Dqz {entropart} | R Documentation |
Similarity-based diversity of a community
Description
Calculates the diversity of order q
of a probability vector according to a similarity matrix.
Usage
Dqz(NorP, q = 1, Z = diag(length(NorP)), ...)
bcDqz(Ns, q = 1, Z = diag(length(Ns)), Correction = "Best", CheckArguments = TRUE)
## S3 method for class 'ProbaVector'
Dqz(NorP, q = 1, Z = diag(length(NorP)), ...,
CheckArguments = TRUE, Ps = NULL)
## S3 method for class 'AbdVector'
Dqz(NorP, q = 1, Z = diag(length(NorP)), Correction = "Best", ...,
CheckArguments = TRUE, Ns = NULL)
## S3 method for class 'integer'
Dqz(NorP, q = 1, Z = diag(length(NorP)), Correction = "Best", ...,
CheckArguments = TRUE, Ns = NULL)
## S3 method for class 'numeric'
Dqz(NorP, q = 1, Z = diag(length(NorP)), Correction = "Best", ...,
CheckArguments = TRUE, Ps = NULL, Ns = NULL)
Arguments
Ps |
A probability vector, summing to 1. |
Ns |
A numeric vector containing species abundances. |
NorP |
A numeric vector, an integer vector, an abundance vector ( |
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 diversity. |
Correction |
A string containing one of the possible corrections: |
... |
Additional arguments. Unused. |
CheckArguments |
Logical; if |
Details
Diversity is calculated following Leinster and Cobbold (2012): it is the reciprocal of the (generalized) average (of order q
) of the community species ordinariness.
A similarity matrix is used (as for Dqz
), not a distance matrix as in Ricotta and Szeidl (2006). See the example.
Bias correction requires the number of individuals. Use bcHqz
and choose the Correction
.
Correction techniques are from Marcon et al. (2014).
Currently, the "Best"
correction is the max value of "HorvitzThomson"
and "MarconZhang"
.
The functions are designed to be used as simply as possible. Dqz
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 bcDqz
is called. Explicit calls to bcDqz
(with bias correction) or to Dqz.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 diversity. The name is that of the bias correction used.
References
Leinster, T. and Cobbold, C. (2012). Measuring diversity: the importance of species similarity. Ecology 93(3): 477-489.
Marcon, E., Zhang, Z. and Herault, B. (2014). The decomposition of similarity-based diversity and its bias correction. HAL hal-00989454(version 3).
See Also
Examples
# Load Paracou data (number of trees per species in two 1-ha plot of a tropical forest)
data(Paracou618)
# Prepare the similarity matrix
DistanceMatrix <- as.matrix(Paracou618.dist)
# Similarity can be 1 minus normalized distances between species
Z <- 1 - DistanceMatrix/max(DistanceMatrix)
# Calculate diversity of order 2
Dqz(Paracou618.MC$Ns, 2, Z)