tsallis {vegan} | R Documentation |

Function `tsallis`

find Tsallis diversities with any scale or the corresponding evenness measures. Function `tsallisaccum`

finds these statistics with accumulating sites.

tsallis(x, scales = seq(0, 2, 0.2), norm = FALSE, hill = FALSE) tsallisaccum(x, scales = seq(0, 2, 0.2), permutations = 100, raw = FALSE, ...) ## S3 method for class 'tsallisaccum': persp(x, theta = 220, phi = 15, col = heat.colors(100), zlim, ...)

`x` |
Community data matrix or plotting object. |

`scales` |
Scales of Tsallis diversity. |

`norm` |
Logical, if `TRUE` diversity values are normalized by their maximum (diversity value at equiprobability conditions). |

`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. |

`theta, phi` |
angles defining the viewing direction. `theta` gives the azimuthal direction and `phi` the colatitude. |

`col` |
Colours used for surface. |

`zlim` |
Limits of vertical axis. |

`...` |
Other arguments which are passed to `tsallis` and to graphical functions. |

The Tsallis diversity (also equivalent to Patil and Taillie diversity) is a one-parametric generalised entropy function, defined as:

*H.q = 1/(q-1)(1-sum(p^q))*

where *q* is a scale parameter, *S* the number of species in the sample (Tsallis 1988, Tothmeresz 1995). This diversity is concave for all *q>0*, but non-additive (Keylock 2005). For *q=0* it gives the number of species minus one, as *q* tends to 1 this gives Shannon diversity, for *q=2* this gives the Simpson index (see function `diversity`

).

If `norm = TRUE`

, `tsallis`

gives values normalized by the maximum:

*H.q(max) = (S^(1-q)-1)/(1-q)*

where *S* is the number of species. As *q* tends to 1, maximum is defined as *ln(S)*.

If `hill = TRUE`

, `tsallis`

gives Hill numbers (numbers equivalents, see Jost 2007):

*D.q = (1-(q-1)*H)^(1/(1-q))*

Details on plotting methods and accumulating values can be found on the help pages of the functions `renyi`

and `renyiaccum`

.

Function `tsallis`

returns a data frame of selected indices. Function `tsallisaccum`

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.

P'eter S'olymos, solymos@ualberta.ca, based on the code of Roeland Kindt and Jari Oksanen written for `renyi`

Tsallis, C. (1988) Possible generalization of Boltzmann-Gibbs statistics.
*J. Stat. Phis.* 52, 479–487.

Tothmeresz, B. (1995) Comparison of different methods for diversity
ordering. *Journal of Vegetation Science* **6**, 283–290.

Patil, G. P. and Taillie, C. (1982) Diversity as a concept and its measurement.
*J. Am. Stat. Ass.* **77**, 548–567.

Keylock, C. J. (2005) Simpson diversity and the Shannon-Wiener index as special cases of a generalized entropy.
*Oikos* **109**, 203–207.

Jost, L (2007) Partitioning diversity into independent alpha and beta components.
*Ecology* **88**, 2427–2439.

Plotting methods and accumulation routines are based on functions `renyi`

and `renyiaccum`

. An object of class 'tsallisaccum' can be used with function `rgl.renyiaccum`

as well. See also settings for `persp`

.

data(BCI) i <- sample(nrow(BCI), 12) x1 <- tsallis(BCI[i,]) x1 diversity(BCI[i,],"simpson") == x1[["2"]] plot(x1) x2 <- tsallis(BCI[i,],norm=TRUE) x2 plot(x2) mod1 <- tsallisaccum(BCI[i,]) plot(mod1, as.table=TRUE, col = c(1, 2, 2)) persp(mod1) mod2 <- tsallisaccum(BCI[i,], norm=TRUE) persp(mod2,theta=100,phi=30)

[Package *vegan* version 1.16-32 Index]