# redundancy: Functional Redundancy of Communities In TPD: Methods for Measuring Functional Diversity Based on Trait Probability Density

## Description

`redundancy` calculates the functional redundancy of communities, considering single or multiple traits. The functional volume (indicated by Functional Richness) occupied by a community with high functional redundancy should not decrease substantially when some species are lost, and vice versa.

## Usage

 `1` ```redundancy(TPDc = NULL) ```

## Arguments

 `TPDc` An object of class "TPDcomm", generated with the `TPDc` function, containing the TPDc of the considered communities.

## Value

`redundancy` returns a list containing the functional redundancy values of all the communities from TDPc, along with the number of species of each community. It also returns a vector with the values of relative redundancy (i.e. redundancy divided by richness minus one).

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```#1. Compute the TPDs of three different species. traits_iris <- iris[, c("Sepal.Length", "Sepal.Width")] sp_iris <- iris\$Species TPDs_iris <- TPDs(species = sp_iris, traits_iris) #2. Compute the TPDc of five different communities: abundances_comm_iris <- matrix(c(c(0.9, 0.05, 0.05), #I. setosa dominates c(0.0, 0.5, 0.5 ), #I. setosa absent c(0.33, 0.33, 0.33), #Equal abundances c(0.1, 0.45, 0.45), #Versicolor and virginica dominate c(0.5, 0, 0.5)), #versicolor absent ncol = 3, byrow = TRUE, dimnames = list(paste0("Comm.",1:5), unique(iris\$Species))) TPDc_iris <- TPDc( TPDs = TPDs_iris, sampUnit = abundances_comm_iris) #3. Estimate functional redundancy FRed_iris <- redundancy(TPDc = TPDc_iris) ```

### Example output

```Loading required package: ggplot2