renyi {vegan} | R Documentation |
Function renyi
find Rényi diversities with any
scale or the corresponding Hill number (Hill 1975). 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", ...)
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. |
... |
Other arguments which are passed to renyi and
xyplot in 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.
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 diveristy 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 r.kindt@cgiar.org and Jari Oksanen
Hill, M.O. (1973). Diversity and evenness: a unifying notation and its consequences. Ecology 54, 427–473.
Tóthmérész, B. (1995). Comparison of different methods for diversity ordering. Journal of Vegetation Science 6, 283–290.
diversity
for diversity indices, and
specaccum
for ordinaty species accumulation curves, and
xyplot
for controlling graphics.
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))