renyi {vegan}R Documentation

Renyi and Hill Diversities and Corresponding Accumulation Curves


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


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, ...)
## S3 method for class 'renyiaccum':
plot (x, what = c("mean", "Qnt 0.025", "Qnt 0.975"), type = "l", 
## S3 method for class 'renyiaccum':
persp (x, theta = 220, col = heat.colors(100), zlim, ...)
rgl.renyiaccum(x, rgl.height = 0.2, ...)


x Community data matrix or plotting object.
scales Scales of Rényi diversity.
hill Calculate Hill numbers.
permutations Number of random permutations in accumulating sites.
raw if FALSE then return summary statistics of permutations, and if TRUE then returns the individual permutations.
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.
rgl.height Scaling of vertical axis.
... Other arguments which are passed to renyi and to graphical functions.


Common diversity indices are special cases of Rényi diversity

H.a = 1/(1-a) log sum(p^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) with a = Inf. 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. Dynamic graphics with rgl.renyiaccum use rgl package, and produces similar surface as persp with a mesh showing the empirical confidence levels.


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.


Roeland Kindt and Jari Oksanen


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

Kindt R, Van Damme P, Simons AJ. 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 and rgl for controlling graphics.


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

[Package vegan version 1.16-32 Index]