renyi {vegan} | R Documentation |

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 r.kindt@cgiar.org and Jari Oksanen

http://www.worldagroforestry.org/treesandmarkets/tree_diversity_analysis.asp

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.

`diversity`

for diversity indices, and
`specaccum`

for ordinary species accumulation curves, and
`xyplot`

, `persp`

and
`rgl`

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)) persp(mod)

[Package *vegan* version 1.16-32 Index]