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
1 2 3 4 5 6 7 8 9 10 11 12  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 
raw 
if 
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 
subset 
logical expression indicating sites (rows) to keep: missing
values are taken as 
what 
Items to be plotted. 
type 
Type of plot, where 
theta 
Angle defining the viewing direction (azimuthal) in

col 
Colours used for surface. Single colour will be passed on,
and vector colours will be
selected by the midpoint of a rectangle in 
zlim 
Limits of vertical axis. 
... 
Other arguments which are passed to 
Details
Common diversity
indices are special cases of
Rényi diversity
H.a = 1/(1a) log sum(p^a)
where a is a scale parameter, and Hill (1975) suggested to use socalled “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. 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 threedimensional 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 r.kindt@cgiar.org and Jari Oksanen
References
http://www.worldagroforestry.org/resources/databases/treediversityanalysis
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: 12531270.
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.renyiaccum
.
Examples
1 2 3 4 5 6 7 