# Estimation of two-assemblage similarity measures

### Description

`SimilarityPair`

: Estimation various similarity indices for two assemblages. The richness-based
indices include the classic two-community Jaccard and Sorensen indices; the abundance-based
indices include the Horn, Morisita-Horn, regional species-overlap, two-community Bray-Curtis and the
abundance-based Jaccard and Sorensen 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 | ```
SimilarityPair(X, datatype = c("abundance", "incidence_freq",
"incidence_raw"), units, nboot = 200)
``` |

### 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 |

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

### Value

a list of ten 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 two-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, regional overlap,
Chao-Jaccard and Chao-Sorensen abundance (or incidence) measures based on species relative abundances.

`$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 overlap measures based on species absolute abundances, as well as the 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`

.

### References

Chao, A., Chazdon, R. L., Colwell, R. K. and Shen, T.-J. (2005). A new statistical approach for assessing similarity of species composition with incidence and abundance data. Ecology Letters, 8, 148-159.

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.

### Examples

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