R: Weighted Averages Scores for Species

wascores {vegan} | R Documentation

## Weighted Averages Scores for Species

### Description

Computes Weighted Averages scores of species for ordination configuration or for environmental variables.

### Usage

    wascores(x, w, expand=FALSE)
    eigengrad(x, w)

### Arguments

`x` | Environmental variables or ordination scores.
`w` | Weights: species abundances.
`expand` | Expand weighted averages so that they have the same weighted variance as the corresponding environmental variables.

### Details

Function `wascores` computes weighted averages. Weighted averages ‘shrink’: they cannot be more extreme than values used for calculating the averages. With `expand = TRUE`, the function ‘dehsrinks’ the weighted averages by making their biased weighted variance equal to the biased weighted variance of the corresponding environmental variable. Function `eigengrad` returns the inverses of squared expansion factors or the attribute `shrinkage` of the `wascores` result for each environmental gradient. This is equal to the constrained eigenvalue of `cca` when only this one gradient was used as a constraint, and describes the strength of the gradient.

### Value

Function `wascores` returns a matrix where species define rows and ordination axes or environmental variables define columns. If `expand = TRUE`, attribute `shrinkage` has the inverses of squared expansion factors or `cca` eigenvalues for the variable. Function `eigengrad` returns only the `shrinkage` attribute.

### Author(s)

Jari Oksanen

### See Also

`monoMDS`, `cca`.

### Examples

    data(varespec)
    data(varechem)
    vare.dist <- vegdist(wisconsin(varespec))
    vare.mds <- monoMDS(vare.dist)
    vare.points <- postMDS(vare.mds$points, vare.dist)
    vare.wa <- wascores(vare.points, varespec)
    plot(scores(vare.points), pch="+", asp=1)
    text(vare.wa, rownames(vare.wa), cex=0.8, col="blue")
    ## Omit rare species (frequency <= 4)
    freq <- apply(varespec>0, 2, sum)
    plot(scores(vare.points), pch="+", asp=1)
    text(vare.wa[freq > 4,], rownames(vare.wa)[freq > 4],cex=0.8,col="blue")
    ## Works for environmental variables, too.
    wascores(varechem, varespec)
    ## And the strengths of these variables are:
    eigengrad(varechem, varespec)

[Package vegan version 2.4-3 Index]