Calculates the diversity of order \(q\) of a probability vector according to a similarity matrix.
Dqz(NorP, q = 1, Z = diag(length(NorP)), ...) bcDqz(Ns, q = 1, Z = diag(length(Ns)), Correction = "Best", CheckArguments = TRUE) # S3 method for ProbaVector Dqz(NorP, q = 1, Z = diag(length(NorP)), ..., CheckArguments = TRUE, Ps = NULL) # S3 method for AbdVector Dqz(NorP, q = 1, Z = diag(length(NorP)), Correction = "Best", ..., CheckArguments = TRUE, Ns = NULL) # S3 method for integer Dqz(NorP, q = 1, Z = diag(length(NorP)), Correction = "Best", ..., CheckArguments = TRUE, Ns = NULL) # S3 method for numeric Dqz(NorP, q = 1, Z = diag(length(NorP)), Correction = "Best", ..., CheckArguments = TRUE, Ps = NULL, Ns = NULL)
A probability vector, summing to 1.
A numeric vector containing species abundances.
A number: the order of diversity. Default is 1.
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.
A string containing one of the possible corrections:
Additional arguments. Unused.
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 techniques are from Marcon et al. (2014).
"Best" correction is the max value of
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
.numeric methods accept
Ns arguments instead of
NorP for backward compatibility.
A named number equal to the calculated diversity. The name is that of the bias correction used.
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).
Eric Marcon <Eric.Marcon@ecofog.gf>
# 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)#> Best #> 1.48295