`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.

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

`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 ( |

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.

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.

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)
``` |

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