EqRao: Third decomposition of diversity introduced in Pavoine et al....

In vmikk/phylonest: Equivalent numbers for biodiversity in a nested hierarchy of multiple scales.

Description

Use when the interest is in beta diversity expressed in terms of pairwise dissimilarities among sites (within regions) and among regions and/or sites within a region have different weights and regions have different weights (due, e.g., to uneven sampling pressures, uneven size of sites or regions).

Usage

EqRao(
  df,
  dis = NULL,
  structures = NULL,
  option = c("eq", "normed1", "normed2"),
  formula = c("QE", "EDI"),
  wopt = c("even", "speciesab"),
  tol = 1e-08,
  metmean = c("harmonic", "arithmetic")
)

Arguments

df	Dataframe or matrix with sites as rows and species as columns. Entries are abundances of species within sites.
dis	Dissimilarity among species (NULL or class 'dist').
structures	Data frame that contains the name of the group (row) of an level (column) to which the site belongs. Sites in structures should be in the same order as in df. Default is NULL.
option	Rescaling type ("eq", "normed1" or "normed2").
formula	Quadratic entropy formula ("QE", "EDI"). "QE" is default.
wopt	Site weighting type ("even", "speciesab"). Default is "even".
tol	A tolerance threshold (a value less than tol is considered equal to zero).
metmean	Mean type - "arithmetic" or "harmonic" (default).

Details

Rescaling types (argument 'option'):

• "eq" - the diversity components are given in terms of equivalent number of species, sites, regions etc.;

• "normed1" - the normed components of diversity will be returned with formula (1 – 1 / E) / (1 - 1 / Emax) [de Bello et al., 2010, Eqn 14];

• "normed2" - the normed components of diversity will be returned with formula (E – 1) / (Emax - 1) [Villéger et al., 2012].

For Eβ, Emax = M (the number of sites). For Eα and Eγ, Emax=S (the number of species in the data set).

Formula type (argument 'formula'):

• "QE" - the definition of the quadratic entropy is following Rao (1982);

• "EDI" - the Euclidean Diversity Index of Champely and Chessel (2002).

Site weighting type (argument 'wopt'):

• "speciesab" - the sites will be weighted by their sum of species’ abundances;

• "even" - the sites will be evenly weighted within the factors defined by the parameter 'structures'.

Mean type (argument 'metmean'):

• "arithmetic" - the calculation of Eβ will be performed using an arithmetic mean;

• "harmonic" - the calculation of Eβ will be performed using an harmonic mean.

For the associated permutation test see randtestEqRao.

Value

A data frame with each component of the selected diversity decomposition.

Author(s)

Sandrine Pavoine, Eric Marcon, Carlo Ricotta.

References

Pavoine S., Marcon E., Ricotta C. (2016) ‘Equivalent numbers’ for species, phylogenetic or functional diversity in a nested hierarchy of multiple scales. Methods Ecol Evol, 7: 1152-1163. DOI:10.1111/2041-210X.12591

de Bello F., Lavergne S., Meynard C.N., Lepš J., Thuiller W. (2010) The partitioning of diversity: showing Theseus a way out of the labyrinth. Journal of Vegetation Science, 21: 992-1000. DOI: 10.1111/j.1654-1103.2010.01195.x

Villéger S., Miranda J.R., Hernandez D.F., Mouillot, D. (2012) Low functional beta-diversity despite high taxonomic beta-diversity among tropical estuarine fish communities. PLoS One, 7, e40679. DOI: 10.1371/journal.pone.0040679

Champely S., Chessel D. (2002) Measuring biological diversity using Euclidean metrics. Environmental and Ecological Statistics, 9, 167-177. DOI: 10.1023/A:1015170104476

Rao C.R. (1982) Diversity and dissimilarity coefficients: a unified approach. Theoretical Population Biology, 21, 24-43. DOI: 10.1016/0040-5809(82)90004-1

See Also

randtestEqRao, EqRS, EqRSintra.

Examples

data(macroloire)
# Taxonomic dissimilarities among species:
dTaxo <- dist.taxo(macroloire$taxo)^2/2
dTaxo <- dTaxo/max(dTaxo)
# Size-based dissimilarities among species
dSize <- dist.prop(macroloire$traits[ ,1:4], method = 2)
# Dissimilarities among species in terms of feeding categories
dFeed <- dist.prop(macroloire$traits[ ,5:11], method = 2)
# Dissimilarities among species in terms of both size and feeding categories
dSF <- (dSize+dFeed)/2

# Table with sites as rows (stations), species as columns and abundances as entries
ab <- as.data.frame(t(macroloire$fau))
# Table with sites as rows and one column only. Entries indicate the geological region associated with each site
stru <- macroloire$envir["Morphoregion"]

EqRao(ab, , stru, option="eq")
EqRao(ab, dTaxo, stru, formula = "QE", option="eq")
EqRao(ab, dSize, stru, formula = "QE", option="eq")
EqRao(ab, dFeed, stru, formula = "QE", option="eq")
EqRao(ab, dSF, stru, formula = "QE", option="eq")

EqRao(ab, , stru, option="normed2")
EqRao(ab, dTaxo, stru, formula = "QE", option="normed2")
EqRao(ab, dSize, stru, formula = "QE", option="normed2")
EqRao(ab, dFeed, stru, formula = "QE", option="normed2")
EqRao(ab, dSF, stru, formula = "QE", option="normed2")

vmikk/phylonest documentation built on Nov. 20, 2019, 4:17 p.m.