R: Indices of Taxonomic Diversity and Distinctness

taxondive {vegan} | R Documentation

## 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

    taxondive(comm, dis, match.force = FALSE)
    taxa2dist(x, varstep = FALSE, check = TRUE, labels)

### Arguments

`comm` | Community data.
`dis` | Taxonomic distances among taxa in `comm`. This should be a `dist` object or a symmetric square matrix.
`match.force` | Force matching of column names in `comm` and labels in `dis`. If `FALSE`, matching only happens when dimensions differ, and in that case the species must be in identical order in both.
`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 `TRUE`, remove all redundant levels which are different for all rows or constant for all rows and regard each row as a different basal taxon (species). If `FALSE` all levels are retained and basal taxa (species) also must be coded as variables (columns). You will get a warning if species are not coded, but you can ignore this if that was your intention.
`labels` | The `labels` attribute of taxonomic distances. Row names will be used if this is not given. Species will be matched by these labels in `comm` and `dis` in `taxondive` if these have different dimensions.

### 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 (n-1) / 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 (n-1) / 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

    ## 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)

[Package vegan version 2.4-3 Index]