evodivparam {adiv}

Parametric Indices of Phylogenetic Diversity

Description

Function evodivparam calculates phylogenetic diversity in communities using parametric indices derived from Tsallis and Hill compositional indices. It can also be applied to functional trees rather than phylogenies, to calculate a functional diversity. The function plot.evodivparam plots the results of function evodivparam.

Usage

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

## S3 method for class 'evodivparam'
plot(x, legend = TRUE, 
    legendposi = "topright", axisLABEL = "Tree-based 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

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 abundance as entry. Species should be labeled as in the phylogenetic tree where they are the tips.

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). If several values are given, only the first one is considered. See details.

q

a vector with nonnegative value(s) for parameter q. See details.

tol

numeric tolerance threshold: values between -tol and tol are considered equal to zero.

x

an object of class evodivparam obtained with function evodivparam.

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 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 "Tree-based 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

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 community.

lty

vector of 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 level of each community.

...

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 to calculate the phylogenetic diversity in community j are: tsallis:

^q{evoTsallis}_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)

hill:

^q{evoHill}_j=\left[\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)}

renyi:

^q{evoRenyi}_j=log(^q{evoHill}_j)

Value

If only one value of q is given, a vector with the phylogenetic diversity of each community is returned. 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 phylogenetic diversity of each community calculated for all values of q.

The function plot.evodivparam returns a graphic.

Author(s)

Sandrine Pavoine [e-mail]

References

The methodologies and scripts were developed by

Pavoine, S., Ricotta, C. (2019) A simple translation from indices of species diversity to indices of phylogenetic diversity. Ecological Indicators, 101, 552–561.

using earlier work by:

Chao, A., Chiu, C.-H., Jost, L. (2010) Phylogenetic diversity measures based on Hill numbers. Philosophical Transactions of the Royal Society London Series B, 365, 3599–3609.

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.

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.

See Also

abgevodivparam, divparam

Examples

## Not run: 
if(require(ape)){

data(batcomm)
phy <- read.tree(text=batcomm$tre)
ab <- batcomm$ab[, phy$tip.label]
plot(evodivparam(phy, ab))
plot(evodivparam(phy, ab, q=seq(0, 10, length=20)))

}

## End(Not run)