trudi: Calculate true diversity of any order
In simba: A Collection of functions for similarity analysis of vegetation data

Description Usage Arguments Details Value Author(s) References See Also Examples

Calculates the gamma, alpha and beta components of true species diversity of a species x sites matrix.

1	trudi(mat, q = 0, weights = TRUE, base = exp(1))

`mat`	Vegetation data. Sites x species matrix. May be binary or quantitative data.
`q`	The order of the diversity. Defaults to 0 which means that rare species have more emphasis. With q = 1 all species contribute exactly according to their relative abundance. For details see references.
`weights`	Logical. Shall the contribution of the sites to the total abundances in the dataset be acknowledged? Per default it is done so (see Tuomisto 2010a,b for details)
`base`	Internally the logarithm of a term is calculated (like in Shannon index) and here it is possible to change the base of that logarithm.

In recent years there has been an intense debate about the calculation of species diversity from vegetation data. Jost (2006) brought the fairly old concept of Hill's (1973) effective number of species back into the debate and elucidated the important difference between entropy and diversity. Combined with the scales concept of Whittaker (alpha, beta, gamma; Jurasinski & Koch 2011) the apologists of strict diversity definition coined the term "true diversity".

The function calculates true diversity components for alpha, beta, and gamma.

Returns a named vector with the values for gamma, beta, and alpha diversity.

Gerald Jurasinski gerald.jurasinski@uni-rostock.de

Hill, M.O. (1973) Diversity and evenness: a unifying notation and its consequences. Ecology 54:427–432

Jost, L. (2006) Entropy and diversity. Oikos 113:363–375

Jost, L. (2007) Partitioning diversity into independent alpha and beta components. Ecology 88:2427–2439

Jost, L. (2009) Mismeasuring biological diversity: response to Hoffmann and Hoffmann (2008). Ecological Economics 68:925–992

Jost, L. (2010) Independence of alpha and beta diversities. Ecology 91:1969–1974

Jurasinski, G.; Koch, M. (2011) Commentary: do we have a consistent terminology for species diversity? We are on the way- Oecologia DOI 10.1007/s00442-011-2126-6

Routledge, R.D. (1979) Diversity indices: which ones are admissible? Journal of Theoretical Biology 76:503–515

Tuomisto, H. (2010a) A diversity of beta diversities: straightening up a concept gone awry. Part 1. Defining beta diversity as a function of alpha and gamma diversity. Ecography 33:2–22

Tuomisto, H. (2010b) A diversity of beta diversities: straightening up a concept gone awry. Part 2. Quantifying beta diversity and related phenomena. Ecography 33:23–45

Tuomisto, H. (2010c) A consistent terminology for species diversity? Yes, it does exist. Oecologia 164:853–860

Tuomisto, H. (2011) Commentary: do we have a consistent terminology for species diversity? Yes, if we choose to use it Oecologia

Whittaker, R.H. (1960) Vegetation of the Siskiyou Mountains, Oregon and California. Ecological Monographs 30:279–338

Wolda, H. (1981) Similarity indices, sample size and diversity. Oecologia 50: 296-302.

diversity for diversity indices.

# load data
data(bernina)
# run trudi with defaults
trudi(veg)
# testing another q
trudi(veg, 2)

## do something more complex: calculating the diversity components
## for the three time steps in the Bernina data
# a vector of q's
qs <- c(0:10)
# calculating diversity components per q per sampling year
div <- by(veg.lst, years, function(x) data.frame(t(sapply(c(0:10), 
function(y) trudi(mama(x), y)))))
# plot the results
par(mfrow=c(1,3), cex=1.1, las=1)
for(i in c(1:3)){
	plot(gamma ~ qs, data=div[[i]], ylim=c(0,80), type="l", 
	main=names(div)[i])
	lines(alpha ~ qs, data=div[[i]], lty=2)
	lines(beta*10 ~ qs, data=div[[i]], col="red4")
}