# Estimation of multiple-community similarity measures

### Description

`SimilarityMult`

: Estimation various *N*-community similarity indices. The richness-based indices
include the classic *N*-community Jaccard and Sorensen indices; the abundance-based indices include the Horn, Morisita-Horn, regional species-overlap, and the *N*-community Bray-Curtis indices.
Three types of data are supported: Type (1) abundance data (datatype="abundance"), Type (2)
incidence-frequency data (datatype="incidence_freq"), and Type (2B) incidence-raw data
(datatype="incidence_raw"); see `SpadeR-package`

details for data input formats.

### Usage

1 2 | ```
SimilarityMult(X, datatype = c("abundance", "incidence_freq",
"incidence_raw"), units, q = 2, nboot = 200, goal = "relative")
``` |

### Arguments

`X` |
a matrix/data.frame of species abundances/incidences. |

`datatype` |
type of input data, "abundance", "incidence_freq" or "incidence_raw". |

`units` |
number of sampling units in each community. For |

`q` |
a specified order to use to compute pairwise similarity measures. If |

`nboot` |
an integer specifying the number of bootstrap replications. |

`goal` |
a specified estimating goal to use to compute pairwise similarity measures:comparing species relative abundances ( |

### Value

a list of fourteen objects:

`$datatype`

for showing the specified data types (abundance or incidence).

`$info`

for summarizing data information.

`$Empirical_richness`

for showing the observed values of the richness-based similarity indices
include the classic *N*-community Jaccard and Sorensen indices.

`$Empirical_relative`

for showing the observed values of the equal-weighted similarity indices
for comparing species relative abundances including Horn, Morisita-Horn and regional overlap measures.

`$Empirical_WtRelative`

for showing the observed value of the Horn similarity index for comparing
size-weighted species relative abundances based on Shannon entropy under equal-effort sampling.

`$Empirical_absolute`

for showing the observed values of the similarity indices for comparing
absolute abundances. These measures include the Shannon-entropy-based measure, Morisita-Horn and the regional species-overlap measures based on species absolute abundance, as well as the *N*-community Bray-Curtis index.
All measures are valid only under equal-effort sampling.

The corresponding four objects for showing the estimated similarity indices are:
`$estimated_richness`

, `$estimated_relative`

, `$estimated_WtRelative`

and `$estimated_absolute`

.

`$pairwise`

and `$similarity.matrix`

for showing respectively the pairwise dis-similarity
estimates (with related statistics) and the similarity matrix for various measures depending on the
diversity order `q`

and the `goal`

aspecified in the function arguments.

`$goal`

for showing the goal specified in the argument goal (absolute or relative) used to compute pairwise similarity.

`$q`

for showing which diversity order `q`

specified to compute pairwise similarity.

### References

Chao, A., and Chiu, C. H. (2016). Bridging the variance and diversity decomposition approaches to beta diversity via similarity and differentiation measures. Methods in Ecology and Evolution, 7, 919-928.

Chao, A., Jost, L., Hsieh, T. C., Ma, K. H., Sherwin, W. B. and Rollins, L. A. (2015). Expected Shannon entropy and Shannon differentiation between subpopulations for neutral genes under the finite island model. Plos One, 10:e0125471.

Chiu, C. H., Jost, L. and Chao, A. (2014). Phylogenetic beta diversity, similarity, and differentiation measures based on Hill numbers. Ecological Monographs, 84, 21-44.

Gotelli, N. G. and Chao, A. (2013). Measuring and estimating species richness, species diver- sity,
and biotic similarity from sampling data. Encyclopedia of Biodiversity, 2nd Edition, Vol. 5, 195-211, Waltham, MA.

### Examples

1 2 3 4 5 6 7 8 9 10 11 | ```
## Not run:
data(SimilarityMultData)
# Type (1) abundance data
SimilarityMult(SimilarityMultData$Abu,"abundance",q=2,nboot=200,"relative")
# Type (2) incidence-frequency data
SimilarityMult(SimilarityMultData$Inci,"incidence_freq",q=2,nboot=200,"relative")
# Type (2B) incidence-raw data
SimilarityMult(SimilarityMultData$Inci_raw,"incidence_raw",
units=c(19,17,15),q=2,nboot=200,"relative")
## End(Not run)
``` |