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)
```

### 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

`isoMDS`, `cca`.

### Examples

```data(varespec)
data(varechem)
library(MASS)  ## isoMDS
vare.dist <- vegdist(wisconsin(varespec))
vare.mds <- isoMDS(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: