Package 'adiv'

Analysis of Diversity

Description

Package adiv focuses on the analysis of biodiversity

Details

Package adiv is dedicated to biodiversity indices used in ecology and conservation biology (see e.g. functions divparam, optimEH, QE). It also treats the concepts of species' originality (e.g. distinctDis, distinctTree, distinctUltra) and of dissimilarities between species and communities (e.g. dissABC, dissRicotta, dsimcom). Focus is placed on species, functional and phylogenetic diversity and on the apportionment of biodiversity across spatial and temporal scales (see for notably functions EqRao, EqRS, EqRSintra). Ordination methods are also available to depict in detail biodiversity patterns in space and/or time (e.g. crossdpcoa, dspca, evoCA, evoNSCA, evopca).

Author(s)

Sandrine Pavoine

Maintainer: Sandrine Pavoine <[email protected]>

---

Apportionment of Parametric Indices of Diversity

Description

Function abgdivparam calculates alpha, beta and gamma components of species diversity using parametric indices derived from Tsallis (HCDT) and Hill compositional indices. Alpha is for within-community diversity, beta for between-community diversity and gamma for the diversity of all combined communities.

Usage

abgdivparam(comm, w = c("speciesab", "even"),
method = c("hillCJC", "hillR", "tsallis"), q = 2, 
option = c("multiplicative", "additive", "proportional", 
"C", "U", "V", "S", "Renyi"), tol = 1e-08)

## S3 method for class 'abgdivparam'
plot(x, legend = TRUE, 
legendposi = "topright", type = "b", 
col = if (is.numeric(x)) NULL else 1:nrow(x$div), 
lty = if (is.numeric(x)) NULL else rep(1, nrow(x$div)), 
pch = if (is.numeric(x)) NULL else 1:nrow(x$div), 
ylim1 = range(x$div[c("Alpha", "Gamma"), ]), ylim2 = NULL, ...)

Arguments

comm	a data frame or a matrix typically with communities as rows, species as columns and an index of abundance as entries.
w	either a numeric vector giving weights for communities (same order as in comm), or a code: one of "even" and "speciesab". If several codes are given, only the first one is used. See details.
method	a string with one of the following codes: "tsallis", "hillR", or "hillCJC". See details.
q	a vector with nonnegative value(s) for parameter q. See details.
option	a string code: either "multiplicative", "additive" or "proportional". If several codes are given, only the first one is used. Only, with method="hillCJC", other options are possible: "C", "U", "V", "S", "Renyi". See details.
tol	numeric tolerance threshold: values between -tol and tol are considered equal to zero.
x	an object of class abgdivparam obtained with function abgdivparam.
legend	a logical. If TRUE a legend is given with the colour, the type of line (etc.) used to define the diversity curve of each diversity level (gamma, alpha, beta).
legendposi	a string that gives the position of the legend to be passed to function legend of the base of R.
type	a string to be passed to the graphic argument type of functions plot and lines used to draw the diversity curve of each diversity level (gamma, alpha, beta).
col	vector of colours to be passed to the graphic argument col of functions plot and lines to define the colour of the diversity curve of each diversity level (gamma, alpha, beta, in that order).
lty	vector of types of line (plain, broken etc.) to be passed to the graphic argument lty of functions plot and lines used to draw the diversity curve of each diversity level (gamma, alpha, beta, in that order).
pch	vector of types of point (open circle, close circle, square etc.) to be passed to the graphic argument pch of functions plot and lines used to draw the diversity level (gamma, alpha, beta, in that order).
ylim1	a vector with two numerics indicating the range to be used to display alpha and gamma diversity.
ylim2	a vector with two numerics indicating the range to be used to display beta diversity.
...	other arguments can be added and passed to the functions plot and lines used to draw the graphic.

Details

Consider j a community (j=1,...,m), $a_{jk}$ the abundance of species k in community j. q is the parameter that increases with the importance given to abundant species compared to rare species in diversity.

The methods available are: tsallis (decomposition of Tsallis or HCDT entropy (Harvda and Charvat 1967; Daroczy 1970; Tsallis 1988) into alpha, beta, gamma components):

$^q\gamma_{Tsallis}=\left[1-\sum_k \left(\sum_{j=1}^m w_j \frac{a_{jk}}{\sum_k a_{jk}}\right)^q \right]/(q-1)$

$^q\alpha_{Tsallis}=\sum_{j=1}^m w_j \left[1-\sum_k \left( \frac{a_{jk}}{\sum_k a_{jk}}\right)^q\right]/(q-1)$

hillR (Routledge decomposition of Hill diversity into alpha, beta, gamma components):

$^q\gamma_{Hill}=\left[\sum_k \left(\sum_{j=1}^m w_j \frac{a_{jk}}{\sum_k a_{jk}}\right)^q \right]^{1/(1-q)}$

$^q\alpha_{Hill-R}=\left[\sum_{j=1}^m w_j \sum_k \left( \frac{a_{jk}}{\sum_k a_{jk}}\right)^q\right]^{1/(1-q)}$

hillCJC (Chiu et al. (2014) decomposition of species diversity into alpha, beta, gamma components, see Supplementary material Appendix 2 in Pavoine (2016) for a justification of the formulas):

$^q\gamma_{Hill}=\left[\sum_k \left(\sum_{j=1}^m w_j \frac{a_{jk}}{\sum_k a_{jk}}\right)^q \right]^{1/(1-q)}$

$^q\alpha_{Hill-CJC}=\frac{1}{m}\left[\sum_k \sum_{j=1}^m (w_j)^q \left( \frac{a_{jk}}{\sum_k a_{jk}}\right)^q\right]^{1/(1-q)}$

Then option "additive" calculates $\beta$ diversity as $\gamma-\alpha$. Option "proportional" calculates $\beta$ as $(\gamma-\alpha)/\gamma$. Option "multiplicative" calculates $\beta$ diversity as $\gamma/\alpha$. Only for method="hillCJC", options "C", "U", "V", "S", use the multiplicative option and also calculate one of the transformations introduced by Chiu et al. (2014): indices $1-C_{qm}$, $1-U_{qm}$, $1-V_{qm}$, and $1-S_{qm}$, respectively. "Renyi" calculates $\beta$ diversity as $ln(\gamma/\alpha)/ln(m)$.

The weights of the sites (argument w) can be "even" (even weights), or "speciesab" (proportional to the summed abundances of all species).

Value

If only one value of q is given, abgdivparam returns a vector with alpha, beta, and gamma diversities. If more than one value of q is given, it returns a list of two objects:

q	the numeric vector of values for q.
div	a data frame with alpha, beta, gamma calculated for all values of q.

Only if method="hillCJC" and option= "C", "U", "V", "S", or "Renyi", the index $1-C_{qm}$ (for "C"), $1-U_{qm}$ (for "U"), $1-V_{qm}$ (for "V"), $1-S_{qm}$ (for "S") or the Renyi transformation (see above, for "Renyi") is also provided in the div data frame under the name "transformed.beta".

The function plot.abgdivparam returns a graphic.

Author(s)

Sandrine Pavoine [email protected]

References

Chiu, C.-H., Jost, L., Chao, A. (2014) Phylogenetic beta diversity, similarity, and differentiation measures based on Hill numbers. Ecological Monographs, 84, 21–44.

Daroczy, Z. (1970) Generalized information functions. Information and Control, 16, 36–51.

Havrda, M., Charvat F. (1967) Quantification method of classification processes: concept of structural alpha- entropy. Kybernetik, 3, 30–35

Hill, M.O. (1973) Diversity and evenness: a unifying notation and its consequences. Ecology, 54, 427–432.

Pavoine, S. (2016) A guide through a family of phylogenetic dissimilarity measures among sites. Oikos, 125, 1719–1732.

Rao, C.R. (1986) Rao's axiomatization of diversity measures. In: Kotz S, Johnson NL, editors. Encyclopedia of Statistical Sciences. New York: Wiley and Sons. pp. 614–617.

Routledge, R.D. (1979) Diversity indices: which ones are admissible? Journal of Theoretical Biology, 76, 503–515.

See Also

divparam, abgevodivparam

Examples

data(batcomm)
abgdivparam(batcomm$ab)
plot(abgdivparam(batcomm$ab))
abgdivparam(batcomm$ab, q=0:4)
plot(abgdivparam(batcomm$ab, q=0:4))

---

Apportionment of Parametric Indices of Phylogenetic Diversity

Description

Function abgevodivparam calculates alpha, beta and gamma components of phylogenetic diversity using parametric indices derived from Tsallis (HCDT) and Hill compositional indices. Alpha is for within-community diversity, beta for between-community diversity and gamma for the diversity of all combined communities.

Usage

abgevodivparam(phyl, comm, w = c("evoab", "even", "speciesab"),
method = c("hillCJC", "hillR", "tsallis"), q = 2, 
option = c("multiplicative", "additive", "proportional", 
"C", "U", "V", "S", "Renyi"), tol = 1e-08)

## S3 method for class 'abgevodivparam'
plot(x, legend = TRUE, 
legendposi = "topright", type = "b", 
col = if (is.numeric(x)) NULL else 1:nrow(x$div), 
lty = if (is.numeric(x)) NULL else rep(1, nrow(x$div)), 
pch = if (is.numeric(x)) NULL else 1:nrow(x$div), 
ylim1 = range(x$div[c("Alpha", "Gamma"), ]), ylim2 = NULL, ...)

Arguments

phyl	an object inheriting the class phylo (see package ape), phylo4 (see package phylobase), or hclust.
comm	a data frame or a matrix typically with communities as rows, species as columns and an index of abundance as entries. Species should be labeled as in the phylogenetic tree where they are the tips.
w	either a numeric vector giving weights for communities (same order as in comm), or a code: one of "even", "evoab", and "speciesab". If several codes are given, only the first one is used. See details.
method	a string with one of the following codes: "tsallis", "hillR", or "hillCJC". See details.
q	a vector with nonnegative value(s) for parameter q. See details.
option	a string code: either "multiplicative", "additive" or "proportional". If several codes are given, only the first one is used. Only, with method="hillCJC", other options are possible: "C", "U", "V", "S", "Renyi". See details.
tol	numeric tolerance threshold: values between -tol and tol are considered equal to zero.
x	an object of class abgevodivparam obtained with function abgevodivparam.
legend	a logical. If TRUE a legend is given with the colour, the type of line (etc.) used to define the diversity curve of each diversity level (gamma, alpha, beta).
legendposi	a string that gives the position of the legend to be passed to function legend of the base of R.
type	a string to be passed to the graphic argument type of functions plot and lines used to draw the diversity curve of each diversity level (gamma, alpha, beta).
col	vector of colours to be passed to the graphic argument col of functions plot and lines to define the colour of the diversity curve of each diversity level (gamma, alpha, beta, in that order).
lty	vector of types of line (plain, broken etc.) to be passed to the graphic argument lty of functions plot and lines used to draw the diversity curve of each diversity level (gamma, alpha, beta, in that order).
pch	vector of types of point (open circle, close circle, square etc.) to be passed to the graphic argument pch of functions plot and lines used to draw the diversity level (gamma, alpha, beta, in that order).
ylim1	a vector with two numerics indicating the range to be used to display alpha and gamma diversity.
ylim2	a vector with two numerics indicating the range to be used to display beta diversity.
...	other arguments can be added and passed to the functions plot and lines used to draw the graphic.

Details

Consider a phylogenetic tree T, $b_T$ the set of branches in T, k a branch, $L_k$ the length of branch k, j a community (j=1,...,m), $a_{jk}$ the abundance associated with branch k in community j (sum of abundance of all species descending from the branch). q is the parameter that increases with the importance given to abundant species compared to rare species in diversity.

The methods available are: tsallis (decomposition of Tsallis or HCDT entropy (Harvda and Charvat 1967; Daroczy 1970; Tsallis 1988) into alpha, beta, gamma components adapted here to phylogenetic diversity):

$^q\gamma_{evoTsallis}=\left[1-\sum_{k \in b_T} L_k \left(\sum_{j=1}^m w_j \frac{a_{jk}}{\sum_{k \in b_T} L_k a_{jk}}\right)^q \right]/(q-1)$

$^q\alpha_{evoTsallis}=\sum_{j=1}^m w_j \left[1-\sum_{k \in b_T} L_k \left( \frac{a_{jk}}{\sum_{k \in b_T} L_k a_{jk}}\right)^q\right]/(q-1)$

hillR (Routledge decomposition of Hill diversity into alpha, beta, gamma components adapted hete to phylogenetic diversity):

$^q\gamma_{evoHill}=\left[\sum_{k \in b_T} L_k \left(\sum_{j=1}^m w_j \frac{a_{jk}}{\sum_{k \in b_T} L_k a_{jk}}\right)^q \right]^{1/(1-q)}$

$^q\alpha_{evoHill-R}=\left[\sum_{j=1}^m w_j \sum_{k \in b_T} L_k \left( \frac{a_{jk}}{\sum_{k \in b_T} L_k a_{jk}}\right)^q\right]^{1/(1-q)}$

hillCJC (Chiu et al. (2014) decomposition of phylogenetic diversity into alpha, beta, gamma components, see Supplementary material Appendix 2 in Pavoine (2016) for a justification of the formulas):

$^q\gamma_{evoHill}=\left[\sum_{k \in b_T} L_k \left(\sum_{j=1}^m w_j \frac{a_{jk}}{\sum_{k \in b_T} L_k a_{jk}}\right)^q \right]^{1/(1-q)}$

$^q\alpha_{evoHill-CJC}=\frac{1}{m}\left[\sum_{k \in b_T} L_k \sum_{j=1}^m (w_j)^q \left( \frac{a_{jk}}{\sum_{k \in b_T} L_k a_{jk}}\right)^q\right]^{1/(1-q)}$

Then option "additive" calculates $\beta$ diversity as $\gamma-\alpha$. Option "proportional" calculates $\beta$ as $(\gamma-\alpha)/\gamma$. Option "multiplicative" calculates $\beta$ diversity as $\gamma/\alpha$. Only for method="hillCJC", options "C", "U", "V", "S", use the multiplicative option and also calculate one of the transformations introduced by Chiu et al. (2014): indices $1-C_{qm}$, $1-U_{qm}$, $1-V_{qm}$, and $1-S_{qm}$, respectively. "Renyi" is the $^qevoD_{Renyi}$ index introduced in Pavoine (2016), see also Supplementary material Appendix 1 in Pavoine (2016).

The weights of the sites (argument w) can be "even" (even weights), "evoab" (proportional to the summed abundances of all evolutionary units), or "speciesab" (proportional to the summed abundances of all species). Note that if the phylogenetic tree is ultrametric (the distance from any species to the root is constant), then options "evoab" and "speciesab" are equivalent.

Value

If only one value of q is given, abgevodivparam returns a vector with alpha, beta, and gamma diversities. If more than one value of q is given, it returns a list of two objects:

q	the numeric vector of values for q.
div	a data frame with alpha, beta, gamma calculated for all values of q.

Only if method="hillCJC" and option= "C", "U", "V", "S", or "Renyi", the index $1-C_{qm}$ (for "C"), $1-U_{qm}$ (for "U"), $1-V_{qm}$ (for "V"), $1-S_{qm}$ (for "S") or the Renyi transformation (see above, for "Renyi" is also provided in the div data frame under the name "transformed.beta".

The function plot.abgevodivparam returns a graphic.

Author(s)

Sandrine Pavoine [email protected]

References

The methodologies and scripts were presented in

Pavoine, S. (2016) A guide through a family of phylogenetic dissimilarity measures among sites. Oikos, 125, 1719–1732.

using earlier work by

Daroczy, Z. (1970) Generalized information functions. Information and Control, 16, 36–51.

Havrda, M., Charvat F. (1967) Quantification method of classification processes: concept of structural alpha- entropy. Kybernetik, 3, 30–35

Hill, M.O. (1973) Diversity and evenness: a unifying notation and its consequences. Ecology, 54, 427–432.

Routledge, R.D. (1979) Diversity indices: which ones are admissible? Journal of Theoretical Biology, 76, 503–515.

Rao, C.R. (1986) Rao's axiomatization of diversity measures. In: Kotz S, Johnson NL, editors. Encyclopedia of Statistical Sciences. New York: Wiley and Sons. pp. 614–617.

Chiu, C.-H., Jost, L., Chao, A. (2014) Phylogenetic beta diversity, similarity, and differentiation measures based on Hill numbers. Ecological Monographs, 84, 21–44.

See Also

evodiss, divparam, evodivparam

Examples

## Not run: 
if(require(ape)){
data(batcomm)
phy <- read.tree(text=batcomm$tre)
ab <- batcomm$ab[,phy$tip.label]
abgevodivparam(phy, ab)
plot(abgevodivparam(phy, ab))
abgevodivparam(phy, ab, q=0:4)
plot(abgevodivparam(phy, ab, q=0:4))
}

## End(Not run)

---

Hierarchical Partitioning of Evolutionary and Ecological Patterns in the Organization of Phylogenetically-Structured Species Assemblages

Description

apd performs Hardy (2008)'s test for phylogenetic structure in species abundance distribution;

aptree apportions the diversity (according to index $I_a$ by Pavoine et al. 2009) within one or several communities between evolutionary periods;

plot.aptree displays the phylogenetic tree with vertical lines at each speciation event (limits of the evolutionary periods), the first period starts at the tips and the last one ends at the root node; the phylogenetic tree is pruned retaining only the species present in at least one of the observed communities;

abgaptree provides the apportionment of alpha, beta and gamma diversities between evolutionary periods, according to index $I_a$ by Pavoine et al. (2009);

rtestaptree performs the test of phylogenetic signal in the differences between communities at each evolutionary periods;

plot.rtestaptree displays the phylogenetic tree with vertical lines at each speciation event (limits of the evolutionary periods; see above); colours are used to highlight the periods where the dissimilarities between communities are different from that expected at random;

tecAptree provides technical information for the apportionment of diversity between evolutionary periods;

pIa calculates the index $I_a$ by Pavoine et al. (2009) within each community.

Usage

apd(phyl, comm, wcom = c("even", "speciesab"), nrep = 99, 
alter = "two-sided", tol = 1e-08)

aptree(phyl, comm, exponent = 2, tol = 1e-08)

## S3 method for class 'aptree'
plot(x, col.line = 'blue', ...)

abgaptree(phyl, comm, exponent = 2, 
wcom = c("even", "speciesab"), tol = 1e-08)

rtestaptree(phyl, comm, nrep = 99, alter = "two-sided", 
exponent = 2, wcom = c("even", "speciesab"), tol = 1e-08)

## S3 method for class 'rtestaptree'
plot(x, col.line = c("blue", "red"), 
alpha = 0.05, ...)

tecAptree(phyl, v = NULL, tol = 1e-08)

pIa(phyl, comm, exponent = 2, tol = 1e-08)

Arguments

phyl	an object inheriting the class phylo (see package ape), phylo4 (see package phylobase), or hclust.
comm	a data frame or a matrix typically with communities as rows, species as columns and presence/absence or an index of abundance as entries. Species should be labeled as in the phylogenetic tree where they are the tips. In function aptree, comm can be a vector that provides the presence/absence or an index of abundance within a single community.
wcom	a numeric vector that gives the weight attributed to the community. The weights must be positive and their sum equals 1.
nrep	a numeric that gives the number of permutations.
alter	a string specifying the alternative hypothesis; it must be one of "greater", "less" or "two-sided".
tol	a numeric. If the absolute value of a statistic is less than tol, this statistic is considered equal to zero.
exponent	a numeric that gives the value of parameter a in index $I_a$.
x	in plot.aptree, x is an object inheriting class aptree obtained with function aptree. In plot.rtestaptree, x is an object inheriting class rtestaptree obtained with function rtestaptree.
col.line	in plot.aptree, col.line is a string which attributes a colour to the vertical lines placed at each speciation event and defining the evolutionary periods. In plot.rtestaptree, it is a vector with two strings. These strings give colours to the vertical lines placed at each speciation event. The first colour is used when the differences between communities at the evolutionary period are not significantly different from random; the second colour is used when they are.
alpha	a numeric: the nominal alpha level for significancy (the p-values calculated with function rtestaptree are compared to alpha to determine the result of the test).
...	further arguments passed to or from other methods.
v	either NULL or a vector that provides the presence/absence or an index of abundance of species within a single community.

Details

The approaches developed in these functions rely on a parametric index of phylogenetic diversity named $I_a$. The parameter a controls the importance given to rare versus abundant species in communities. Index $I_a$ generalizes Rao's quadratic entropy (QE) applied to phylogenetic distances between species (when a=2) and Faith's Phylogenetic Diversity index (PD) (when a=0). When a tends towards 1, the index is a generalization of the Shannon index of diversity applied to phylogenetic data in addition to abundance data. In Pavoine et al. (2009), we developed this index and demonstrated how it can be used to partition diversity simultaneously across evolutionary periods in the phylogeny and across spatial (e.g. local communities in a region) and/or time units (e.g. a community investigated yearly).

Value

The function apd returns an object of class randtest with the results of the test (see function randtest in package ade4).

The function aptree returns a data frame with the evolutionary periods as rows, the communities as columns and the diversity values as entries.

The function plot.aptree returns a graph.

The function abgaptree returns a data frame with the evolutionary periods as rows, alpha diversity, beta diversity and gamma diversity as columns and the diversity values as entries.

The function rtestaptree returns an object of class krandtest with the results of the permutation tests. (see function krandtest in package ade4)

The function plot.rtestaptree returns a graph.

The function tecAptree returns a list. If v is NULL, the values of the list are:

h	the height at which each evolutionary period ends;
plength	period length;
ngroups	number of monophyletic groups per evolutionary period;
list	list of the species per monophyletic group at each evolutionary period;
call	original call.

If v contains a vector of presence/absence or abundance, the following object is added in the output:

relab

the relative abundance (sum of species' presences or abundances depending on v) of each monophyletic group at each evolutionary period.

The function pIa returns a data frame with communities as rows and only one column. This column gives, for each community, the value taken by index $I_a$ of phylogenetic diversity developed by Pavoine et al. (2009).

Author(s)

Sandrine Pavoine [email protected] with contributions of Stephane Dray.

References

Pavoine, S., Love, M., Bonsall, M.B. (2009) Hierarchical partitioning of evolutionary and ecological patterns in the organization of phylogenetically-structured species assemblages: application to rockfish (genus: Sebastes) in the Southern California Bight. Ecology Letters, 12, 898–908.

See Also

QE

Examples

## Not run: 
if(require(ape)){
data(rockfish)
phy <- read.tree(text=rockfish$tre)
ABG <- abgaptree(phy, rockfish$fau, wcom="speciesab")
colSums(ABG)
A <- aptree(phy, rockfish$fau)
colSums(A)
plot(A, cex=0.5)
P <- pIa(phy, rockfish$fau)
P
T <- apd(phy, rockfish$fau)
plot(T)
#R <- rtestaptree(phy, rockfish$fau, nrep=999, wcom="speciesab")
#plot(R)
TA <- tecAptree(phy)
TA$h
}

## End(Not run)

---

Bat Abundance and Phylogeny Along a Disturbance Gradient in a Neotropical Rainforest

Description

The data were collected by Medellin et al. (2000) on bats in four habitats in the Selva Lacandona of Chiapas, Mexico. Two phylogenetic trees were obtained, one with Fritz et al. (2009) phylogeny pruned for retaining only the species present in Medellin et al. data set; the other one using a consensus tree obtained from 9999 credible trees developed by Upham et al. (2019) and obtained from vertlife.org (see Pavoine and Ricotta (2021) for more details).

Usage

data("batcomm")

Format

batcomm is a list of two components:

ab, a data frame with habitats as rows, species as columns and abundance of species in habitats as entries.

tre, a phylogenetic tree in newick format for all bat species in ab.

ab2, a data frame with habitats as rows, species as columns and abundance of species in habitats as entries.

tre2, a phylogenetic tree in newick format for all bat species in ab.

Details

In ab and ab2, four habitat types were analyzed: F=rainforest; P=cacao plantations; O=old fields; C=cornfields (Pavoine 2016).

ab and tre contain species names as in Medellin et al. (2000). ab2 and tre2 contain species names as in Upham et al. (2019).

Synonyms used are: Pteronotus_parnelii / Pteronotus_parnellii; Phyllostomus_stenops / Phylloderma_stenops; Tonatia_brasiliense / Lophostoma_brasiliense; Tonatia_evotis / Lophostoma_evotis; Micronycteris_brachyotis / Lampronycteris_brachyotis; Vampyrodes_major / Vampyrodes_caraccioli.

tre was obtained using Fritz et al. (2009) and tre2 using Upham et al. (2019). The resolution of the bat phylogeny obtained from Fritz is uncertain especially at the older nodes (Pavoine 2016).

Source

http://www.oikosjournal.org/appendix/oik-03262

References

Fritz, S.A., Bininda-Emonds, O.R.P., Purvis, A. (2009) Geographic variation in predictors of mammalian extinction risk: big is bad, but only in the tropics. Ecology Letters, 12, 538–549.

Medellin, R., Equihua M., Amin, M.A. (2000) Bat diversity and abundance as indicators of disturbance in Neotropical rainforest. Conservation Biology, 14, 1666–1675.

Pavoine, S. (2016) A guide through a family of phylogenetic dissimilarity measures among sites. Oikos, 125, 1719–1732.

Pavoine, S., Ricotta, C. (2021) On the relationships between rarity, uniqueness, distinctiveness, originality and functional/phylogenetic diversity. Contact authors for information on this study

Upham, N.S., Esselstyn, J.A., Jetz, W. (2019) Inferring the mammal tree: Species-level sets of phylogenies for questions in ecology, evolution, and conservation. PloS Biology, 17, e3000494.

Examples

## Not run: 
if(require(ape)){
data(batcomm)
phy <- read.tree(text=batcomm$tre)
plot(phy)
ab <- batcomm$ab[,phy$tip.label]
plot(abgevodivparam(phy, ab, q=0:4))

phy2 <- read.tree(text=batcomm$tre2)
plot(phy2)
ab2 <- batcomm$ab2[,phy2$tip.label]
plot(abgevodivparam(phy2, ab2, q=0:4))
}

## End(Not run)

---

Multiple-Site Dissimilarity Measure for Species Presence/Absence Data

Description

Functions betastatjac and betastatsor calculate multiple-site dissimilarity (beta diversity). The first one is derived from Jaccard coefficient of similarity and the second from Sorensen coefficient. These proposed dissimilarity indices are additively partitioned into species nestedness and turnover.

Usage

betastatjac(comm)

betastatsor(comm)

Arguments

comm	a data frame typically with communities as rows, species as columns and presence/absence (1/0) as entries.

Value

The two functions return a vector of 4 values:

beta	Ricotta and Pavoine (2015) $\beta^+$ relative measure of additive beta diversity (multiple-site dissimilarity);
betaT	Ricotta and Pavoine (2015) $\beta_T$ contribution of species turnover to multiple-site dissimilarity;
betaN	Ricotta and Pavoine (2015) $\beta_N$ contribution of species nestedness to multiple-site dissimilarity;
sim	Ricotta and Pavoine (2015) $\bar{\beta}^{\times}$ relative measure of multiple-site similarity.

Author(s)

Sandrine Pavoine [email protected]

References

Ricotta, C. and Pavoine, S. (2015) A multiple-site dissimilarity measure for species presence/absence data and its relationship with nestedness and turnover. Ecological Indicators, 54, 203–206.

Examples

data(RP15EI)
# Scripts used in Figure 1 of Ricotta and Pavoine (2015)
betastatjac(RP15EI$M1)
betastatjac(RP15EI$M2)
betastatjac(RP15EI$M3)
betastatjac(RP15EI$M4)

#see also
betastatsor(RP15EI$M1)
betastatsor(RP15EI$M2)
betastatsor(RP15EI$M3)
betastatsor(RP15EI$M4)

---

Plot-to-plot functional or phylogenetic dissimilarity and uniqueness

Description

The function betaTreeUniqueness calculates Ricotta et al. (2020) plot-to-plot functional or phylogenetic beta uniqueness (index named $U_F$ for functional data and $U_P$ for phylogenetic data in Ricotta et al. 2020).

Usage

betaTreeUniqueness(mtree, comm, height = NULL, tol = 0.001)

Arguments

mtree	an object inheriting the class phylo (see package ape), phylo4 (see package phylobase), or hclust. The tree must be ultrametric: equal distance from any tip to the root.
comm	a matrix containing the relative or absolute abundance of all species in plots. Columns are species and plots are rows. Column labels (species names) should be assigned as in mtree.
height	either NULL or a numeric. See details.
tol	a tolerance threshold. A value between -tol and tol is considered as zero. See details.

Details

Object mtree defines a tree with species as tips. If argument height is NULL, then the root of the tree will be placed at the most recent common ancestor of all species occurring in the set of plots (given in object comm). An alternative position for the root can be given by specifying the height of the tree (argument height). In that case, height must be higher than the distance between tips and the most recent common ancestor of all species.

The tolerance threshold tol is particularly important if your tree is not exactly ultrametric due to approximation problems. In that case, the distance from tip to root varies according to the tip considered, although it should not (variations are due to approximation problems). A difference smaller than tol in the distance to root for two species will thus be considered as null.

Value

The function returns a matrix with the values of the functional or phylogenetic beta uniqueness for each pair of plots.

Author(s)

Sandrine Pavoine [email protected]

References

Ricotta, C., Laroche, F., Szeidl, L., Pavoine, S. (2020) From alpha to beta functional and phylogenetic redundancy. Methods in Ecology and Evolution, 11, 487–493.

See Also

DP for plot-to-plot dissimilarities, treeUniqueness for alpha uniqueness

Examples

## Not run: 
if(require(ape)){
data(RutorGlacier)
phy <- read.tree(text=RutorGlacier$TreeNW)
plot(phy)

ab <- RutorGlacier$Abund[, phy$tip.label]

# Phylogenetic beta Uniqueness between plots
# (Ricotta et al. 2020)
Up <- betaTreeUniqueness(phy, ab, tol=0.00001)
}

## End(Not run)

---

Algorithmic index of plot-to-plot functional (or phylogenetic) dissimilarity and uniqueness

Description

The function betaUniqueness calculates uniqueness and redundancy taking account of functional dissimilarities between species using equation 5 and 6 in Ricotta et al. (2021). Note that functional dissimilarities could be replaced by any other type of dissimilarities between species, including phylogenetic dissimilarities.

Usage

betaUniqueness(comm, dis, Nind = 10000)

Arguments

comm	a matrix containing the relative or absolute abundance of all species in plots. Columns are species and plots are rows. Column labels (species names) should be assigned as in dis.
dis	a matrix or an object of class dist providing the functional dissimilarities between species (dissimilarities are nonnegative, symmetric, and the dissimilarity between a species and itself is zero). Species here must be in the same order as in the columns of comm.
Nind	an integer. The algorithmic index will be applied by assuming that each plot contains Nind individuals. The highest Nind, the most precise the index value will be (see Gregorius et al. 2003, for more details).

Value

The function betaUniqueness returns a list with the following objects:

- betaUniqueness: a matrix with the values of the proposed beta uniqueness ($U\beta$=DKG/DR) for each pair of plots (Ricotta et al. (2021), eq. 6);

- betaRedundancy: a matrix with the values of the proposed beta redundancy ($R\beta$=1-DKG/DR) for each pair of plots (Ricotta et al. (2021), eq. 5);

- dissimilarityGap: a matrix with the values of the dissimilarity gap index (DR-DKG) for each pair of plots;

- DR: a matrix with the values of the species-based (Rogers) dissimilarity index (DR) for each pair of plots (Ricotta et al. (2021), eq. 4);

- DKG: a matrix with the values of the algorithmic functional dissimilarity index (DKG) for each pair of plots (Ricotta et al. (2021), eq. 3).

Author(s)

Sandrine Pavoine [email protected]

References

Ricotta, C., Kosman, E., Laroche, F., Pavoine, S. (2021) Beta redundancy for functional ecology. Methods in Ecology and Evolution, 12, 1062–1069. doi:10.1111/2041-210X.13587

Gregorius, H.-R., Gillet, E.M., Ziehe, M. (2003) Measuring differences of trait distributions between populations. Biometrical Journal, 8, 959–973. doi:10.1002/bimj.200390063

See Also

betaTreeUniqueness adapted to the use of phylogenetic trees with species as tips, dislptransport for the algorithmic functional dissimilarity index (DKG in Ricotta et al. 2021), and uniqueness for alpha uniqueness

Examples

## Not run: 
data(RutorGlacier)
fundis <- dist(scale(RutorGlacier$Traits2[1:6]))
fundis <- fundis/max(fundis)
frameDKG <- betaUniqueness(RutorGlacier$Abund, fundis)

f1 <- unlist(sapply(1:58, function(i) rep(RutorGlacier$Fac[i], 59-i)))
f2 <- unlist(sapply(1:58, function(i) RutorGlacier$Fac[-(1:i)]))
f <- paste(f1, f2, sep="-")
F <- factor(f, levels=c("early-early", "mid-mid", "late-late", "early-mid", 
    "mid-late", "early-late"))

vbetaU_A <- as.vector(as.dist(frameDKG$betaUniqueness))

boxplot(vbetaU_A~F, ylab="Beta uniqueness", xlab="Compared successional stages")
# See Ricotta et al. 2021 Electronic Appendix 3 for for details

## End(Not run)

---

Avian Communities along Successional Forest Gradients

Description

The density of bird species in 3 locations in the Mediterranean region and 2 locations in the central Europe region were collected by Blondel and Farre (1988) along a gradient of habitats. The densities and a phylogenetic tree are provided for all observed species.

Usage

data("birdData")

Format

birdData is a list of 4 objects:

fau, a data frame with communities as rows, species as columns and densities as entries. The names of the communities start with the first three letters of the location and end with the seral stage number. See details.

tre, a string. It contains the phylogeny in a newick format.

facA, a factor. It indicates which location each community belongs to.

facB, a factor. It indicates which seral stage each community belongs to.

Details

The locations are Alg = Algeria, Bur = Burgundy, Cor = Corsica Island, Pol = Poland, Pro = Provence.

Three are in the Mediterranean region (Provence, southern France; Corsica Island, southern France; and north east Algeria) and two in the central European region (Burgundy, central France; and Poland).

In each location, a habitat gradient has been conventionally divided into six seral stages (intermediate stages found in forest ecosystems advancing towards their climax stage after a disturbance event) in such a way that all five selected habitat gradients match one another reasonably well in terms of the number, patterns and overall structure of habitats: from low bushy vegetation, less than 1 m height (stage 1), to forests with trees at least 20 m high (stage 6).

The composite phylogenetic tree was obtained based on Davis' supertree: a strict consensus of 2000 trees (see details in Text S5 of Pavoine et al. 2013).

Source

Dataset S1 in Pavoine et al. (2013)

References

Blondel, J. and Farre, H. (1988) The convergent trajectories of bird communities along ecological successions in European forests. OEcologia (Berlin), 75, 83–93.

Davis, K.E. (2008) Reweaving the tapestry: a supertree of birds [PhD thesis]. Glasgow, U.K.: University of Glasgow.

Pavoine, S., Blondel, J., Dufour, A.-B., Gasc, A., Bonsall, M.B. (2013) A new technique for analysing interacting factors affecting biodiversity patterns: crossed-DPCoA. PloS One, 8, e54530.

Examples

## Not run: 
if(require(ape) && require(adephylo)){
data(birdData)
phy <- read.tree(text=birdData$tre)
phydis <- sqrt(distTips(phy, method="nNodes")+1)

fau <- birdData$fau[, phy$tip.label]
facA <- birdData$facA
facB <- birdData$facB

cd_mainB <- crossdpcoa_maineffect(fau, facB, facA, phydis, w=rep(1/30, 30), scannf = FALSE)
s.label(cd_mainB$l2)
}

## End(Not run)

---

Matrices of Intra- and Inter-Specific Similarities

Description

The function CFprop calculates the matrix CF of intra- (diagonal) and inter-specific (off-diagonal) similarities as defined in the main text of Pavoine and Izsak (2014), and matrix CwF as defined in Appendix S3 of Pavoine and Izsak (2014) for weighting functional attributes. The function multiCFprop calculates matrices CwmF1, CwmF2, CwmF3 when several functional traits are considered (Appendix S3 of Pavoine and Izsak 2014). Traits and the attributes of the traits can be weighted. These two functions consider functional traits expressed as proportion (compositional) vectors. The functions CFbinary and multiCFbinary are the equivalents of CFprop and multiCFprop when traits are expressed as binary vectors as shown in Appendix S3 of Pavoine and Izsak (2014).

Usage

CFbinary(df, wA = rep(1, ncol(df)))

multiCFbinary(Ktab, w.attributes = lapply(Ktab, function(x) rep(1, ncol(x))), 
w.traits = rep(1/length(Ktab), length(Ktab)), 
labels = rownames(Ktab[[1]]), solution = c(2, 1))

CFprop(df, wA = rep(1, ncol(df)))

multiCFprop(Ktab, w.attributes = lapply(Ktab, function(x) rep(1, ncol(x))), 
w.traits = rep(1/length(Ktab), length(Ktab)), 
labels = rownames(Ktab[[1]]), solution = c(2, 1))

Arguments

df	a data frame or a matrix with species (or any entities of interest) as rows, functional attributes as columns, and proportions (for CFprop) or 0/1 values (for CFbinary) as entries. The sum of the columns will be standardized to equal 1 in function CFprop but not in CFbinary.
wA	a vector of weights that should be given to the attributes (same order as the columns of df).
Ktab	a list of data frames, each of which represents a trait. For a given trait, the data frame should have species (or any entities of interest) as rows, functional attributes as columns, and proportions (for multiCFprop) or 0/1 values (for multiCFbinary) as entries. The sum of the columns will be standardized to equal 1 in function multiCFprop but not in multiCFbinary.
w.attributes	a list of weights that should be given to the attributes of each trait. Traits should be in the same order as they appear in the list of tables Ktab. The attributes of a trait should be ordered as the columns of the corresponding data frame in Ktab.
w.traits	a numeric vector of weights that should be given to the traits (same order as the tables of Ktab).
labels	a vector of strings that gives the names of the species (or the other entities of interest; same order as the rows of all tables in Ktab).
solution	a numeric value (either 1 or 2) that indicates which equations are used to summarize the information given by several traits among the 2 approaches given in Appendix S3 of Pavoine and Izsak (2014) page 9. If a vector is given, only the first value of the vector is considered.

Value

A matrix with nonnegative values

Author(s)

Sandrine Pavoine [email protected]

References

Pavoine, S. and Izsak, J. (2014) New biodiversity measure that includes consistent interspecific and intraspecific components. Methods in Ecology and Evolution, 5, 165–172.

See Also

qHdiv

---

Crossed-DPCoA

Description

Crossed-DPCoA typically analyzes the phylogenetic or functional compositions of communities according to two factors affecting the communities (e.g. space and time; habitat and region)

The function crossdpcoa_maineffect obtains the space of DPCoA (the double principal coordinate analysis) where species are placed according to their functional traits or phylogeny and communities are placed at the center of their species. Next, levels of each factor are placed at the center of their communities. The function crossdpcoa_maineffect determines the principal axes of the positions of the levels of one of the factors in this space and projects species' points on these principal axes. The main effect of the factor named facA is analysed by this process (Pavoine et al. 2013).

The function crossdpcoa_version1 performs version 1 of the crossed DPCoA in Pavoine et al. (2013) where the effect of factor facA on the diversity of communities, given factor facB, is analysed.

The function crossdpcoa_version2 performs version 2 of the crossed DPCoA in Pavoine et al. (2013) where the effect of factor facA on the diversity of communities, given factor facB, is also analysed.

Usage

crossdpcoa_maineffect(df, facA, facB, dis = NULL, 
scannf = TRUE, nf = 2, w = c("classic", "independence"), 
tol = 1e-07)

crossdpcoa_version1(df, facA, facB, dis = NULL, 
scannf = TRUE, nf = 2, w = c("classic", "independence"), 
tol = 1e-07)

crossdpcoa_version2(df, facA, facB, dis = NULL, 
scannf = TRUE, nf = 2, w = c("classic", "independence"), 
tol = 1e-07)

Arguments

df	a data frame or a matrix of 0/1 or nonnegative values. As an exemple, I consider below a communities x species data frame or matrix with abundances as entries.
facA	a factor with the same length as the number of rows (communities) in df.
facB	another factor with the same length as the number of rows (communities) in df.
dis	an object of class dist that contains the distances among species (e.g. functional or phylogenetic distances). If NULL equidistances are used among species. The distances must have Euclidean properties. Distances are integrated in the Euclidean Diversity Index (Champely and Chessel 2002), which corresponds to a particular formulation of Rao (1982) quadratic entropy. For example the diversity within a community i is $EDI=\sum_{k=1}^S\sum_{l=1}^S p_{k|i}p_{k|j}\frac{d_{kl}^2}{2}$, where S is the number of species, $p_{k|i}$ is the relative abundance of species k within community i; $d_{kl}$ is the (phylogenetic or functional) dissimilarity between species k and l.
scannf	a logical value indicating whether the screeplot (with eigenvalues) should be displayed.
nf	if scannf is FALSE, an integer indicating the number of kept axes.
w	either a string or a numeric vector of positive values that indicates how the rows of df (the communities) should be weighted. If w="classic", the weights are defined from the sum of the values in each row (e.g. sum of all species abundances within a community). If w="independence", then the weight attributed to a row of df (a community) is the product of the weight attributed to a level of factor A with the weight attributed to a level of factor B. If a vector of strings is given, only the first one is retained. If numeric, values in w must be in the same order as the rows of df (see Pavoine et al. 2013 for details on the definition of these weights).
tol	a numeric tolerance threshold: a value between -tol and tol is considered as null.

Value

The functions crossdpcoa_maineffect, crossdpcoa_version1 and crossdpcoa_version2 return a list containing the following information used for computing the crossed-DPCoA:

l1	coordinates of the columns of df (the species).
l2	coordinates of the levels of factor A.
l3	(for functions crossdpcoa_version1 and crossdpcoa_version2 only) coordinates of the rows of df (the communities).
eig	the eigenvalues.
lX	the weights attributed to the columns of df (species).
lA	the weights attributed to the levels of factor A.
lB	the weights attributed to the levels of factor B.
lC	the weights attributed to the rows of df (communities).
div	a numeric vector with the apportionment of Rao's quadratic diversity (APQE).
call	the call function.

Author(s)

Sandrine Pavoine [email protected]

References

Pavoine, S., Blondel, J., Dufour, A.-B., Gasc, A., Bonsall, M.B. (2013) A new technique for analysing interacting factors affecting biodiversity patterns: crossed-DPCoA. PloS One, 8, e54530.

Examples

## Not run: 
if(require(ape) && require(phylobase) && require(adephylo) 
   && require(adegraphics)){
O <- adegpar()$plabels$optim
adegpar("plabels.optim" = TRUE)

data(birdData)
phy <- read.tree(text=birdData$tre)
phydis <- sqrt(distTips(phy, method="nNodes")+1)

fau <- birdData$fau[, phy$tip.label]
facA <- birdData$facA
facB <- birdData$facB

#Here factor B is put first to analyze 
#the main effect of the strata:
cd_mainB <- crossdpcoa_maineffect(fau, facB, facA, phydis, w=rep(1/30, 30), scannf = FALSE)
barplot(cd_mainB$eig)
cd_mainB$eig[1:2]/sum(cd_mainB$eig)

#Positions of the levels of factor B on its principal axes:
s.label(cd_mainB$l2)
# The "d" value on graphs indicates the length of the edge of a grid cell (scale of the graphic). 

#The coordinates of the species on the same axes 
# can be displayed in front of the phylogeny 
# (several possibilities are provided below, 
# the last one use package adephylo)):
mainBl1.4d <- phylo4d(phy, as.matrix(cd_mainB$l1))
dotp4d(mainBl1.4d, center = FALSE, scale = FALSE)
barp4d(mainBl1.4d, center = FALSE, scale = FALSE)
gridp4d(mainBl1.4d, center = FALSE, scale = FALSE)
parmar <- par()$mar
par(mar=rep(.1,4))
table.phylo4d(mainBl1.4d, show.node=FALSE, symbol="squares",
    center=FALSE, scale=FALSE, cex.label=0.5, ratio.tree=0.7)
par(mar=parmar)

#If factor A is put first, the analysis focus 
#on the main effect of the region:
cd_mainA <- crossdpcoa_maineffect(fau, facA, facB, phydis, w=rep(1/30, 30), scannf = FALSE)
barplot(cd_mainA$eig)
cd_mainA$eig[1:2]/sum(cd_mainA$eig)

#Positions of the levels of factor A on its principal axes:
s.label(cd_mainA$l2)
# The "d" value on graphs indicates the length of the edge of a grid cell (scale of the graphic). 

#The coordinates of the species on the same axes 
# can be displayed in front of the phylogeny
# (several possibilities are provided below, 
# the last one use package adephylo)):
mainAl1.4d <- phylo4d(phy, as.matrix(cd_mainA$l1))
dotp4d(mainAl1.4d, center = FALSE, scale = FALSE)
barp4d(mainAl1.4d, center = FALSE, scale = FALSE)
gridp4d(mainAl1.4d, center = FALSE, scale = FALSE)
parmar <- par()$mar
par(mar=rep(.1,4))
table.phylo4d(mainAl1.4d, show.node=FALSE, symbol="squares", 
   center=FALSE, scale=FALSE, cex.label=0.5, ratio.tree=0.7)
par(mar=parmar)

#Crossed DPCoA Version 1
cd_v1 <- crossdpcoa_version1(fau, facA, facB, phydis, w=rep(1/30, 30), scannf = FALSE)
#Proportion of SS(A) expressed by the two first axes:
cd_v1$eig[1:2]/sum(cd_v1$eig)
#To view the positions of the locations on the first two axes, write:
s.label(cd_v1$l2)
#To view the positions of all communities on the first two axes, write:
s.label(cd_v1$l3)
#To view the positions of the species on the first two axes in front of the phylogeny, write:
v1l1.4d <- phylo4d(phy, as.matrix(cd_v1$l1))
# (then several functions can be used as shown below, 
# the last function, table.phylo4d, is from package adephylo)):
dotp4d(v1l1.4d, center = FALSE, scale = FALSE)
barp4d(v1l1.4d, center = FALSE, scale = FALSE)
gridp4d(v1l1.4d, center = FALSE, scale = FALSE)
parmar <- par()$mar
par(mar=rep(.1,4))
table.phylo4d(v1l1.4d, show.node=FALSE, symbol="squares", 
   center=FALSE, scale=FALSE, cex.label=0.5, ratio.tree=0.7)
par(mar=parmar)

#Crossed DPCoA Version 2
#Crossed DPCoA version 2 can now be performed as follows:
cd_v2 <- crossdpcoa_version2(fau, facA, facB, phydis, w=rep(1/30, 30), scannf = FALSE)
#Proportion of variation among levels of factor A 
#in the subspace orthogonal to the principal axes of B
#expressed by the two first axes:
cd_v2$eig[1:2]/sum(cd_v2$eig)
#To view the positions of the locations on the first two axes, write:
s.label(cd_v2$l2)
#To view the positions of all communities on the first two axes, write:
s.label(cd_v2$l3)
#To view the positions of the species on the first two axes in front of the phylogeny, write:
v2l1.4d <- phylo4d(phy, as.matrix(cd_v2$l1))
# (then several functions can be used as shown below, 
# the last function, table.phylo4d, is from package adephylo)):
dotp4d(v2l1.4d, center = FALSE, scale = FALSE)
barp4d(v2l1.4d, center = FALSE, scale = FALSE)
gridp4d(v2l1.4d, center = FALSE, scale = FALSE)
parmar <- par()$mar
par(mar=rep(.1,4))
table.phylo4d(v2l1.4d, show.node=FALSE, symbol="squares", 
   center=FALSE, scale=FALSE, cex.label=0.5, ratio.tree=0.7)
par(mar=parmar)

adegpar("plabels.optim" = O)
}

## End(Not run)

---

Indicator species analysis in the framework of multivariate analysis of variance

Description

"Consider N plots distributed among K groups; plots are composed of species whose abundances within each plot are known. The QT, QB and QW statistics defined in [Ricotta et al. 2021] aim at evaluating the average difference, in terms of species identity and abundance, between any two plots (QT), between two plots within a group (QW), and the gap between QT and QW (=QB) due to compositional differences between groups of plots. The function dbMANOVAspecies calculates QT, QB and QW as in [Ricotta et al. 2021] and the species-centered components QTs, QBs and QWs. It also calculates the SES values (equation 7 [in Ricotta et al. 2021]) associated with QB and QBs and allows tests for the significance of the SES values (H0 = the SES value is similar as that expected by randomly permuting plots among groups of plots and H1 = the SES value of is greater than that expected by randomly permuting plots among groups of plots). The function dbMANOVAspecies_pairwise complements function dbMANOVAspecies by performing post-hoc tests for all pairs of groups. It must be executed in the same R environment (workspace) as function dbMANOVAspecies. A third function named summary.dbMANOVAspecies_pairwise provides a short summary of the results of function dbMANOVAspecies_pairwise (with SES and P values)" (Ricotta et al. 2021, Appendix 3).

Usage

dbMANOVAspecies(comm, groups, nrep = 999, method = c("Euclidean", "Manhattan", 
    "Canberra", "BrayCurtis"), global = TRUE, species = TRUE, padjust = "none", 
    tol = 1e-8)
    
    dbMANOVAspecies_pairwise(dbobj, signif = TRUE, salpha = 0.05, nrep = NULL)
    
    ## S3 method for class 'dbMANOVAspecies_pairwise'
summary(object, DIGITS = 3, ...)

Arguments

comm	a matrix of N plots $\times$ S species containing the relative or absolute abundance of all species. Columns are species and plots are rows.
groups	a vector of characters or a factor with the names of the groups associated with plots. Names of groups must be listed in the same order as plots in object comm. For example, the first value of groups gives the name of the group for the first plot (first row in object comm).
nrep	a numeric that gives the number of permutations to be done. nrep can be set to NULL in function dbMANOVAspecies_pairwise, in which case the number of permutations used to built object dbobj (first argument of function dbMANOVAspecies_pairwise) is used by default.
method	a string, one of "Euclidean" (to perform the Euclidean distance), "Manhattan" (to select the Manhattan distance), "Canberra" (to perform the Canberra distance), "BrayCurtis" (to opt for the BrayCurtis distance).
global	a logical. If TRUE the global test (using the SES of QB) is performed. The global test can be performed in addition to one test per species.
species	a logical. If TRUE one test per species is performed. If species = FALSE, then argument global is ignored and the global test is performed.
padjust	a method of correction for multiple tests one of p.adjust.methods (see ?p.adjust.methods for possible choices); choose "none" if you don't need any correction for multiple tests. The argument padjust is ignored if species = FALSE.
tol	a numeric tolerance threshold. Any value between -tol and tol will be considered as equal to zero.
dbobj	an object of class "dbMANOVAspecies" obtained with function dbMANOVAspecies.
signif	a logical. If TRUE, the post-hoc tests are performed only for species that were associated with significant tests in object dbobj.
salpha	a numeric. The level of significance (nominal alpha error) for P values (must be between 0 and 1). Ignored if signif = FALSE.
object	an object of class "dbMANOVAspecies_pairwise" obtained with function dbMANOVAspecies_pairwise.
DIGITS	integer indicating the number of decimal places to retain when displaying the results. If NULL, all decimals are retained.
...	further arguments passed to or from other methods.

Value

dbMANOVAspecies returns a list with the following objects:

-observations: a vector or a data frame with the observed values of statistics (QT, QB and QW) (if global = TRUE) and/or the contribution each species has to these statistics (if species = TRUE);

-test: an object of class randtest or krandtest with the results of the test for the global differences, in terms of species composition, between groups of plots (if global = TRUE) and/or for the contribution each species has in these differences (if species = TRUE). dbMANOVAspecies_pairwise provides in a list the same objects as function dbMANOVAspecies but for each pair of groups (see examples below).

If only a global test was performed, summary.dbMANOVAspecies_pairwise provides a data frame with two rows named "SES" for the SES values (of the QB statistic) and "pvalue" for the P values and as many columns as there are pairs of groups of plots. Columns are named according to the two groups that are compared. For example, if there are two groups named Group1 and Group2, they are compared in column named "Group1:Group2". Else, it provides a data frame with species names as rows (in addition to a row named GLOBAL if a global test was also performed) and as columns the SES, P values, and if relevant adjusted P values, for each combination of two groups. Consider that Group1 and Group2 are the names of two groups. The column names that correspond to the comparison between Group1 and Group2 are written Group1:Group2.SES (for the SES values), Group1:Group2.pvalue (for the P values), and Group1:Group2.adj.pvalue (for the P values adjusted after correction for multiple tests, if a correction was done). NAs (= missing values) may be present in the data frame for species that are absent from two compared groups of plots. NAs may also be present in the data frame if signif = TRUE was used in function dbMANOVAspecies_pairwise for species that were associated to a non-significant test when performing function dbMANOVAspecies.

Author(s)

Sandrine Pavoine [email protected]

References

Ricotta, C., Pavoine, S., Cerabolini, B.E.L., Pillar, V.D. (2021) A new method for indicator species analysis in the framework of multivariate analysis of variance. Journal of Vegetation Science, 32, e13013. doi:10.1111/jvs.13013

Examples

## Not run: 
data(RutorGlacier)
Qspecies <- dbMANOVAspecies(RutorGlacier$Abund, RutorGlacier$Fac, 
    nrep=9999, global=TRUE)
Qspecies_adj <- dbMANOVAspecies(RutorGlacier$Abund, RutorGlacier$Fac, 
    nrep=9999, global=FALSE, padj = "BY")
# In Qspecies and Qspecies_adj, Column "Std.Obs" contains the SES values.
# Now for all species that showed significant compositional difference among 
# the three groups of plots (with a nominal alpha error of 0.05), we can test for 
# pairwise differences among all pairs of groups thanks to function 
# dbMANOVAspecies_pairwise as shown below:

# without any correction for multiple tests
Qspeciespairwise <- dbMANOVAspecies_pairwise(Qspecies)
summary(Qspeciespairwise)
# NAs are present in the data frame above for species that were associated 
# to non-significant test in object Qspecies (where tests were done over all groups);
# and also, for species that are absent from the two compared groups of plots 
# (e.g. species Adenostyles leucophylla, in mid- and late-successional stages).

# with correction for multiple test
Qspeciespairwise_adj <- dbMANOVAspecies_pairwise(Qspecies_adj)
summary(Qspeciespairwise_adj)
# Here again, NAs are present in the data frame above for species that were 
# associated to non-significant test in object Qspecies_adj 
# (where tests were done over all groups); and also, for species that are absent 
# from the two compared groups of plots (e.g. species Adenostyles leucophylla, 
# in mid- and late-successional stages).

# See Ricotta et al. 2021 Appendix 3 for details.

## End(Not run)

---

Decomposition of trait-based diversity along the nodes of a phylogenetic tree

Description

The function decdiv calculates trait-based differences between the lineages that descend from a node of a phylogenetic tree in one or several communities (using presence/absence or abundance data).

The function plot.decdiv plots the result of function decdiv for one of the communities.

The function rtestdecdiv tests, for one community (with presence/absence or abundance data), if the representation of trait diversity on the phylogenetic tree highlights a nonrandom pattern.

Usage

decdiv(phyl, comm, dis = NULL, tol = 1e-08, option = 1:5, 
     formula = c("QE", "EDI"))

## S3 method for class 'decdiv'
plot(x, ncom = 1, col = "black", 
    csize = 1, legend = TRUE, ...)

rtestdecdiv(phyl, vecab, dis = NULL, tol = 1e-08, 
    option = 1:5, formula = c("QE", "EDI"), 
    vranking = c("complexity", "droot"), 
    ties.method = c("average", "first", "last", "random", 
    "max", "min"), statistic = 1:3, optiontest = NULL, nrep = 99)

Arguments

phyl	an object inheriting the class phylo (see package ape), phylo4 (see package phylobase) or hclust with species as tips. To ease the interpretation of the results, I advise you to add labels to the nodes of the phylogeny. For example, If your phylogeny is named 'tree' and is of class phylo, you can name the nodes with the following command: tree$node.label <- paste("n", 1:tree$Nnode, sep=""). Use plot(tree, show.node.label=TRUE) to see the result. If it is of class phylo4, you can use: nodeLabels(tree) <- paste("n", 1:nNodes(tree), sep="").
comm	a vector with species presence/absence or an index of abundance as entries, or a data frame or a matrix typically with communities as rows, species as columns and presence/absence or an index of abundance as entries. Species names in comm must be similar as in phyl. Even if comm is a vector, each entry needs to have a species name (use function name to attribute names to a vector).
dis	either NULL or an object of class dist that contains the trait-based distances among species. If NULL, the Gini-Simpson index is used.
tol	a tolerance threshold (a value between -tol and tol is considered equal to zero)
option	a numeric (either 1, 2, 3, 4 or 5) indicating the option to use to calculate the contribution of each node of the phylogenetic tree to trait-based diversity. See details. If several values are given, the function retains only the first one.
formula	either "QE" (default) or "EDI". See details. If several values are given, the function retains only the first one.
x	an object of class decdiv.
ncom	if comm is a matrix, the number of its row corresponding to the focal community for which the results of decdiv will be plotted. Igored if comm is a vector.
col	the color of circles displayed at each node.
csize	a positive numeric giving the scale for plotting the circle at each node. 1 is the default size; if zero, no circle is drawn.
legend	a logical indicating whether the legend for the circle size needs to be displayed.
...	further arguments that can be specified to the internal use of function plot.phylo (argument y.lim cannot be modified).
vecab	a numeric vector giving the presence/absence(1/0) or abundance(non-negative value) of species in a community.
vranking	a string with 2 possible values: either "complexity" for a ranking according to the complexity of the subtree rooted on each interior node (see Pavoine et al. 2010 for an explanation), or "droot" for ordering interior nodes by the distance between them and the root node of the tree.
ties.method	a string to be passed to function rank of the base of R. It can be one of "average", "first", "last", "random", "max", "min".
statistic	a numeric value or a vector of numeric values. Possible values are 1, 2, or 3. They correspond to the three statistics S1, S2 and S3, respectively, developed by Pavoine et al. (eqs. 5 to 7 in Pavoine et al. 2010).
optiontest	a vector of strings specifying the alternative hypothesis of each test, which must be one of "greater", "less" or "two-sided". If null, then statistic=1 is associated with "greater" and statistic=2 and =3 with "two-sided". See function as.randtest of package ade4 for details on these alternatives. The length of the vector given to optiontest must be equal to that given to statistic.
nrep	numeric; the number of permutations to be done in each permutation test.

Details

The function decdiv relies on Rao's (1982) quadratic entropy (QE) to measure the trait-based diversity of a set of species. Two formulas for QE have been introduced in the literature one is the original formula by Rao (1982) (which corresponds to formula = "QE") and the other one introduced by Champely and Chessel (2002), named Euclidean Diversity Index (which corresponds to formula = "EDI"). See function QE for more details.

In function decdiv, each node has a weight proportional to the summed relative abundance of its descending species (or to the relative number of descending species if presence/absence data are used).

With option = 1, the function decdiv apportions trait-based diversity across the nodes of a phylogenetic tree using the algorithm defined in Pavoine et al. (2010). In that case the value at a given node is equal to the weight of a node times a measure of beta trait-based diversity between the lineages that descend from the node. The sum of all values attributed to the nodes of a phylogeny is equal to the total trait-based diversity of the species (tips of the phylogeny) as defined by Rao's quadratic entropy. In case of dichotomic trees, only two lineages descend from a given node. Here I consider a more general case where more than two lineages may descend from a node (polytomy). The beta trait-based diversity among the lineages that descend from a node is measured here as the average trait-based dissimilarity between any two of these descending lineages. With option = 1, the trait-based dissimilarity between two lineages is measured by Rao's DISC index (gamma diversity [average trait-based dissimilarity between any two species descending from the node] - alpha diversity [average trait-based dissimilarity between any two species descending from one of the lineages branched to the node]).

In the present version of function decdiv, I have added other options. Options 2 and 3 code different ways of measuring trait-based differences between lineages, standardized between 0 and 1: with option = 2, the formula is (gamma - alpha) / (1 - alpha) * M / (M - 1), where gamma and alpha are defined above (for option = 1) and M is the number of lineages descending from the node; with option = 3, the formula is (gamma - alpha) / (1 - gamma) / (M - 1).

Options 4 and 5 decompose the result given by option = 1. option = 4 returns gamma minus alpha (a measure of beta functional diversity between the lineages that descend from a node). option = 5 returns the weights of the nodes (the summed relative abundance of its descending species or the relative number of descending species if presence/absence data are used).

Values for option different from 1 needs that values in dis (the trait-based dissimilarities between species) are bounded between 0 and 1 if formula = QE or sqrt(2) if formula = EDI. If they are not bounded, the function decdiv will bound them using the maximum observed value in dis.

The argument ties.method in rtestdecdiv allows you to explicitly take into account potential ties when ranking nodes according to their complexity or their distance to root (see Pavoine et al. 2010 for more details on the permutation test implemented in rtestdecdiv).

Value

Function decdiv returns a matrix with nodes of the phylogenetic tree as rows and the decomposition of trait-based diversity in communities as columns. An attribute of this matrix is the phylogenetic tree (of class phylo with specified names for nodes). If the nodes of phyl had no names, the function decdiv automatically attributed names to them.

Author(s)

Sandrine Pavoine [email protected]

References

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

Pavoine, S., Baguette, M., Bonsall, M.B. (2010) Decomposition of trait diversity among the nodes of a phylogenetic tree. Ecological Monographs, 80, 485–507.

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

Examples

## Not run: 
if(require(ape) && require(adephylo)){
data(ungulates)
ung.phy <- read.tree(text=ungulates$tre)
ung.phy$node.label
plot(ung.phy, show.node.label=TRUE)
# Regaring traits, we log-tranformed the first three traits 
# measuring volumes 
# and we standardized all the traits (mean=0; variance=1).
tab <- cbind.data.frame(afbw = log(ungulates$tab$afbw),
mnw = log(ungulates$tab$mnw), fnw = log(ungulates$tab$fnw),
ls = ungulates$tab$ls)
ung.tab0 <- data.frame(scalewt(tab))
ung.tab0 <- data.frame(scalewt(log(ungulates$tab)))
ung.pres <- rep(1, nrow(ung.tab0))
names(ung.pres) <- rownames(ung.tab0)
ung.dec1 <- decdiv(ung.phy, ung.pres, dist(ung.tab0), 
    option=1, formula = "EDI")
plot.decdiv(ung.dec1)

ung.dec2 <- decdiv(ung.phy, ung.pres, dist(ung.tab0), 
    option=2, formula = "EDI")
plot.decdiv(ung.dec2)

ung.dec3 <- decdiv(ung.phy, ung.pres, dist(ung.tab0), 
    option=3, formula = "EDI")
plot.decdiv(ung.dec3)

ung.dec4 <- decdiv(ung.phy, ung.pres, dist(ung.tab0), 
    option=4, formula = "EDI")
plot.decdiv(ung.dec4)

ung.dec5 <- decdiv(ung.phy, ung.pres, dist(ung.tab0), 
    option=5, formula = "EDI")
plot.decdiv(ung.dec5)
}

## End(Not run)

---

Algorithmic index of plot-to-plot functional (or phylogenetic) dissimilarity

Description

The function dislptransport calculates the DKG measure of dissimilarity (Kosman 1996; Gregorius et al. 2003) applied here to functional differences between plots (eq. 3 in Ricotta et al. 2021).

Usage

dislptransport(comm, dis, diag = FALSE, upper = FALSE, Nind = 10000)

Arguments

comm	a matrix containing the relative or absolute abundance of all species in plots. Columns are species and plots are rows. Column labels (species names) should be assigned as in dis.
dis	a matrix or an object of class dist providing the functional dissimilarities between species (dissimilarities are nonnegative, symmetric, and the dissimilarity between a species and itself is zero). Species here must be in the same order as in the columns of comm.
diag	logical value indicating whether the diagonal of the dissimilarity matrix should be printed by print.dist.
upper	logical value indicating whether the upper triangle of the distance matrix should be printed by print.dist.
Nind	an integer. The algorithmic index will be applied by assuming that each plot contains Nind individuals. The highest Nind, the most precise the index value will be (see Gregorius et al. 2003, for more details).

Value

The function dislptransport returns an object of class dist matrix with the values of the dissimilarity index DKG (Ricotta et al. 2021) for each pair of plots.

Author(s)

Sandrine Pavoine [email protected]

References

Ricotta, C., Kosman, E., Laroche, F., Pavoine, S. (2021) Beta redundancy for functional ecology. Methods in Ecology and Evolution, 12, 1062–1069. doi:10.1111/2041-210X.13587

Gregorius, H.-R., Gillet, E.M., Ziehe, M. (2003) Measuring differences of trait distributions between populations. Biometrical Journal, 8, 959–973. doi:10.1002/bimj.200390063

Kosman, E. (1996) Difference and diversity of plant pathogen populations: a new approach for measuring. Phytopathology, 86, 1152–1155.

See Also

betaUniqueness for plot-to-plot functional (or phylogenetic) uniqueness indices.

Examples

## Not run: 
data(RutorGlacier)
fundis <- dist(scale(RutorGlacier$Traits2[1:6]))
fundis <- fundis/max(fundis)
DKG <- dislptransport(RutorGlacier$Abund, fundis)

## End(Not run)

---

Phylogenetic and Functional Similarity between Communities

Description

Coefficients of similarity between communities that rely on the presence/absence of species are generally based on various combinations of the matching/mismatching components of the classical 2 x 2 contingency table. Three of these components are: a=the number of species shared by the two communities; b=the number of species in the first community that are not in the second; c=the number of species in the second community that are not in the first. These coefficients are extended in dissABC to include phylogenetic or functional information on species (Ricotta and Pavoine 2015).

Usage

dissABC(comm, dis, option = 1:4, method = c("J", "S", "O", "K", "SS","Si"))

Arguments

comm	a data frame or a matrix typically with communities as rows, species as columns and relative abundance or absolute abundance as entries. Column labels (species names) should be assigned as in the object dis.
dis	a matrix (or data frame) of (phylogenetic or functional) dissimilarities among species rescaled in the range [0, 1] or an object of class dist containing these dissimilarities [obtained by functions like dsimFun in this package adiv, vegdist in package vegan, gowdis in package FD, or dist.ktab in package ade4 for functional dissimilarities, or functions like dsimTree in this package adiv, cophenetic.phylo in package ape or distTips in package adephylo for phylogenetic dissimilarities]. See also function dsimTaxo for taxonomic data. Note that dissimilarities among species need first to be rescaled in the range [0, 1]. If the dissimilarities are outside the range 0-1, a warning message is displayed and each dissimilarity is divided by the maximum over all pair-wise dissimilarities.
option	a numeric, either 1, 2, 3, or 4 (if several values are given only the first one is considered). See details.
method	a character or string, either "J", "S", "O", "K", "SS", or "Si" (if several values are given only the first one is considered). See details.

Details

To obtain the dissimilarities among plots, one needs to choose the equations to be used for the (phylogenetic or functional) components A, B, and C thanks to argument option and the way the components will be combined, thanks to argument method.

Let $\mathbf{D}=(d_{ij})$ a matrix of (functional, morphological or phylogenetic) dissimilarities between pairs of species with $d_{ij} = d_{ji}$ and $d_{ii} = 0$. If the dissimilarity coefficient d is in the range [0, 1], it is possible to define a corresponding similarity coefficient s as the complement of d: s = 1 - d. Let $x_{ik}$ the abundance of species i in community k. S(kh) is the number of species in the pooled communities k and h (i.e. the species for which $min\{x_{ik}, x_{ih}\} > 0$). The (absolute) abundance of species similar to i in plot k is

$Z_{ik}=\sum_{j=1}^{S(kh)}x_{jk}s_{ij}$

.

If option=1, equations 6-8 of the main text of Ricotta and Pavoine (2015) are used for calculating components A, B, C:

$A=\sum_{i=1}^{S(kh)}min\{Z_{ik}, Z_{ih}\}$

$B=\sum_{i=1}^{S(kh)}(max\{Z_{ik}, Z_{ih}\}-Z_{ih})$

$C=\sum_{i=1}^{S(kh)}(max\{Z_{ik}, Z_{ih}\}-Z_{ik})$

If option=2, equations A1-A3 from Appendix S1 of Ricotta and Pavoine (2015) are used.

If option=3, equations A5-A7 from Appendix S1 of Ricotta and Pavoine (2015) are used.

If option=4, equations A10-A12 from Appendix S1 of Ricotta and Pavoine (2015) are used.

If method="J"=the Jaccard index is used:

$\frac{A}{A+B+C}$

If method="S"=the Sorensen index is used:

$\frac{2A}{2A+B+C}$

If method="O"=the Ochiai index is used:

$A/(\sqrt{A+B}\sqrt{A+C})$

If method="K", the Kulczynski index is used:

$\frac{1}{2}\left(\frac{A}{A+B}+\frac{A}{A+C}\right)$

If method="SS", the Sokal-Sneath index is used:

$\frac{A}{A+2B+2C}$

If method="Si", the Simpson index is used:

$\frac{A}{A+min(B,C)}$

Value

Function dissABC returns a matrix with the values of the proposed similarities among communities based on interspecies resemblances.

Author(s)

Sandrine Pavoine [email protected]

References

Ricotta, C. and Pavoine, S. (2015) Measuring similarity among plots including similarity among species: an extension of traditional approaches. Journal of Vegetation Science, 26, 1061–1067.

See Also

discomQE, evodiss

Examples

data(RP15JVS)
dissABC(RP15JVS$ab, RP15JVS$D1, method="J", option=1)
J <- as.matrix(dissABC(RP15JVS$ab, RP15JVS$D1, method="J", option=1))[, 1]
SS <- as.matrix(dissABC(RP15JVS$ab, RP15JVS$D1, method="SS", option=1))[, 1]
S <- as.matrix(dissABC(RP15JVS$ab, RP15JVS$D1, method="S", option=1))[, 1]
O <- as.matrix(dissABC(RP15JVS$ab, RP15JVS$D1, method="O", option=1))[, 1]
K <- as.matrix(dissABC(RP15JVS$ab, RP15JVS$D1, method="K", option=1))[, 1]
plot(1:9, J, 
xlab="Number of the plots which plot 1 is compared to",
 ylab="Similarity", type="b", ylim=c(0,1), pch=18)
lines(1:9, SS, type="b", pch=15)
lines(1:9, S, type="b", pch=17)
lines(1:9, O, type="b", pch=12)
lines(1:9, K, type="b", pch=1)
legend("bottomleft", 
c("Jaccard","Sokal-Sneath","Sorensen","Ochiai","Kulczynski"), 
pch=c(18,15,17,12,1), lty=1)

---

Plot-to-Plot Functional or Phylogenetic Dissimilarity

Description

The function calculates plot-to-plot functional or phylogenetic dissimilarity based on index $D_{AB}$ in Ricotta et al. (2015).

Usage

dissRicotta(comm, dis)

Arguments

comm

a matrix of the relative or absolute abundance of species in communities. Columns are species and communities are rows. Column labels (species names) should be assigned as in dis.

dis

a matrix of (functional or phylogenetic) dissimilarities rescaled in the range [0, 1] or an object of class dist [obtained by functions like dsimFun in this package adiv, vegdist in package vegan, gowdis in package FD, or dist.ktab in package ade4 for functional dissimilarities, or functions like dsimTree in this package adiv, cophenetic.phylo in package ape or distTips in package adephylo for phylogenetic dissimilarities; See also function dsimTaxo for taxonomic data].

Value

The function returns a semi-matrix of class dist with the values of the proposed dissimilarities for each pair of plots. Note that dissimilarities among species need first to be rescaled in the range [0, 1]. If the dissimilarities are outside the range 0-1 (as it is usually the case in phylogenetic studies for instance), a warning message is displayed and all dissimilarities are divided by the maximum observed dissimilarity.

Author(s)

Giovanni Bacaro and Sandrine Pavoine [email protected]

References

Ricotta, C., Bacaro, G., Pavoine, S. (2015) A cautionary note on some phylogenetic dissimilarity measures. Journal of Plant Ecology, 8, 12–16.

Examples

## Not run: 
if(require(ape)){
# Phylogenetic tree
s<-"test(((v:20,w:20):10,(x:20,y:20):10):15,z:45):5;"
plot(test <- read.tree(text=s))

# Phylogenetic distances among species
tdist <- cophenetic(test)/100

# Matrix of abundances of the species in four communities; 
# communities A and C are identical;
# communities B and D are identical;
comm <- t(data.frame(A = rep(0.2, 5), 
B = c(0.1, 0.2, 0.2, 0, 0.5), C = rep(0.2, 5), 
D = c(0.1, 0.2, 0.2, 0, 0.5), row.names = letters[22:26]))

# Index DAB
dissRicotta(comm, tdist)
}

## End(Not run)

---

Abundance-based measures of species' rarity, functional or phylogenetic distinctiveness and functional or phylogenetic effective originality

Description

The function calculates parametric indices of species' rarity and functional or phylogenetic distinctiveness and effective originality according to Pavoine and Ricotta (2021).

Usage

distinctAb(comm, disORtree, method = c("Q", "KY", "KstarI"), palpha = 2, 
    option = c("asymmetric", "symmetric"), tol = 1e-10)

Arguments

comm	a data frame or a matrix typically with communities as rows, species as columns and abundance as entry. Species should be labelled as in object disORtree.
disORtree	an object inheriting the class dist, giving the FP-dissimilarities between species, or inheriting the class phylo (see package ape), phylo4 (see package phylobase), or hclust, where species are tips.
method	a string either "Q" for the quadratic entropy, "KY" for index $^{\alpha}K$ (if disORtree is of class dist) or $^{\alpha}Y$ if disORtree is of class phylo, phylo4 or hclust; or "KstarI" for index $^{\alpha}K*$ (if disORtree is of class dist) or $^{\alpha}I$ if disORtree is of class phylo, phylo4 or hclust. If several values are given, only the first one is considered.
palpha	a numeric, nonnegative value for parameter $\alpha$. palpha is ignored if method = "Q".
option	a string either "asymmetric", or"symmetric" The parameter option is only used if disORtree is of class phylo, phylo4 or hclust If option="symmetric", the distance between two tips on a tree is defined as half the sum of branch length on the smallest path that connects the two species; while if option="asymmetric" the distance between a tip i and a tip j on a tree is defined as the sum of branch lengths between tip i and its most recent ancestor with tip j. If the tree is ultrametric, the two options are equivalent.
tol	numeric tolerance threshold: values between -tol and tol are considered equal to zero.

Value

If palpha <= 1, then, the function returns a list of four objects of class data.frame (with communities as rows and species as columns): TotContr provides for each species in each community the effective originality multiplied by the relative abundance; EffOriPres provides for each species present in each community the effective originality; NA for absent species; DistinctPres provides for each species present in each community the distinctiveness; NA for absent species; Rarity provides for each species in each community the rarity (maximum rarity for absent species).

Else, the function returns a list with the three objects of class data.frame presented above and two additional objects also of class data.frame: EffOriAll provides for each species its effective originality compared with the composition of each community; even absent species have a value considering they have zero abundance so maximum rarity and considering their functional dissimilarity or phylogenetic dissimilarity with all species present in each community; DistinctAll provides for each species its effective originality compared with the composition of each community; even absent species have a value considering they have zero abundance so maximum rarity and considering their functional dissimilarity or phylogenetic dissimilarity with all species present in each community.

Author(s)

Sandrine Pavoine [email protected]

References

Pavoine, S., Ricotta, C. (2021) On the relationships between rarity, uniqueness, distinctiveness, originality and functional/phylogenetic diversity. BiorXiv. doi:10.1101/2021.08.09.455640

See Also

distinctDis, distinctTopo, distinctTree, distinctUltra

Examples

## Not run: 
if(require(ape) && require(adephylo) && require(phylobase)){
data(batcomm)
phy <- read.tree(text=batcomm$tre2)
disAb <- distinctAb(batcomm$ab2, phy, method="Q") 
U.4d <- phylo4d(phy, t(disAb[[2]]))
dotp4d(U.4d, center = FALSE, scale = FALSE, data.xlim = range(t(disAb[[2]]), na.rm=TRUE), 
    tree.ratio = 0.20, dot.cex=2)
title("Effective originality associated with quadratic entropy (diversity)")
}

## End(Not run)

---

Dissimilarity-based Species' Originality

Description

The function calculates five indices of species' originality.

Usage

distinctDis(dis, method = c("Rb", "AV", "FV", "NN", "Dstar", "full"), 
    palpha = 0, standardized = FALSE)

Arguments

dis	an object of class dist containing pair-wise (functional or phylogenetic) dissimilarities between species.
method	a vector of strings. Possible values are "Rb", "AV", "FV", "NN", "Dstar" and "full". "Rb" is for Pavoine et al. (2017) index Rb; "AV" is for AV, the average dissimilarity between a species and all others in a set (Eiswerth and Haney 1992; Ricotta 2004); "FV" is for FV, the average dissimilarity between a species and any other (including the focal species itself) (Schmera et al. 2009); "NN" is for the minimum dissimilarity between a species and any other (the dissimilarity to its Nearest Neighbor) (Pavoine et al. 2017); Dstar is the parametric indices $^{\alpha}D*$ developed by Pavoine and Ricotta (2021, Appendix B); "full" returns all indices.
palpha	a numeric which provides the value of parameter $\alpha$ in index $^{\alpha}D*$ developed by Pavoine and Ricotta (2021, Appendix B).
standardized	a logical. If TRUE, the vector of originalities is divided by its sum (transforming absolute originalities into relative originalities).

Value

A data frame with species as rows and originality indices as columns.

Author(s)

Sandrine Pavoine [email protected]

References

Eiswerth, M.E. and Haney, J.C. (1992) Allocating conservation expenditures: accounting for inter-species genetic distinctiveness. Ecological Economics, 5, 235–249.

Pavoine, S., Bonsall, M.B., Dupaix, A., Jacob, U., Ricotta, C. (2017) From phylogenetic to functional originality: guide through indices and new developments. Ecological Indicators, 82, 196–205.

Pavoine, S., Ricotta, C. (2021) On the relationships between rarity, uniqueness, distinctiveness, originality and functional/phylogenetic diversity. BiorXiv. doi:10.1101/2021.08.09.455640

Ricotta, C. (2004) A parametric diversity measure combining the relative abundances and taxonomic distinctiveness of species. Diversity and Distributions, 10, 143–146.

Schmera, D., Podani, J., Eros, T. (2009) Measuring the contribution of community members to functional diversity. Oikos, 118, 961–971.

See Also

distinctTopo, distinctTree, distinctUltra

Examples

e <- rlnorm(10)
e <- sort(e)
names(e) <- paste("s", 1:10, sep="")
d <- dist(e)
barplot(e)

D <- distinctDis(d, standardized = TRUE)

par(mfrow=c(4,2))
plot(e, D[,1], xlab="trait", ylab="Rb")
plot(e, D[,2], xlab="trait", ylab="AV")
plot(e, D[,3], xlab="trait", ylab="FV")
plot(e, D[,4], xlab="trait", ylab="NN")

plot(D[,1], D[,2], xlab="Rb", ylab="AV")
plot(D[,1], D[,3], xlab="Rb", ylab="FV")
plot(D[,2], D[,3], xlab="AV", ylab="FV")
plot(D[,2], D[,4], xlab="AV", ylab="NN")
par(mfrow=c(1,1))

---

Topology-based Species' Originality

Description

The function calculates three indices of species' originality that rely on the topology of (phylogenetic) trees. Trees with polytomies are allowed.

Usage

distinctTopo(phyl, method = c("VW","M","A","full"), standardized = FALSE)

Arguments

phyl	an object inheriting the class phylo (see package ape), phylo4 (see package phylobase), or hclust.
method	a character or string or a vector of characters/strings. Possible values are "VW", "M", "A" and "full". "VW" is for Vane-Wright et al. index (Vane-Wright et al. 1991); "M" is for May index (May 1990); "A" is for Pavoine et al. index of originality derived from Abouheif (1999) (Pavoine et al. 2008); and "full" returns all indices.
standardized	a logical. If FALSE, the minimum score is scaled to 1 as in May (1990). If TRUE, the vector of originalities is divided by its sum (transforming absolute originalities into relative originalities).

Value

A data frame with species as rows and originality indices as columns.

Author(s)

Sandrine Pavoine [email protected] with contributions of Stephane Dray

References

May, R.M. (1990) Taxonomy as destiny. Nature, 347, 129–130.

Vane-Wright, R.I., Humphries, C.J., Williams, P.H. (1991) What to protect? Systematics and the agony of choice. Biological Conservation, 55, 235–254.

Abouheif, E. (1999) A method for testing the assumption of phylogenetic independence in comparative data. Evolutionary Ecology Research, 1, 895–909.

Pavoine, S., Ollier, S., Pontier, D., Chessel, D. (2008) Testing for phylogenetic signal in phenotypic traits: new matrices of phylogenetic proximities. Theoretical Population Biology, 73, 79–91.

See Also

distinctDis, distinctTree, distinctUltra

Examples

## Not run: 
if(require(ape) && require(adephylo) && require(phylobase)){
data(carni70, package = "adephylo")
tre <- read.tree(text=carni70$tre)
U <- distinctTopo(tre, standardized = TRUE)
U.4d <- phylo4d(tre, as.matrix(U))
dotp4d(U.4d, center = FALSE, scale = FALSE)
barp4d(U.4d, center = FALSE, scale = FALSE)
gridp4d(U.4d, center = FALSE, scale = FALSE)

parmar <- par()$mar
par(mar=rep(.1,4))
table.phylo4d(U.4d, show.node=FALSE, symbol="squares", center=FALSE, scale=FALSE, cex.symbol=2)
par(mar=parmar)
}

## End(Not run)

---

Tree-based Species' Originality

Description

The function calculates indices of species' originality that rely on the structure and branch lengths of (phylogenetic) trees. Trees with polytomies are allowed.

Usage

distinctTree(phyl, method = c("ED", "ES", "Delta*"), palpha = 0, standardized = FALSE)

Arguments

phyl	an object inheriting the class phylo (see package ape), phylo4 (see package phylobase) or hclust.
method	a string or a vector of strings. Possible values are "ED", "ES", and "Delta*". "ED" is for the evolutionary distinctiveness, also named fair-proportion, index (Redding 2003; Isaac et al. 2007); "ES" is for the Equal-Splits index (Redding and Mooers 2006); "Delta*" is for the parametric $^{\alpha}\Delta$ index of Pavoine and Ricotta (2021).
palpha	a numeric value or a numeric vector of values for parameter $\alpha$ of $^{\alpha}\Delta$ index by Pavoine and Ricotta (2021).
standardized	a logical. If TRUE, the vector of originalities is divided by its sum (transforming absolute originalities into relative originalities).

Value

A data frame with species as rows and originality indices as columns.

Author(s)

Sandrine Pavoine [email protected]

References

Isaac, N.J., Turvey, S.T., Collen, B., Waterman, C., Baillie, J.E. (2007) Mammals on the EDGE: conservation priorities based on threat and phylogeny. PloS ONE, 2, e296.

Pavoine, S., Ricotta, C. (2021) On the relationships between rarity, uniqueness, distinctiveness, originality and functional/phylogenetic diversity. BiorXiv. doi:10.1101/2021.08.09.455640

Redding, D.W. (2003) Incorporating genetic distinctness and reserve occupancy into a conservation priorisation approach. Master thesis: University of East Anglia, Norwich.

Redding, D.W., Mooers, A.O. (2006) Incorporating evolutionary measures into conservation prioritization. Conservation Biology, 20, 1670–1678.

See Also

distinctDis, distinctTopo, distinctUltra

Examples

## Not run: 
if(require(ape) && require(adephylo) && require(phylobase)){
data(carni70, package = "adephylo")
tre <- read.tree(text=carni70$tre)
U <- distinctTree(tre, standardize = TRUE)
U.4d <- phylo4d(tre, as.matrix(U))
dotp4d(U.4d, center = FALSE, scale = FALSE)
barp4d(U.4d, center = FALSE, scale = FALSE)
gridp4d(U.4d, center = FALSE, scale = FALSE)

parmar <- par()$mar
par(mar=rep(.1,4))
table.phylo4d(U.4d, show.node=FALSE, symbol="squares", center=FALSE, scale=FALSE, cex.symbol=2)
par(mar=parmar)
}

## End(Not run)

---

Ultrametric Tree-based Species' Originality

Description

The function calculates two indices of species' originality that rely on the structure and branch lengths of ultrametric (phylogenetic) trees. Trees with polytomies are allowed.

Usage

distinctUltra(phyl, method = c("Qb","2Hb"))

Arguments

phyl	an object inheriting the class phylo (see package ape), phylo4 (see package phylobase), or hclust, with ultrametric properties.
method	a string or a vector of strings. Possible values are Qb and 2Hb. Qb is for the Pavoine et al. QE-based (also named Qb) index (Pavoine et al. 2005); 2Hb is for Pavoine et al. 2H-based index (which could also be named more shortly as 2Hb) (vector that maximizes index $^2H$, Pavoine and Izsak 2014).

Value

A data frame with species as rows and originality indices as columns.

Author(s)

Sandrine Pavoine [email protected] with contributions of Stephane Dray

References

Pavoine, S., Ollier, S., Dufour, A.B. (2005) Is the originality of a species measurable? Ecology Letters, 8, 579–586.

Pavoine, S. and Izsak, J. (2014) New biodiversity measure that includes consistent interspecific and intraspecific components. Methods in Ecology and Evolution, 5, 165–172.

See Also

distinctDis, distinctTopo, distinctTree

Examples

## Not run: 
if(require(ape) && require(adephylo) && require(phylobase)){
data(carni70, package = "adephylo")
tre <- read.tree(text=carni70$tre)
U <- distinctUltra(tre)
U.4d <- phylo4d(tre, as.matrix(U))

dotp4d(U.4d, center = FALSE, scale = FALSE)
barp4d(U.4d, center = FALSE, scale = FALSE)
gridp4d(U.4d, center = FALSE, scale = FALSE)

parmar <- par()$mar
par(mar=rep(.1,4))
table.phylo4d(U.4d, show.node=FALSE, symbol="squares", center=FALSE, scale=FALSE, cex.symbol=2)
par(mar=parmar)
}

## End(Not run)

---

Marczewski-Steinhaus Coefficient

Description

The function calculates the Marczewski-Steinhaus coefficient of dissimilarity between pairs of entities (e.g. communities)

Usage

distMS(comm, diag = FALSE, upper = FALSE)

Arguments

comm	a data frame or a matrix of nonnegative values (e.g. abundance of species (columns) within communities (rows) to obtain dissimilarities between communities).
diag	a logical value indicating whether the diagonal of the distance matrix should be printed by function print.dist.
upper	a logical value indicating whether the upper triangle of the distance matrix should be printed by function print.dist.

Value

an object of class dist

Note

This function is a modification of function dist.quant from library ade4 where other dissimilarity coefficients can be found.

Author(s)

Sandrine Pavoine [email protected]

References

Orloci, L. (1978) Multivariate Analysis in Vegetation Research. The Hague: Junk.

Legendre, P. and Legendre, L. (1998) Numerical Ecology. Amsterdam: Elsevier.

Ricotta, C., de Bello, F., Moretti, M., Caccianiga, M., Cerabolini, B.E., Pavoine, S. (2016). Measuring the functional redundancy of biological communities: a quantitative guide. Methods in Ecology and Evolution, 7, 1386–1395.

Examples

data(birdData)
distMS(birdData$fau)

---

Parametric Indices of Species Diversity

Description

The function divparam calculates parametric diversity indices. The parameter controls the relative importance given to rare versus abundant species in a community. The function plot.divparam plots the results of function divparam.

Usage

divparam(comm, method = c("hill", "tsallis", "renyi"), q = 2, tol = 1e-08)

## S3 method for class 'divparam'
plot(x, legend = TRUE, 
legendposi = "topright", axisLABEL = "Diversity", type = "b", 
col = if (is.numeric(x)) NULL 
else sample(colors(distinct = TRUE), nrow(x$div)), 
lty = if (is.numeric(x)) NULL else rep(1, nrow(x$div)), 
pch = if (is.numeric(x)) NULL else rep(19, nrow(x$div)), 
...)

Arguments

comm	a data frame or a matrix typically with communities as rows, species as columns and abundance as entry.
method	a string: either "hill" for the Hill numbers (Hill 1973), "tsallis" for the Tsallis or HCDT entropy (Harvda and Charvat 1967; Daroczy 1970; Tsallis 1988), or "renyi" for Renyi's entropy (Renyi 1960).
q	a positive numeric or a vector of positive numerics that gives values for the q parameter.
tol	numeric tolerance threshold: values between -tol and tol are considered equal to zero.
x	an object of class divparam obtained with function divparam.
legend	a logical. If TRUE a legend is given with the colour, the type of line (etc.) used to define the diversity curve of each community.
legendposi	a string or a numeric that gives the position of the legend to be passed to function legend of the base of R.
axisLABEL	a string to display on the main axis of the plot to designate what we are measuring. The default is "Diversity".
type	a string to be passed to the graphic argument type of functions plot and lines used to draw the diversity curve of each community.
col	colours to be passed to the graphic argument col of functions plot and lines to define the colour of the diversity curve of each community.
lty	type of line (plain, broken etc.) to be passed to the graphic argument lty of functions plot and lines used to draw the diversity curve of each community.
pch	type of point (open circle, close circle, square etc.) to be passed to the graphic argument pch of functions plot and lines used to draw the diversity curve of each community.
...	other arguments can be added and passed to the functions plot and lines used to draw the graphic.

Value

If only a single value of q is given, function divparam returns a vector with the diversities of the communities. If more than one value of q is given, a list of two objects is returned:

q	the vector of values for q
div	a data frame with the diversities of the communities calculated for all values of q

The function plot.divparam returns a graphic.

Author(s)

Sandrine Pavoine [email protected]

References

Daroczy, Z. (1970) Generalized information functions. Information and Control, 16, 36–51.

Havrda, M., Charvat, F. (1967) Quantification method of classification processes: concept of structural alpha-entropy. Kybernatica, 3, 30–35.

Hill, M.O. (1973) Diversity and evenness: a unifying notation and its consequences. Ecology, 54, 427–432.

Renyi, A. (1960) On measures of entropy and information. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, 1, 547–561.

Tsallis, C. (1988) Possible generalization of Boltzmann-Gibbs statistics. Journal of Statistical Physics, 52, 480–487.

Examples

data(batcomm)
ab <- batcomm$ab
plot(divparam(ab))
plot(divparam(ab, q=0:4))

---

Plot-to-plot functional or phylogenetic dissimilarity

Description

The function DP calculates Ricotta et al. (2020) plot-to-plot functional or phylogenetic beta uniqueness (index named $D_F$ for functional data and $D_P$ for phylogenetic data, calculated with equation 2 in Ricotta et al. 2020).

Usage

DP(mtree, comm, height = NULL, diag = FALSE, upper = FALSE, tol = 0.001)

Arguments

mtree	an object inheriting the class phylo (see package ape), phylo4 (see package phylobase), or hclust. The tree must be ultrametric: equal distance from any tip to the root.
comm	a matrix containing the relative or absolute abundance of all species in plots. Columns are species and plots are rows. Column labels (species names) should be assigned as in mtree.
height	either NULL or a numeric. See details.
diag	a logical value indicating whether the diagonal of the distance matrix should be printed by function print.dist.
upper	a logical value indicating whether the upper triangle of the distance matrix should be printed by function print.dist.
tol	a tolerance threshold. A value between -tol and tol is considered as zero. See details.

Details

Object mtree defines a tree with species as tips. If argument height is NULL, then the root of the tree will be placed at the most recent common ancestor of all species occurring in the set of plots (given in object comm). An alternative position for the root can be given by specifying the height of the tree (argument height). In that case, height must be higher than the distance between tips and the most recent common ancestor of all species.

The tolerance threshold tol is particularly important if your tree is not exactly ultrametric due to approximation problems. In that case, the distance from tip to root varies according to the tip considered, although it should not (variations are due to approximation problems). A difference smaller than tol in the distance to root for two species will thus be considered as null.

Value

The function returns a (semi-)matrix of class dist with the values of the proposed dissimilarities for each pair of plots.

Author(s)

Sandrine Pavoine [email protected]

References

Ricotta, C., Laroche, F., Szeidl, L., Pavoine, S. (2020) From alpha to beta functional and phylogenetic redundancy. Methods in Ecology and Evolution. In press.

See Also

betaTreeUniqueness for beta uniqueness, treeUniqueness for alpha uniqueness

Examples

## Not run: 
if(require(ape) && require(ade4)){
data(RutorGlacier)
phy <- read.tree(text=RutorGlacier$TreeNW)
plot(phy)

ab <- RutorGlacier$Abund[, phy$tip.label]

# Phylogenetic dissimilarities between plots
# (Ricotta et al. 2020)
Dp <- DP(phy, ab, tol=0.00001)
# Principal Coordinate Analysis of the dissimilarities
pcoDp <- dudi.pco(sqrt(Dp), full=TRUE)
s.class(pcoDp$li, as.factor(RutorGlacier$Fac))
}

## End(Not run)

---

Functional or Phylogenetic Similarity between Species and Communities

Description

The R function dsimcom calculates Pavoine and Ricotta (2014) coefficients SSokal-Sneath, SJaccard, SSorensen, SOchiai, and Sbeta of similarities among communities or their complements (1-S, dissimilarities).

Function SQ calculates Pavoine and Ricotta (2014) index $S_Q$ (similarities between communities) and its complements $1-S_Q$ (dissimilarities between communities).

The functions dsimTax and dsimTree calculate pair-wise taxonomic and phylogenetic (dis)similarities between species, respectively. dsimTree can also be used to calculate pair-wise functional (dis)similarities between species if a functional dendrogram is used to describe species.

Function dsimFun calculates pair-wise functional (dis)similaties between species.

Usage

dsimcom(comm, Sigma = NULL, method = 1:5, 
option = c("relative", "absolute"), 
type = c("similarity", "dissimilarity"))

SQ(comm, Sigma = NULL, type = c("similarity", "dissimilarity"))

dsimTaxo(tax, method = c(1, 2, 3, 4, 5), 
type = c("similarity", "dissimilarity"))

dsimTree(phyl, method = c(1, 2, 3, 4, 5), rootedge = NULL, 
type = c("similarity", "dissimilarity"))

dsimFun(df, vartype = c("Q", "N", "M", "P"), method = 1:5, 
type = c("similarity", "dissimilarity"))

Arguments

comm	a data frame or matrix with communities as rows, species as columns and non-negative values as entries.
Sigma	matrix of similarities among species (species as rows and columns in the same order as in comm; values in Sigma are bounded between 0 and 1). The matrix must be nonnegative definite, i.e. all its eigenvalues are nonnegative. Functions dsimTaxo, dsimTree and dsimFun can be used to obtain Sigma as these functions lead to nonnegative definite matrices.
method	an integer (1, 2, 3, 4, 5) indicating which basic coefficient should be used: Sokal-Sneath, Jaccard, Sorensen, Ochiai, beta, respectively.
option	a string. If option = "relative", the rows of comm are standardized into proportions that sum to 1. If option = "absolute", raw values are retained in comm.
tax	an object of class taxo (of package ade4).
type	a string. If type = "similarity", the functions dsimcom and SQ calculates similarities (S) between communities and the functions dsimTaxo, dsimTree and dsimFun calculates similarities between species. If type = "dissimilarity", the functions dsimcom and SQ calculates dissimilarities (1-S) between communities and the functions dsimTaxo, dsimTree and dsimFun calculates dissimilarities between species.
phyl	an object inheriting the class phylo (see package ape), phylo4 (see package phylobase), or hclust.
rootedge	a numeric equal to the length of the branch at the nearest common ancestor of all species (here referred to as the root node). This branch is thus anterior to the root. It is ignored if rootedge is NULL.
df	either a data frame, a matrix or an object of class ktab of package ade4. If class ktab is used, each data frame must contain a single type of traits (see argument vartype).
vartype	a vector of characters indicating the type of traits used in each data frame of df: "Q" for quantitative; "N" for nominal; "M" for multichoice; "P" for traits that can be expressed as proportions. Values in type must be in the same order as data frames in df (one value per table).

Details

Formulas for the indices are given in Pavoine and Ricotta (2014) main text and appendixes.

Value

If type = "similarities", a matrix of similarities between communities. If type = "dissimilarities", an object of class dist with the dissimilarities between communities.

Author(s)

Sandrine Pavoine [email protected]

References

Pavoine, S., Ricotta, C. (2014) Functional and phylogenetic similarity among communities. Methods in Ecology and Evolution, 5, 666–675.

Examples

## Not run: 
if(require(ade4)){
data(macroloire, package="ade4") 

Ssokalsneath <- dsimcom(t(macroloire$fau), method=1, option=c("relative"))
Sjaccard <- dsimcom(t(macroloire$fau), method=2, option=c("relative"))
Ssorensen <- dsimcom(t(macroloire$fau), method=3, option=c("relative"))
Sochiai <- dsimcom(t(macroloire$fau), method=4, option=c("relative"))
Sbeta <- dsimcom(t(macroloire$fau), method=5, option=c("relative"))

SQUNIF <- SQ(t(macroloire$fau))

# The taxonomy is contained in macroloire$taxo

s_species_sokalsneath_taxo <- dsimTaxo(macroloire$taxo, method=1) # Using formula a/(a+2b+2c) 
# (see notations below)
s_species_jaccard_taxo <- dsimTaxo(macroloire$taxo, method=2) # Using formula a/(a+b+c) 
s_species_sorensen_taxo <- dsimTaxo(macroloire$taxo, method=3) # Using formula 2a/(2a+b+c) 
s_species_ochiai_taxo <- dsimTaxo(macroloire$taxo, method=4) # Using a/sqrt((a+b)(a+c)) 
s_species_beta_taxo <- dsimTaxo(macroloire$taxo, method=5) # Using 4a/(4a+b+c)


# To check that these matrices of taxonomic similarities 
# among species are positive semidefinite (p.s.d.)
# we have to verify that their eigenvalues are all nonnegative:
all(eigen(s_species_sokalsneath_taxo)$val>-(1e-8))
all(eigen(s_species_jaccard_taxo)$val>-(1e-8))
all(eigen(s_species_sorensen_taxo)$val>-(1e-8))
all(eigen(s_species_ochiai_taxo)$val>-(1e-8))
all(eigen(s_species_beta_taxo)$val>-(1e-8))

# Compositions of the communities
m <- t(macroloire$fau[rownames(s_species_sokalsneath_taxo), ])
# Taxomonic similarities among species
s <- s_species_sokalsneath_taxo

Ssokalsneath_taxo <- dsimcom(m, s, method = 1)
SQwith_species_sokalsneath_taxo <- SQ(m, s)

# Compositions of the communities
m <- t(macroloire$fau[rownames(s_species_jaccard_taxo), ])
# Taxonomic similarities among species
s <- s_species_jaccard_taxo  
Sjaccard_taxo <- dsimcom(m, s, method = 2)
SQwith_species_jaccard_taxo <- SQ(m, s)

# Compositions of the communities
m <- t(macroloire$fau[rownames(s_species_sorensen_taxo), ])
# Taxonomic similarities among species
s <- s_species_sorensen_taxo  

Ssorensen_taxo <- dsimcom(m, s, method = 3)
SQwith_species_sorensen_taxo <- SQ(m, s)

# Compositions of the communities
m <- t(macroloire$fau[rownames(s_species_ochiai_taxo), ])
# Taxonomic similarities among species
s <- s_species_ochiai_taxo  

Sochiai_taxo <- dsimcom(m, s, method = 4)
SQwith_species_ochiai_taxo <- SQ(m, s)


# Compositions of the communities
m <- t(macroloire$fau[rownames(s_species_beta_taxo), ])
# Taxonomic similarities among species
s <- s_species_beta_taxo  

Sbeta_taxo <- dsimcom(m, s, method = 5)
SQwith_species_beta_taxo <- SQ(m, s)

# The matrix named feed below contains feeding attributes as rows,
# species as columns, and affinities (proportions) as entries.
feed <- macroloire$traits[ ,-(1:4)]

# Feeding habits comprise seven categories: engulfers, shredders, scrapers,
# deposit-feeders, active filter-feeders, passive filter-feeders and piercers, in this order.

# Functional similarities among species are computed as indicated in the main text
s_species_sokalsneath_feed <- dsimFun(feed, vartype = "P", method=1)
s_species_jaccard_feed <- dsimFun(feed, vartype = "P", method=2)
s_species_sorensen_feed <- dsimFun(feed, vartype = "P", method=3)
s_species_ochiai_feed <- dsimFun(feed, vartype = "P", method=4)
s_species_beta_feed <- dsimFun(feed, vartype = "P", method=5)

all(eigen(s_species_sokalsneath_feed)$val>-(1e-8))
all(eigen(s_species_jaccard_feed)$val>-(1e-8))
all(eigen(s_species_sorensen_feed)$val>-(1e-8))
all(eigen(s_species_ochiai_feed)$val>-(1e-8))
all(eigen(s_species_beta_feed)$val>-(1e-8))

Ssokalsneath_feed <- dsimcom(t(macroloire$fau), s_species_sokalsneath_feed, method=1)
SQwith_species_sokalsneath_feed <- SQ(t(macroloire$fau), s_species_sokalsneath_feed)

Sjaccard_feed <- dsimcom(t(macroloire$fau), s_species_jaccard_feed, method=2)
SQwith_species_jaccard_feed <- SQ(t(macroloire$fau), s_species_jaccard_feed)

Ssorensen_feed <- dsimcom(t(macroloire$fau), s_species_sorensen_feed, method=3)
SQwith_species_sorensen_feed <- SQ(t(macroloire$fau), s_species_sorensen_feed)

Sochiai_feed <- dsimcom(t(macroloire$fau), s_species_ochiai_feed, method=4)
SQwith_species_ochiai_feed <- SQ(t(macroloire$fau), s_species_ochiai_feed)

Sbeta_feed <- dsimcom(t(macroloire$fau), s_species_sorensen_feed, method=5)


all(eigen(Ssokalsneath_feed)$val>-(1e-8))
all(eigen(Sjaccard_feed)$val>-(1e-8))
all(eigen(Ssorensen_feed)$val>-(1e-8))
all(eigen(Sochiai_feed)$val>-(1e-8))
all(eigen(Sbeta_feed)$val>-(1e-8))


par(mfrow=c(3, 5))
plot(SQUNIF, Ssokalsneath, xlim=c(0,1), ylim=c(0,1), asp=1)
segments(0, 0, 1,1)
plot(SQUNIF, Sjaccard, xlim=c(0,1), ylim=c(0,1) , asp=1)
segments(0, 0, 1,1)
plot(SQUNIF, Ssorensen, xlim=c(0,1), ylim=c(0,1) , asp=1)
segments(0, 0, 1,1)
plot(SQUNIF, Sochiai, xlim=c(0,1), ylim=c(0,1) , asp=1)
segments(0, 0, 1,1)
plot(SQUNIF, Sbeta, xlim=c(0,1), ylim=c(0,1) , asp=1)
segments(0, 0, 1,1)

plot(SQwith_species_sokalsneath_taxo, Ssokalsneath_taxo, xlim=c(0,1), ylim=c(0,1), asp=1)
segments(0, 0, 1,1)
plot(SQwith_species_jaccard_taxo, Sjaccard_taxo, xlim=c(0,1), ylim=c(0,1) , asp=1)
segments(0, 0, 1,1)
plot(SQwith_species_sorensen_taxo, Ssorensen_taxo, xlim=c(0,1), ylim=c(0,1) , asp=1)
segments(0, 0, 1,1)
plot(SQwith_species_ochiai_taxo, Sochiai_taxo, xlim=c(0,1), ylim=c(0,1) , asp=1)
segments(0, 0, 1,1)
plot(SQwith_species_beta_taxo, Sbeta_taxo, xlim=c(0,1), ylim=c(0,1) , asp=1)
segments(0, 0, 1,1)

plot(SQwith_species_sokalsneath_feed, Ssokalsneath_feed, xlim=c(0,1), ylim=c(0,1), asp=1)
segments(0, 0, 1,1)
plot(SQwith_species_jaccard_feed, Sjaccard_feed, xlim=c(0,1), ylim=c(0,1) , asp=1)
segments(0, 0, 1,1)
plot(SQwith_species_sorensen_feed, Ssorensen_feed, xlim=c(0,1), ylim=c(0,1) , asp=1)
segments(0, 0, 1,1)
plot(SQwith_species_ochiai_feed, Sochiai_feed, xlim=c(0,1), ylim=c(0,1) , asp=1)
segments(0, 0, 1,1)
plot(SQwith_species_sorensen_feed, Sbeta_feed, xlim=c(0,1), ylim=c(0,1) , asp=1)
segments(0, 0, 1,1)

par(mfrow=c(1,1))
}

## End(Not run)

---