SimilarityMult: Estimation of multiple-community similarity measures
In SpadeR: Species-Richness Prediction and Diversity Estimation with R

Description Usage Arguments Value References Examples

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 `datatype = "incidence_raw"`, users must specify the number of sampling units taken from each community. This argument is not needed for "abundance" and "incidence_freq" data.
`q`	a specified order to use to compute pairwise similarity measures. If `q = 0`, this function computes the estimated pairwise richness-based Jaccard and Sorensen similarity indices. If `q = 1` and `goal=relative`, this function computes the estimated pairwise equal-weighted and size-weighted Horn indices based on Shannon entropy; If `q = 1` and `goal=absolute`, this function computes the estimated pairwise Shannon-entropy-based measure for comparing absolute abundances. If `q = 2` and `goal=relative`, this function computes the estimated pairwise Morisita-Horn and regional species-overlap indices based on species relative abundances. If `q = 2` and `goal=absolute`, this function computes the estimated pairwise Morisita-Horn and regional species-overlap indices based on species absolute abundances.
`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 (`goal=relative`) or comparing species absolute abundances (`goal=absolute`).

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.

## 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)