 1987). Morisita and HornMorisita indices should be able to handle different sample sizes (Wolda 1981), and Mountford (1962) index for presenceabsence data should be able to handle unknown (and variable) sample sizes.
vegdist(x, method="bray", diag=FALSE, upper=FALSE)
x |
Community data matrix. |
method |
Dissimilarity index, partial match to "manhattan" ,
"euclidean" , "canberra" , "bray" , "kulczynski" ,
"jaccard" , "gower" , "morisita" , "horn" or
"mountford" . |
diag |
Compute diagonals. |
upper |
Return only the upper diagonal. |
Jaccard and Mountford indices are discussed below. The other indices are defined as:
euclidean | d[jk] = sqrt(sum (x[ij]-x[ik])^2) |
manhattan | d[jk] = sum(abs(x[ij] - x[ik])) |
gower | d[jk] = sum (abs(x[ij]-x[ik])/(max(x[i])-min(x[i])) |
canberra | d[jk] = (1/NZ) sum ((x[ij]-x[ik])/(x[ij]+x[ik])) |
where NZ is the number of non-zero entries. | |
bray | d[jk] = (sum abs(x[ij]-x[ik])/(sum (x[ij]+x[ik])) |
kulczynski | d[jk] 1 - 0.5*((sum min(x[ij],x[ik])/(sum x[ij]) + (sum min(x[ij],x[ik])/(sum x[ik])) |
morisita | {d[jk] = 2*sum(x[ij]*x[ik])/((lambda[j]+lambda[k]) * sum(x[ij])*sum(x[ik])) } |
where lambda[j] = sum(x[ij]*(x[ij]-1))/sum(x[ij])*sum(x[ij]-1) | |
horn | Like morisita , but lambda[j] = sum(x[ij]^2)/(sum(x[ij])^2) |
Jaccard index is computed as 2B/(1+B), where B is BrayCurtis dissimilarity.
Mountford index is defined as M = 1/α where α is
the parameter of Fisher's logseries assuming that the compared
communities are samples from the same community
(cf. fisherfit
, fisher.alpha
). The index
M is found as the positive root of equation exp(a*M) + exp(b*M) = 1 +
exp((a+b-j)*M), where j is the number of species occurring in
both communities, and a and b are the number of species in
each separate community (so the index uses presenceabsence
information). Mountford index is usually misrepresented in the
literature: indeed Mountford (1962) suggested an approximation to be used as starting
value in iterations, but the proper index is defined as the root of the equation
above. The function vegdist
solves M with the Newton
method. Please note that if either a or b are equal to
j, one of the communities could be a subset of other, and the
dissimilarity is 0 meaning that non-identical objects may be
regarded as similar and the index is non-metric. The Mountford index
is in the range 0 ... log(2), but the dissimilarities are
divided by log(2)
so that the results will be in the conventional range 0 ... 1.
Morisita index can be used with genuine count data only. Its HornMorisita variant is able to handle any abundance data.
Euclidean and Manhattan dissimilarities are not good in gradient separation without proper standardization but are still included for comparison and special needs.
BrayCurtis and Jaccard indices are rank-order similar, and some
other indices become identical or rank-order similar after some
standardizations, especially with presence/absence transformation of
equalizing site totals with decostand
.
The naming conventions vary. The one adopted here is traditional
rather than truthful to priority. The abbreviation "horn"
for
the HornMorisita index is misleading, since there is a separate
Horn index. The abbreviation will be changed if that index is implemented in
vegan
.
Should provide a drop-in replacement for dist
and
return a distance object of the same type.
The function is an alternative to dist
adding
some ecologically meaningful indices. Both methods should produce
similar types of objects which can be interchanged in any method
accepting either. Manhattan and Euclidean dissimilarities should be
identical in both methods, and Canberra dissimilarity may be similar.
Jari Oksanen
Faith, D.P, Minchin, P.R. and Belbin, L. (1987). Compositional dissimilarity as a robust measure of ecological distance. Vegetatio 69, 5768.
Mountford, M. D. (1962). An index of similarity and its application to classification problems. In: P.W.Murphy (ed.), Progress in Soil Zoology, 4350. Butterworths.
Wolda, H. (1981). Similarity indices, sample size and diversity. Oecologia 50, 296302.
decostand
, dist
,
rankindex
, isoMDS
, stepacross
.
data(varespec) vare.dist <- vegdist(varespec) # Orlóci's Chord distance: range 0 .. sqrt(2) vare.dist <- vegdist(decostand(varespec, "norm"), "euclidean")