evoeveparam {adiv}

Parametric Indices of Phylogenetic evenness

Description

Function evoeveparam calculates phylogenetic evenness (evenness in features, which are branch units of a phylogenetic tree) in communities. It uses parametric indices derived from Tsallis and Hill compositional indices, and named qfeveHCDT, qfeveHill, and qfeveRenyi in Pavoine and Ricotta (2019). evoeveparam can also be applied to functional trees rather than phylogenies, to calculate a functional evenness. The function plot.evoeveparam plots the results of function evoeveparam.

Usage

evoeveparam(phyl, comm, method = c("hill", "tsallis", "renyi"), 
    q = 2, option = 1:3, H = NULL, tol = 1e-8)

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

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 (object phyl) where they are the tips.

method

a string: either "hill" for qfeveHill using the Hill numbers (Hill 1973), "tsallis" for qfeveHCDT using the Tsallis or HCDT entropy (Harvda and Charvat 1967; Daroczy 1970; Tsallis 1988), or "renyi" for qfeveRenyi using 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 of functions qfeveHCDT, qfeveHill, and qfeveRenyi.

option

an integer (either 1, 2 or 3). If 1, the (Hill, Tsallis or Renyi) diversity index is divided by the value it would have if species had same abundance and were independent, if 2, the diversity is divided by the value it would have if species had same abundance, were independent, and at the maximum observed distance from tip to root, if 3, the diversity is divided by the value it would have if species had same abundance, were independent, and at a distance equal to H from the root of the tree. Options 1 and 2 are equivalent in case of an ultrametric tree.

H

a numeric; H must be higher than the largest observed distance from tip to root.

tol

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

x

an object of class evoeveparam obtained with function evoeveparam.

legend

a logical. If TRUE a legend is given with the colour, the type of line (etc.) used to define the evenness 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 evenness".

type

a string to be passed to the graphic argument type of functions plot and lines used to draw the evenness 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 evenness 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 evenness 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 evenness level of each community.

...

other arguments can be added and passed to the functions plot and lines used to draw the graphic.

Details

Function evoeveparam calculates feature evenness (features = branch units on a phylogenetic [or functional] tree) using parametric indices qfeveHCDT (with method=tsallis), qfeveHill (with method=hill), qfeveRenyi (with method=renyi) developed in Pavoine and Ricotta (2019). Note that Pavoine and Ricotta (2019) recommend the use of index qfeveHill (with method=hill).

Value

If only one value of q is given, the function evoeveparam returns a vector with the evenness values for 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;

eve

a data frame with the phylogenetic evenness in each community calculated for all values of q.

The function plot.evoeveparam 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

evodivparam, evouniparam

Examples

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

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

}

## End(Not run)