Taxonomic Diversity Index (Delta)

Calculates the taxonomic diversity index (Delta) from Warwick & Clarke (1995). This is the average weighted path length between every pair of individuals, including same-species pairs (weighted 0).

Usage

delta(community, tax_tree, weights = NULL)

Arguments

community

A named numeric vector of species abundances.

tax_tree

A data frame with taxonomic hierarchy.

weights

Optional numeric vector of path weights for each taxonomic level. If NULL, a linear scale is used (1, 2, 3, ...).

Value

A numeric value representing taxonomic diversity (Delta).

Details

$$\Delta = \frac{\sum\sum_{i<j} w_{ij} x_i x_j + \sum_i 0 \cdot x_i(x_i-1)/2}{\sum\sum_{i<j} x_i x_j + \sum_i x_i(x_i-1)/2}$$

References

Warwick, R.M. & Clarke, K.R. (1995). New 'biodiversity' measures reveal a decrease in taxonomic distinctness with increasing stress. Marine Ecology Progress Series, 129, 301-305.

See also

delta_star() for taxonomic distinctness (excluding same-species), avtd() for presence/absence-based AvTD, ozkan_pto() for Deng entropy-based alternative.

Examples

comm <- c(sp1 = 5, sp2 = 3, sp3 = 3, sp4 = 1, sp5 = 3)
tax <- data.frame(
  Species = paste0("sp", 1:5),
  Genus = c("G1", "G1", "G2", "G2", "G2"),
  Family = c("F1", "F1", "F1", "F2", "F2"),
  stringsAsFactors = FALSE
)
delta(comm, tax)
#> [1] 1.352381