QE {adiv} | R Documentation |

Function `QE`

calculates Rao's quadratic entropy within communities

Function `discomQE`

calculates Rao's dissimilarities between communities

QE(comm, dis = NULL, formula = c("QE", "EDI"), scale = FALSE) discomQE(comm, dis = NULL, structures = NULL, formula = c("QE", "EDI"))

`comm` |
a data frame or a matrix with communities as rows and species as columns. Entries are abundances of species within communities. If presences/absences (1/0) are used a given species in a community of S species will be considered to have a relative abundance of 1/S. |

`dis` |
either |

`formula` |
either |

`scale` |
a logical value indicating whether or not the diversity coefficient should be scaled by its maximal value over all species abundance distributions. |

`structures` |
either NULL or a data frame that contains, in the |

If `formula = "QE"`

, the definition of the quadratic entropy is:

*QE(p_i,D)=sum_k,l p_k|i p_k|j d_kl*

where *p_i=(p_1|i, ..., p_k|i, ..., p_S|i)* is the vector of relative species abundance within community *i*; *S* is the number of species; *D=(d_kl)* is the matrix of (phylogenetic or functional) dissimilarities among species, and *d_kl* is the (phylogenetic or functional) dissimilarity between species
*k* and *l*. For the calculations of dissimilarities between communities see the description of the apportionment of quadratic entropy in Pavoine et al. (2016) and references therein.

If `formula = "EDI"`

, the definition of the quadratic entropy is:

*EDI(p_i,D)=sum_k,l p_k|i p_k|j (d_kl^2)/2*

EDI stands for the Euclidean Diversity Index of Champely and Chessel (2002) (equation 3 in Pavoine et al. 2004). If EDI is used, the dissimilarities between communities calculated by `discomQE`

are obtained as in equation 4 in Pavoine et al. (2004).

In both cases, if `dis = NULL`

, the quadratic entropy is equal to Gini-Simpson entropy:

*H_GS(p_i)=1 - sum_k (p_k|i)^2*

.

For using function `discomQE`

, the Euclidean properties are expected for object `dis`

. See function `is.euclid`

of package ade4. These properties are not necessary for using function `QE`

. Note that `discomQE`

can be used if `dis = NULL`

. In that case species are considered to be equidifferent (i.e. the dissimilarity between any two species is a constant; such dissimilarities have Euclidean properties).

Function `QE`

returns a data frame with communities as rows and the diversity within communities as columns.

If `structures`

is `NULL`

, function `discomQE`

returns an object of class `dist`

. Otherwise it returns a list of objects of class `dist`

.

Sandrine Pavoine sandrine.pavoine@mnhn.fr

Gini, C. (1912) *Variabilita e mutabilita*. Universite di Cagliari III, Parte II.

Simpson, E.H. (1949) Measurement of diversity. *Nature*, **163**, 688.

Rao, C.R. (1982) Diversity and dissimilarity coefficients: a unified approach. *Theoretical Population Biology*, **21**, 24–43.

Champely, S. and Chessel, D. (2002) Measuring biological diversity using Euclidean metrics. *Environmental and Ecological Statistics*, **9**, 167–177.

Pavoine, S., Dufour, A.B., Chessel, D. (2004) From dissimilarities among species to dissimilarities among communities: a double principal coordinate analysis. *Journal of Theoretical Biology*, **228:**, 523–537.

Pavoine, S., Marcon, E., Ricotta, C. (2016) "Equivalent numbers" for species, phylogenetic, or functional diversity in a nested hierarchy of multiple scales. *Methods in Ecology and Evolution*, **7**, 1152–1163.

## Not run: if(require(ade4)){ # First case study (community level, bird diversity): data(ecomor, package="ade4") # taxonomic dissimilarities between species dtaxo <- dist.taxo(ecomor$taxo) # quadratic entropy QE(t(ecomor$habitat), dtaxo, formula="EDI") QE(t(ecomor$habitat), dtaxo^2/2, formula="QE") table.value(as.matrix(discomQE(t(ecomor$habitat), dtaxo, formula="EDI"))) EDIcom <- discomQE(t(ecomor$habitat), dtaxo, formula="EDI") QEcom <- discomQE(t(ecomor$habitat), dtaxo^2/2, formula="QE") QEcom EDIcom^2/2 # display of the results bird.QE <- QE(t(ecomor$habitat), dtaxo, formula="EDI") dotchart(bird.QE$diversity, labels = rownames(bird.QE), xlab = "Taxonomic diversity", ylab="Habitats") # Second case study (population level, human genetic diversity): data(humDNAm, package="ade4") # quadratic entropy QE(t(humDNAm$samples), humDNAm$distances/2, formula="QE") QE(t(humDNAm$samples), sqrt(humDNAm$distances), formula="EDI") QEhumDNA.dist <- discomQE(t(humDNAm$samples), humDNAm$distances/2, humDNAm$structures) is.euclid(QEhumDNA.dist$communities) is.euclid(QEhumDNA.dist$regions) EDIhumDNA.dist <- discomQE(t(humDNAm$samples), sqrt(humDNAm$distances), humDNAm$structures, formula="EDI") is.euclid(EDIhumDNA.dist$communities) is.euclid(EDIhumDNA.dist$regions) QEhumDNA.dist$communities EDIhumDNA.dist$communities^2/2 # display of the results hum.QE <- QE(t(humDNAm$samples), humDNAm$distances/2, formula="QE") dotchart(hum.QE$diversity, labels = rownames(hum.QE), xlab = "Genetic diversity", ylab="Populations") } ## End(Not run)

[Package *adiv* version 2.1.1 Index]