apqe {ade4}R Documentation

Apportionment of Quadratic Entropy


The hierarchical apportionment of quadratic entropy defined by Rao (1982).


apqe(samples, dis = NULL, structures)
## S3 method for class 'apqe':
print(x, full = FALSE, ...)


samples a data frame with haplotypes (or genotypes) as rows, populations as columns and abundance or presence-absence as entries
dis an object of class dist computed from Euclidean distance. If dis is null, equidistances are used.
structures a data frame that contains, in the jth row and the kth column, the name of the group of level k to which the jth population belongs
x an object of class apqe
full a logical value that indicates whether the original data ('distances', 'samples', 'structures') should be printed
... ... further arguments passed to or from other methods


Returns a list of class apqe
call call
results a data frame that contains the components of diversity.


Sandrine Pavoine pavoine@mnhn.fr


Rao, C.R. (1982) Diversity: its measurement, decomposition, apportionment and analysis. Sankhya: The Indian Journal of Statistics, A44, 1–22.

Pavoine S. and Dol├ędec S. (2005) The apportionment of quadratic entropy: a useful alternative for partitioning diversity in ecological data. Environmental and Ecological Statistics, 12, 125–138.


ecomor.phylog <- taxo2phylog(ecomor$taxo)
apqe(ecomor$habitat, ecomor.phylog$Wdist)

Worked out examples

> library(ade4)
> ### Name: apqe
> ### Title: Apportionment of Quadratic Entropy
> ### Aliases: apqe print.apqe
> ### Keywords: multivariate
> ### ** Examples
> data(ecomor)
> ecomor.phylog <- taxo2phylog(ecomor$taxo)
> apqe(ecomor$habitat, ecomor.phylog$Wdist)
apqe(samples = ecomor$habitat, dis = ecomor.phylog$Wdist)

Between samples 0.04253396
Within samples  0.94719472
Total           0.98972868


[Package ade4 Index]