dissABC {adiv} | R Documentation |

## Phylogenetic and Functional Similarity between Communities

### Description

Coefficients of similarity between communities that rely on the presence/absence of species are generally based on various combinations of the matching/mismatching components of the classical 2 x 2 contingency table. Three of these components are: a=the number of species shared by the two communities; b=the number of species in the first community that are not in the second; c=the number of species in the second community that are not in the first. These coefficients are extended in `dissABC`

to include phylogenetic or functional information on species (Ricotta and Pavoine 2015).

### Usage

```
dissABC(comm, dis, option = 1:4, method = c("J", "S", "O", "K", "SS","Si"))
```

### Arguments

`comm` |
a data frame or a matrix typically with communities as rows, species as columns and relative abundance or absolute abundance as entries. Column labels (species names) should be assigned as in the object |

`dis` |
a matrix (or data frame) of (phylogenetic or functional) dissimilarities among species rescaled in the range [0, 1] or an object of class |

`option` |
a numeric, either 1, 2, 3, or 4 (if several values are given only the first one is considered). See details. |

`method` |
a character or string, either |

### Details

To obtain the dissimilarities among plots, one needs to choose the equations to be used for the (phylogenetic or functional) components A, B, and C thanks to argument `option`

and the way the components will be combined, thanks to argument `method`

.

Let `\mathbf{D}=(d_{ij})`

a matrix of (functional, morphological or phylogenetic) dissimilarities between pairs of species with `d_{ij} = d_{ji}`

and `d_{ii} = 0`

. If the dissimilarity coefficient *d* is in the range [0, 1], it is possible to define a corresponding similarity coefficient *s* as the complement of *d*: *s* = 1 - *d*. Let `x_{ik}`

the abundance of species *i* in community *k*. *S(kh)* is the number of species in the pooled communities *k* and *h* (i.e. the species for which `min\{x_{ik}, x_{ih}\} > 0`

). The (absolute) abundance of species similar to *i* in plot *k* is

`Z_{ik}=\sum_{j=1}^{S(kh)}x_{jk}s_{ij}`

.

If `option=1`

, equations 6-8 of the main text of Ricotta and Pavoine (2015) are used for calculating components A, B, C:

`A=\sum_{i=1}^{S(kh)}min\{Z_{ik}, Z_{ih}\}`

`B=\sum_{i=1}^{S(kh)}(max\{Z_{ik}, Z_{ih}\}-Z_{ih})`

`C=\sum_{i=1}^{S(kh)}(max\{Z_{ik}, Z_{ih}\}-Z_{ik})`

If `option=2`

, equations A1-A3 from Appendix S1 of Ricotta and Pavoine (2015) are used.

If `option=3`

, equations A5-A7 from Appendix S1 of Ricotta and Pavoine (2015) are used.

If `option=4`

, equations A10-A12 from Appendix S1 of Ricotta and Pavoine (2015) are used.

If `method="J"`

=the Jaccard index is used:

`\frac{A}{A+B+C}`

If `method="S"`

=the Sorensen index is used:

`\frac{2A}{2A+B+C}`

If `method="O"`

=the Ochiai index is used:

`A/(\sqrt{A+B}\sqrt{A+C})`

If `method="K"`

, the Kulczynski index is used:

`\frac{1}{2}\left(\frac{A}{A+B}+\frac{A}{A+C}\right)`

If `method="SS"`

, the Sokal-Sneath index is used:

`\frac{A}{A+2B+2C}`

If `method="Si"`

, the Simpson index is used:

`\frac{A}{A+min(B,C)}`

### Value

Function `dissABC`

returns a matrix with the values of the proposed similarities among communities based on interspecies resemblances.

### Author(s)

Sandrine Pavoine sandrine.pavoine@mnhn.fr

### References

Ricotta, C. and Pavoine, S. (2015) Measuring similarity among plots including similarity among species: an extension of traditional approaches. *Journal of Vegetation Science*, **26**, 1061–1067.

### See Also

### Examples

```
data(RP15JVS)
dissABC(RP15JVS$ab, RP15JVS$D1, method="J", option=1)
J <- as.matrix(dissABC(RP15JVS$ab, RP15JVS$D1, method="J", option=1))[, 1]
SS <- as.matrix(dissABC(RP15JVS$ab, RP15JVS$D1, method="SS", option=1))[, 1]
S <- as.matrix(dissABC(RP15JVS$ab, RP15JVS$D1, method="S", option=1))[, 1]
O <- as.matrix(dissABC(RP15JVS$ab, RP15JVS$D1, method="O", option=1))[, 1]
K <- as.matrix(dissABC(RP15JVS$ab, RP15JVS$D1, method="K", option=1))[, 1]
plot(1:9, J,
xlab="Number of the plots which plot 1 is compared to",
ylab="Similarity", type="b", ylim=c(0,1), pch=18)
lines(1:9, SS, type="b", pch=15)
lines(1:9, S, type="b", pch=17)
lines(1:9, O, type="b", pch=12)
lines(1:9, K, type="b", pch=1)
legend("bottomleft",
c("Jaccard","Sokal-Sneath","Sorensen","Ochiai","Kulczynski"),
pch=c(18,15,17,12,1), lty=1)
```

*adiv*version 2.2.1 Index]