renyi: Renyi and Hill Diversities and Corresponding Accumulation...

In vegan: Community Ecology Package

Renyi and Hill Diversities and Corresponding Accumulation Curves

Description

Function renyi find Rényi diversities with any scale or the corresponding Hill number (Hill 1973). Function renyiaccum finds these statistics with accumulating sites.

Usage

renyi(x, scales = c(0, 0.25, 0.5, 1, 2, 4, 8, 16, 32, 64, Inf),
   hill = FALSE)
## S3 method for class 'renyi'
plot(x, ...)
renyiaccum(x, scales = c(0, 0.5, 1, 2, 4, Inf), permutations = 100,
    raw = FALSE, collector = FALSE, subset, ...)
## S3 method for class 'renyiaccum'
plot(x, what = c("Collector", "mean", "Qnt 0.025", "Qnt 0.975"),
    type = "l",
    ...)
## S3 method for class 'renyiaccum'
persp(x, theta = 220, col = heat.colors(100), zlim, ...)

Arguments

x	Community data matrix or plotting object.
scales	Scales of Rényi diversity.
hill	Calculate Hill numbers.
permutations	Usually an integer giving the number permutations, but can also be a list of control values for the permutations as returned by the function how, or a permutation matrix where each row gives the permuted indices.
raw	if FALSE then return summary statistics of permutations, and if TRUE then returns the individual permutations.
collector	Accumulate the diversities in the order the sites are in the data set, and the collector curve can be plotted against summary of permutations. The argument is ignored if raw = TRUE.
subset	logical expression indicating sites (rows) to keep: missing values are taken as FALSE.
what	Items to be plotted.
type	Type of plot, where type = "l" means lines.
theta	Angle defining the viewing direction (azimuthal) in persp.
col	Colours used for surface. Single colour will be passed on, and vector colours will be selected by the midpoint of a rectangle in persp.
zlim	Limits of vertical axis.
...	Other arguments which are passed to renyi and to graphical functions.

Details

Common diversity indices are special cases of Rényi diversity

H_a = \frac{1}{1-a} \log \sum p_i^a

where a is a scale parameter, and Hill (1975) suggested to use so-called ‘Hill numbers’ defined as N_a = \exp(H_a). Some Hill numbers are the number of species with a = 0, \exp(H') or the exponent of Shannon diversity with a = 1, inverse Simpson with a = 2 and 1/ \max(p_i) with a = \infty. According to the theory of diversity ordering, one community can be regarded as more diverse than another only if its Rényi diversities are all higher (Tóthmérész 1995).

The plot method for renyi uses lattice graphics, and displays the diversity values against each scale in separate panel for each site together with minimum, maximum and median values in the complete data.

Function renyiaccum is similar to specaccum but finds Rényi or Hill diversities at given scales for random permutations of accumulated sites. Its plot function uses lattice function xyplot to display the accumulation curves for each value of scales in a separate panel. In addition, it has a persp method to plot the diversity surface against scale and number and sites. Similar dynamic graphics can be made with rgl.renyiaccum in vegan3d package.

Value

Function renyi returns a data frame of selected indices. Function renyiaccum with argument raw = FALSE returns a three-dimensional array, where the first dimension are the accumulated sites, second dimension are the diversity scales, and third dimension are the summary statistics mean, stdev, min, max, Qnt 0.025 and Qnt 0.975. With argument raw = TRUE the statistics on the third dimension are replaced with individual permutation results.

Author(s)

Roeland Kindt and Jari Oksanen

References

Hill, M.O. (1973). Diversity and evenness: a unifying notation and its consequences. Ecology 54, 427–473.

Kindt, R., Van Damme, P., Simons, A.J. (2006). Tree diversity in western Kenya: using profiles to characterise richness and evenness. Biodiversity and Conservation 15, 1253–1270.

Tóthmérész, B. (1995). Comparison of different methods for diversity ordering. Journal of Vegetation Science 6, 283–290.

See Also

diversity for diversity indices, and specaccum for ordinary species accumulation curves, and xyplot, persp.

Examples

data(BCI)
i <- sample(nrow(BCI), 12)
mod <- renyi(BCI[i,])
plot(mod)
mod <- renyiaccum(BCI[i,])
plot(mod, as.table=TRUE, col = c(1, 2, 2))
persp(mod)

vegan documentation built on Sept. 11, 2024, 7:57 p.m.