## Parametric Indices of Species Diversity

### Description

The function `divparam` calculates parametric diversity indices. The parameter controls the relative importance given to rare versus abundant species in a community. The function `plot.divparam` plots the results of function `divparam`.

### Usage

```divparam(comm, method = c("hill", "tsallis", "renyi"), q = 2, tol = 1e-08)

## S3 method for class 'divparam'
plot(x, legend = TRUE,
legendposi = "topright", axisLABEL = "Diversity", type = "b",
col = if (is.numeric(x)) NULL
else sample(colors(distinct = TRUE), nrow(x\$div)),
lty = if (is.numeric(x)) NULL else rep(1, nrow(x\$div)),
pch = if (is.numeric(x)) NULL else rep(19, nrow(x\$div)),
...)
```

### Arguments

 `comm` a data frame or a matrix typically with communities as rows, species as columns and abundance as entry. `method` a string: either "hill" for the Hill numbers (Hill 1973), "tsallis" for the Tsallis or HCDT entropy (Harvda and Charvat 1967; Daroczy 1970; Tsallis 1988), or "renyi" for Renyi's entropy (Renyi 1960). `q` a positive numeric or a vector of positive numerics that gives values for the `q` parameter. `tol` numeric tolerance threshold: values between -tol and tol are considered equal to zero. `x` an object of class `divparam` obtained with function `divparam`. `legend` a logical. If TRUE a legend is given with the colour, the type of line (etc.) used to define the diversity curve of each community. `legendposi` a string or a numeric that gives the position of the legend to be passed to function `legend` of the base of R. `axisLABEL` a string to display on the main axis of the plot to designate what we are measuring. The default is `"Diversity"`. `type` a string to be passed to the graphic argument `type` of functions `plot` and `lines` used to draw the diversity curve of each community. `col` colours to be passed to the graphic argument `col` of functions `plot` and `lines` to define the colour of the diversity curve of each community. `lty` type of line (plain, broken etc.) to be passed to the graphic argument `lty` of functions `plot` and `lines` used to draw the diversity curve of each community. `pch` type of point (open circle, close circle, square etc.) to be passed to the graphic argument `pch` of functions `plot` and `lines` used to draw the diversity curve of each community. `...` other arguments can be added and passed to the functions `plot` and `lines` used to draw the graphic.

### Value

If only a single value of `q` is given, function `divparam` returns a vector with the diversities of the communities. If more than one value of `q` is given, a list of two objects is returned:

 `q` the vector of values for `q` `div` a data frame with the diversities of the communities calculated for all values of `q`

The function `plot.divparam` returns a graphic.

### Author(s)

Sandrine Pavoine sandrine.pavoine@mnhn.fr

### References

Daroczy, Z. (1970) Generalized information functions. Information and Control, 16, 36–51.

Havrda, M., Charvat, F. (1967) Quantification method of classification processes: concept of structural alpha-entropy. Kybernatica, 3, 30–35.

Hill, M.O. (1973) Diversity and evenness: a unifying notation and its consequences. Ecology, 54, 427–432.

Renyi, A. (1960) On measures of entropy and information. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, 1, 547–561.

Tsallis, C. (1988) Possible generalization of Boltzmann-Gibbs statistics. Journal of Statistical Physics, 52, 480–487.

### Examples

```data(batcomm)
ab <- batcomm\$ab
plot(divparam(ab))
plot(divparam(ab, q=0:4))
```