PADDis {adiv} | R Documentation |

## Functional Dissimilarity Measures for Presence-Absence Data

### Description

Functions `PADDis`

, `DJac`

and `Jac`

calculate the dissimilarity coefficients introduced in Ricotta et al. (2016). These dissimilarity coefficients use traditional mismatching components a, b and c of the 2 x 2 contingency table expressed as to include functional or phylogenetic differences among species and noted A, B, C. Components B and C represent the functional or phylogenetic uniqueness of community X compared with community Y and vice versa. Component A represents the functional or phylogenetic similarities between communities X and Y.

### Usage

```
PADDis(comm, dis, method = NULL, diag = FALSE, upper = FALSE)
DJac(comm, dis, diag = FALSE, upper = FALSE)
Jac(comm, diag = FALSE, upper = FALSE)
```

### Arguments

`comm` |
a matrix or a data frame with communities (or plots, assemblages, etc.) as rows and species as columns containing the incidence (0/1) of all species in the communities. |

`dis` |
an object of class |

`method` |
an integer between 0 and 6. If |

`diag` |
a logical value indicating whether the diagonal of the distance matrix should be printed by function |

`upper` |
a logical value indicating whether the upper triangle of the distance matrix should be printed by function |

### Details

In `PADDIS`

, dissimilarities among communities are calculated with the following formulas:

Generalized Jaccard dissimilarity, with method = 1

`\frac{B+C}{a+b+c}`

Generalized Sorensen dissimilarity, with method = 2

`\frac{B+C}{2a+b+c}`

Generalized Sokal and Sneath dissimilarity, with method = 3

`\frac{2(B+C)}{a+2(b+c)}`

Generalized Ochiai dissimilarity, with method = 4

`\frac{\sqrt{A+B}\sqrt{A+C}-A}{\sqrt{a+b}\sqrt{a+c}}`

Generalized Simpson dissimilarity, with method = 5

`\frac{min\{B+C\}}{a+min\{b+c\}}`

Generalized Kulczynski dissimilarity, with method = 6

`0.5*(\frac{B}{a+b}+\frac{C}{a+c})`

`DJac`

and `Jac`

use the additive decomposition of the Jaccard index into turnover and richness difference. `DJac`

takes into account the (functional or phylogenetic) dissimilarities among species while `Jac`

does not.

### Value

In function `PADDis`

, if `method=0`

, then the function `PADDis`

returns 6 matrices corresponding to the a, b, c, A, B, and C values per pair of communities. Otherwise, it returns an object of class `dist`

corresponding to the dissimilarities among communities.

Functions `DJac`

and `Jac`

return a list of three objects of class `dist`

:

`J` |
for the full dissimilarities between communities; |

`JRepl` |
for the turnover component of the dissimilarities; |

`JRich` |
for the component of difference in richness. |

### Author(s)

Sandrine Pavoine sandrine.pavoine@mnhn.fr

### References

Ricotta, C., Podani, J., Pavoine, S. (2016) A family of functional dissimilarity measures for presence and absence data. *Ecology and Evolution*, **6**, 5383–5389

### Examples

```
data(RPP16EE)
Com <- RPP16EE$Com
Dis <- as.dist(RPP16EE$Dis)
J <- Jac(Com)
DJ <- DJac(Com, Dis)
plot(c(as.matrix(DJ$J)[1,]), ylab="Dissimilarity",
xlab="Plot-to-plot comparison", pch=15, type="b",
ylim=c(0,1), main="Jaccard")
lines(c(as.matrix(J$J)[1,]), type="b", pch=18)
legend("bottomright", legend=c("P/A scores", "functional data"),
pch=c(15,18), lty=1)
plot(c(as.matrix(DJ$JRepl)[1,]), ylab="Dissimilarity",
xlab="Plot-to-plot comparison", pch=15, type="b",
ylim=c(0,1), main="Species replacement")
lines(c(as.matrix(J$JRepl)[1,]), type="b", pch=18)
legend("bottomright", legend=c("P/A scores", "functional data"),
pch=c(15,18), lty=1)
#Use the following instruction to obtain all components:
PADDis(Com, Dis, method=0)
```

*adiv*version 2.2.1 Index]