vegan (version 2.7-6)

tolerance: Species tolerances and sample heterogeneities.

Description

Species tolerances and sample heterogeneities.

Usage

tolerance(x, ...)
# S3 method for cca
tolerance(x, choices = 1:2, which = c("species","sites"),
          scaling = "species", useN2 = TRUE, hill = FALSE, ...)
# S3 method for decorana
tolerance(x, data, choices = 1:4,
          which = c("sites", "species"), useN2 = TRUE, ...)

Value

Matrix of tolerances/heterogeneities with some additional attributes: which, scaling, and N2, the latter of which will be NA if useN2 = FALSE or N2 could not be estimated.

Author

Gavin L. Simpson and Jari Oksanen (decorana method).

Arguments

x

object of class "cca".

choices

numeric; which ordination axes to compute tolerances and heterogeneities for. Defaults to axes 1 and 2.

which

character; one of "species" or "sites", indicating whether species tolerances or sample heterogeneities respectively are computed.

scaling

character or numeric; the ordination scaling to use. See scores.cca for details.

hill

logical; if scaling is a character, these control whether Hill's scaling is used for (C)CA respectively. See scores.cca for details.

useN2

logical; should the bias in the tolerances / heterogeneities be reduced via scaling by Hill's N2?

data

Original input data used in decorana. If missing, the function tries to get the same data as used in decorana call.

...

arguments passed to other methods.

Details

Species tolerance is a measure of response widths in the ordination space and it is estimated as a weighted dispersion of species scores to their site score. It describes the specialist vs. generalist responses of species. For sampling units it is a measure of weighted dispersion of species scores within a sampling unit and describes the heterogeneity of species composition in a sampling unit. Sum of squared tolerances is a measure of weighted within-species or within-site variation, while eigenvalue is a measure of between-species or between-site variation (see Examples).

Function implements Eq 6.47 and 6.48 from the Canoco 4.5 Reference Manual (pages 178--179).

Examples

data(dune, dune.env)
mod <- cca(dune ~ ., data = dune.env)

## defaults to species tolerances
tolerance(mod)

## sample heterogeneities for CCA axes 1:6
tolerance(mod, which = "sites", choices = 1:6)
## average should be 1 with scaling = "sites", hill = TRUE
tol <- tolerance(mod, which = "sites", scaling = "sites", hill = TRUE,
   choices = 1:4)
colMeans(tol)
apply(tol, 2, sd)
## Rescaling tries to set all tolerances to 1
tol <- tolerance(decorana(dune))
colMeans(tol)
apply(tol, 2, sd)

## Relation of tolerances (within-species variation) and eigenvalues
## (between-species variation) - with adequate 'scaling'.
tol <- tolerance(mod, what = "species", scaling = "sites", choices=1:4)
w <- weights(mod, "species")
all.equal(colSums(tol^2 * w),
          1 - eigenvals(mod)[1:4])