entropart (version 1.2.0)

HqzBeta: Similarity-based beta entropy of a community

Description

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

Usage

HqzBeta(Ps, Pexp = NULL, q = 1, Z = diag(length(Ps)), CheckArguments = TRUE) 
bcHqzBeta(Ns, Nexp = NULL, q = 1, Z = diag(length(Ns)), Correction = "Best",
          CheckArguments = TRUE)

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.

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

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.

Value

• A number equal to the calculated entropy.

Details

The derivation of similarity-based beta entropy can be found in Marcon and Zhang (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.

References

Jost (2007), Partitioning diversity into independent alpha and beta components. Ecology 88(10): 2427-2439. Marcon, E. and Zhang, Z. (2014). The decomposition of similarity-based diversity and its bias correction. HAL hal-00989454(version 1).

Examples

# 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 <- Paracou618.MC$Ps
  # Probability distribution of the first plot
  Ps1 <- Paracou618.MC$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, 2, Z)