# HqzBeta: Similarity-based beta entropy of a community In entropart: Entropy Partitioning to Measure Diversity

## Description

Calculates the similarity-based beta entropy of order q of a community belonging to a metacommunity.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```HqzBeta(NorP, NorPexp = NULL, q = 1, Z = diag(length(Ps)), Correction = "Best", CheckArguments = TRUE, Ps = NULL, Ns = NULL, Pexp = NULL, Nexp = NULL) bcHqzBeta(Ns, Nexp = NULL, q = 1, Z = diag(length(Ns)), Correction = "Best", CheckArguments = TRUE) ## S3 method for class 'ProbaVector' HqzBeta(NorP, NorPexp = NULL, q = 1, Z = diag(length(Ps)), Correction = "Best", CheckArguments = TRUE, Ps = NULL, Ns = NULL, Pexp = NULL, Nexp = NULL) ## S3 method for class 'AbdVector' HqzBeta(NorP, NorPexp = NULL, q = 1, Z = diag(length(Ps)), Correction = "Best", CheckArguments = TRUE, Ps = NULL, Ns = NULL, Pexp = NULL, Nexp = NULL) ## S3 method for class 'integer' HqzBeta(NorP, NorPexp = NULL, q = 1, Z = diag(length(Ps)), Correction = "Best", CheckArguments = TRUE, Ps = NULL, Ns = NULL, Pexp = NULL, Nexp = NULL) ## S3 method for class 'numeric' HqzBeta(NorP, NorPexp = NULL, q = 1, Z = diag(length(Ps)), Correction = "Best", CheckArguments = TRUE, Ps = NULL, Ns = NULL, Pexp = NULL, Nexp = NULL) ```

## Arguments

 `Ps` The probability vector of species of the community. `Pexp` The probability vector of species of the metacommunity. `Ns` A numeric vector containing species abundances of the community. `Nexp` A numeric vector containing species abundances of the metacommunity. `NorP` A numeric vector, an integer vector, an abundance vector (`AbdVector`) or a probability vector (`ProbaVector`). Contains either abundances or probabilities of the community. `NorPexp` A numeric vector, an integer vector, an abundance vector (`AbdVector`) or a probability vector (`ProbaVector`). Contains either abundances or probabilities of the metacommunity. `q` A number, the order of diversity. Default is 1. `Z` A relatedness matrix, i.e. a square matrix whose terms are all positive, strictly positive on the diagonal. Generally, the matrix is a similarity matrix, i.e. the diagonal terms equal 1 and other terms are between 0 and 1. Default is the identity matrix to calculate neutral entropy. `Correction` A string containing one of the possible corrections: currently, no correction is available so `"Best"`, the default value, is equivalent to `"None"`. `CheckArguments` Logical; if `TRUE`, the function arguments are verified. Should be set to `FALSE` to save time when the arguments have been checked elsewhere.

## Details

The derivation of similarity-based beta entropy can be found in Marcon et al. (2014).

Bias correction requires the number of individuals.

Note that beta entropy value is related to alpha entropy (if q is not 1) and cannot be compared accross communities (Jost, 2007). Beta entropy of a community is not meaningful in general, do rather calculate the `BetaDiversity` of the metacommunity.

The functions are designed to be used as simply as possible. `HqzBeta` is a generic method. If its first argument is an abundance vector, an integer vector or a numeric vector which does not sum to 1, the bias corrected function `bcHqzBeta` is called. Explicit calls to `bcHqzBeta` (with bias correction) or to `HqzBeta.ProbaVector` (without correction) are possible to avoid ambiguity. The `.integer` and `.numeric` methods accept `Ps` or `Ns` arguments instead of `NorP` for backward compatibility.

## Value

A named number equal to the calculated entropy. The name is that of the bias correction used.

## Author(s)

Eric Marcon <[email protected]>

## References

Jost (2007), Partitioning diversity into independent alpha and beta components. Ecology 88(10): 2427-2439.

Marcon, E., Zhang, Z. and Herault, B. (2014). The decomposition of similarity-based diversity and its bias correction. HAL hal-00989454(version 3).

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ``` # Load Paracou data (number of trees per species in two 1-ha plot of a tropical forest) data(Paracou618) # Ps is the vector of probabilities Ps <- as.ProbaVector(Paracou618.MC\$Ps) # Probability distribution of the first plot Ps1 <- as.ProbaVector(Paracou618.MC\$Psi[, 1]) # Prepare the similarity matrix DistanceMatrix <- as.matrix(Paracou618.dist) # Similarity can be 1 minus normalized distances between species Z <- 1 - DistanceMatrix/max(DistanceMatrix) # Divergence of order 2 between plot 1 and the whole forest HqzBeta(Ps1, Ps, q=2, Z) ```

entropart documentation built on Nov. 23, 2017, 1:03 a.m.