Indices of Taxonomic Diversity and Distinctness
Description
Function finds indices of taxonomic diversity and distinctness, which are averaged taxonomic distances among species or individuals in the community (Clarke & Warwick 1998, 2001)
Usage
1 2 
Arguments
comm 
Community data. 
dis 
Taxonomic distances among taxa in 
match.force 
Force matching of column names in 
x 
Classification table with a row for each species or other basic taxon, and columns for identifiers of its classification at higher levels. 
varstep 
Vary step lengths between successive levels relative to proportional loss of the number of distinct classes. 
check 
If 
labels 
The 
Details
Clarke & Warwick (1998, 2001) suggested several alternative indices of taxonomic diversity or distinctness. Two basic indices are called taxonomic diversity (Δ) and distinctness (Δ^*):
Δ = (∑ ∑_{i<j} ω_{ij} x_i x_j)/(n (n1) / 2) 
Δ^* = (∑ ∑_{i<j} ω_{ij} x_i x_j)/(∑ ∑_{i<j} x_i x_j) 
The equations give the index value for a single site, and summation goes over species i and j. Here ω are taxonomic distances among taxa, and x are species abundances, and n is the total abundance for a site. With presence/absence data both indices reduce to the same index Δ^+, and for this index Clarke & Warwick (1998) also have an estimate of its standard deviation. Clarke & Warwick (2001) presented two new indices: sΔ^+ is the product of species richness and Δ^+, and index of variation in taxonomic distinctness (Λ^+) defined as
Λ^+ = (∑ ∑_{i<j} ω_{ij}^2)/(n (n1) / 2)  (Δ^+)^2 
The dis
argument must be species dissimilarities. These must be
similar to dissimilarities produced by dist
. It is
customary to have integer steps of taxonomic hierarchies, but other
kind of dissimilarities can be used, such as those from phylogenetic
trees or genetic differences. Further, the dis
need not be
taxonomic, but other species classifications can be used.
Function taxa2dist
can produce a suitable dist
object
from a classification table. Each species (or basic taxon) corresponds
to a row of the classification table, and columns give the
classification at different levels. With varstep = FALSE
the
successive levels will be separated by equal steps, and with
varstep = TRUE
the step length is relative to the proportional
decrease in the number of classes (Clarke & Warwick 1999).
With check = TRUE
, the function removes classes which are distinct for all
species or which combine all species into one class, and assumes that
each row presents a distinct basic taxon. The function scales
the distances so that longest path length between
taxa is 100 (not necessarily when check = FALSE
).
Function plot.taxondive
plots Δ^+ against Number of
species, together with expectation and its approximate 2*sd
limits. Function summary.taxondive
finds the z values and
their significances from Normal distribution for Δ^+.
Value
Function returns an object of class taxondive
with following items:
Species 
Number of species for each site. 
D, Dstar, Dplus, SDplus, Lambda 
Δ, Δ^*, Δ^+, sΔ^+ and Λ^+ for each site. 
sd.Dplus 
Standard deviation of Δ^+. 
ED, EDstar, EDplus 
Expected values of corresponding statistics. 
Function taxa2dist
returns an object of class "dist"
, with
an attribute "steps"
for the step lengths between successive levels.
Note
The function is still preliminary and may change. The scaling of taxonomic dissimilarities influences the results. If you multiply taxonomic distances (or step lengths) by a constant, the values of all Deltas will be multiplied with the same constant, and the value of Λ^+ by the square of the constant.
Author(s)
Jari Oksanen
References
Clarke, K.R & Warwick, R.M. (1998) A taxonomic distinctness index and its statistical properties. Journal of Applied Ecology 35, 523–531.
Clarke, K.R. & Warwick, R.M. (1999) The taxonomic distinctness measure of biodiversity: weighting of step lengths between hierarchical levels. Marine Ecology Progress Series 184: 21–29.
Clarke, K.R. & Warwick, R.M. (2001) A further biodiversity index applicable to species lists: variation in taxonomic distinctness. Marine Ecology Progress Series 216, 265–278.
See Also
diversity
.
Examples
1 2 3 4 5 6 7 8 9 10 11  ## Preliminary: needs better data and some support functions
data(dune)
data(dune.taxon)
# Taxonomic distances from a classification table with variable step lengths.
taxdis < taxa2dist(dune.taxon, varstep=TRUE)
plot(hclust(taxdis), hang = 1)
# Indices
mod < taxondive(dune, taxdis)
mod
summary(mod)
plot(mod)
