# wascores: Weighted Averages Scores for Species In pattakosn/Rworkshop: Community Ecology Package

## Description

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

## Usage

 ```1 2``` ```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

`monoMDS`, `cca`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```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) ```