rare_Rao {adiv} | R Documentation |

## Functional Rarefaction for Species Abundance Data

### Description

The function `Rare_Rao`

performs distance-based rarefaction curves using species abundance data. It finds the expected functional diversity (if functional distances between species are used) as a function of the sampling effort. Two approaches are available: an analytical solution, a resampling approach.

### Usage

```
rare_Rao(comm, dis, sim = TRUE, resampling = 999, formula = c("QE", "EDI"))
```

### Arguments

`comm` |
a data frame or a matrix with samples as rows, species as columns, and abundance or frequency as entries. If presences/absences (1/0) are given, the relative abundance of a given species in a community of S species will be considered equal to 1/S. |

`dis` |
an object of class |

`sim` |
a logical; if |

`resampling` |
a numeric; number of times data are resampled to calculate the mean functional rarefaction curve (used if |

`formula` |
either |

### Details

If `formula = "QE"`

, the definition of the quadratic entropy is:

`QE(\mathbf{p}_i,\mathbf{D})=\sum_{k=1}^S\sum_{l=1}^S p_{k|i}p_{k|j}d_{kl}`

where `\mathbf{p}_i=(p_{1|i}, ..., p_{k|i}, ..., p_{S|i})`

is the vector of relative species abundance within sample *i*; *S* is the number of species; `\mathbf{D}=(d_{kl})`

is the matrix of (phylogenetic or functional) dissimilarities among species, and `d_{kl}`

is the (phylogenetic or functional) dissimilarity between species
*k* and *l*.

If `formula = "EDI"`

, the definition of the quadratic entropy is:

`EDI(\mathbf{p}_i,\mathbf{D})=\sum_{k=1}^S\sum_{l=1}^S p_{k|i}p_{k|j}\frac{d_{kl}^2}{2}`

EDI stands for the Euclidean Diversity Index of Champely and Chessel (2002) (equation 3 in Pavoine et al. 2004).

In both cases, if `dis = NULL`

, the quadratic entropy is equal to Gini-Simpson entropy:

`H_{GS}(\mathbf{p}_i)=1 - \sum_{k=1}^S p_{k|i}^2`

### Value

If `sim = TRUE`

, the function returns a data frame containing the Expected Rao Quadratic Entropy (column 'ExpRao'), the limits of the 95% Confidence Interval (columns 'LeftIC' and 'RightIC') for each subsample dimension (M) out of the total set of samples (N). If `sim = FALSE`

, the function returns a data frame containing the analytical solution for the Expected Rao Quadratic Entropy (column 'ExpRao') for each subsample dimension (M) out of the total set of samples (N).

### Author(s)

Giovanni Bacaro and Sandrine Pavoine sandrine.pavoine@mnhn.fr

### References

Ricotta, C., Pavoine, S., Bacaro, G., Acosta, A. (2012) Functional rarefaction for species abundance data. *Methods in Ecology and Evolution*, **3**, 519–525.

Champely, S. and Chessel, D. (2002) Measuring biological diversity using Euclideanmetrics. *Environmental and Ecological Statistics*, **9**, 167–177.

Pavoine, S., Dufour, A.B., Chessel, D. (2004) From dissimilarities among species to dissimilarities among communities: a double principal coordinate analysis. *Journal of Theoretical Biology*, **228**, 523–537.

### See Also

### Examples

```
## Not run:
if(require(ade4)){
data(aviurba, package="ade4")
# Trait-based distances between bird species:
distances<-dist.ktab(ktab.list.df(list(aviurba$traits)), type = "N")
# The distances should be squared Euclidean;
# note that Euclidean distances can be used
# as they also are squared Euclidean.
# Species abundances in sites
abundances<- aviurba$fau
# Rarefaction of functional diversity
rare_Rao(abundances, distances, sim = TRUE, resampling = 100)
rare_Rao(abundances, distances, sim = FALSE)
}
## End(Not run)
```

*adiv*version 2.2.1 Index]