vegan (version 2.0-10)

renyi: Renyi and Hill Diversities and Corresponding Accumulation Curves

Description

Function renyi find Rényi{Renyi} 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, ...)
rgl.renyiaccum(x, rgl.height = 0.2, ...)

Arguments

x

Community data matrix or plotting object.

scales

Scales of Rényi{Renyi} 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.

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.

rgl.height

Scaling of vertical axis.

...

Other arguments which are passed to renyi and to graphical functions.

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.

encoding

UTF-8

Details

Common diversity indices are special cases of Rényi{Renyi} 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{Renyi} diversities are all higher (Tóthmérész{Tothmeresz} 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{Renyi} 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.

References

http://www.worldagroforestry.org/resources/databases/tree-diversity-analysis

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{Tothmeresz}, 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.

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)