R: Rao's quadratic entropy

rao.diversity {SYNCSA} | R Documentation

## Rao's quadratic entropy

### Description

Calculates Rao's quadratic entropy, functional and phylogenetic redundancy.

### Usage

    rao.diversity(
      comm,
      traits = NULL,
      phylodist = NULL,
      checkdata = TRUE,
      ord = "metric",
      put.together = NULL,
      standardize = TRUE,
      ...
    )

### Arguments

`comm` | Community data, with species as columns and sampling units as rows. This matrix can contain either presence/absence or abundance data. Alternatively comm can be an object of class metacommunity.data, an alternative way to set all data.frames/matrices. When you use the class metacommunity.data the arguments traits, phylodist and put.together must be null. See details.
`traits` | Data frame or matrix data of species described by traits, with traits as columns and species as rows (Default traits = NULL).
`phylodist` | Matrix containing phylogenetic distance between species (Default phylodist = NULL).
`checkdata` | Logical argument (TRUE or FALSE) to check if species sequence in the community data follows the same order as the one in the trait and in the phylodist matrices (Default checkdata = TRUE).
`ord` | Method to be used for ordinal variables, see `gowdis` (Default ord = "metric").
`put.together` | List to specify group of traits. Each group specify receive the same weight that one trait outside any group, in the way each group is considered as unique trait (Default put.together = NULL). This argument must be a list, see examples in `syncsa`.
`standardize` | Logical argument (TRUE or FALSE) to specify if standardize phylogenetic distance to range into range 0 to 1. (Default standardize = TRUE).
`...` | Parameters for `gowdis` function.

### Details

Rao's quadratic entropy is a measure of diversity of ecological communities defined by Rao (1982) and is based on the proportion of the abundance of species present in a community and some measure of dissimilarity among them. The dissimilarity range from 0 to 1 and is based on a set of specified functional traits or in the phylogenetic dissimilarity.

For the trait data, the function calculates the square root of the one-complement of Gower's similarity index, in order to have a dissimilarity matrix with Euclidean metric properties. Gower's index ranges from 0 to 1 and can handle traits measured indifferent scales. When the species are completely different in terms of their traits, Rao quadratic entropy is equivalent to the Gini-Simpson index. Traits data can be numeric, factor or ordered factor. For this be considered traits data must be of data.frame class and containing each variable type determined. For additional details and requirements of function please see `gowdis`.

Functional redundancy is defined purely as the difference between species diversity and Rao's quadratic entropy based on their functional dissimilarity (de Bello et al. 2007). The same definition is used for phylogenetic redundancy.

Package SYNCSA requires that the species and community sequence in the data.frame or matrix must be the same for all dataframe/matrices. The function `organize.syncsa` organizes the data for the functions of the package, placing the matrices of community, traits, phylogenetic distance in the same order. The function use of function organize.syncsa is not requered for run the functions, but is recommended. In this way the arguments comm, traits, phylodist, as well as the argument put.together, can be specified them as normal arguments or by passing them with the object returned by the function `organize.syncsa` using, in this case only the argument comm. Using the object returned by organize.syncsa, the comm argument is used as an alternative way of entering to set all data.frames/matrices, and therefore the other arguments (traits, phylodist and put.together) must be null.

### Value

`Simpson` | Gini-Simpson index within each community (equivalent to Rao quadratic entropy with null, crisp, similarities).
`FunRao` | Rao quadratic entropy within each community, considering trait distance.
`FunRedundancy` | Functional redundancy in each community.
`PhyRao` | Rao quadratic entropy within each community, considering phylogenetic distance.
`PhyRedundancy` | Phylogenetic redundancy in each community.

### Note

IMPORTANT: The sequence species show up in community data matrix MUST be the same as they show up in traits and phylodist matrices. See details and `organize.syncsa`.

### Author(s)

Vanderlei Julio Debastiani <vanderleidebastiani@yahoo.com.br>

### References

de Bello, F.; Leps, J.; Lavorel, S. & Moretti, M. (2007). Importance of species abundance for assessment of trait composition: an example based on pollinator communities. Community Ecology, 8, 163:170.

Pillar, V.D.; Blanco, C.C.; Muler, S.C.; Sosinski, E.E.; Joner, F. & Duarte, L.d.S. (2013). Functional redundancy and stability in plant communities. Journal of Vegetation Science, 24, 963:974.

Rao, C.R. (1982). Diversity and dissimilarity coefficients: a unified approach. Theoretical Population Biology, 21, 24:43.

### See Also

`organize.syncsa`, `gowdis`, `syncsa`

### Examples

    data(ADRS)
    rao.diversity(ADRS$community)
    rao.diversity(ADRS$community, traits = ADRS$traits)

[Package SYNCSA version 1.3.4 Index]