bioenv {vegan} R Documentation

## Best Subset of Environmental Variables with Maximum (Rank) Correlation with Community Dissimilarities

### Description

Function finds the best subset of environmental variables, so that the Euclidean distances of scaled environmental variables have the maximum (rank) correlation with community dissimilarities.

### Usage

```## Default S3 method:
bioenv(comm, env, method = "spearman", index = "bray",
upto = ncol(env), trace = FALSE, partial = NULL, ...)
## S3 method for class 'formula':
bioenv(formula, data, ...)
```

### Arguments

 `comm` Community data frame. `env` Data frame of continuous environmental variables. `method` The correlation method used in `cor`. `index` The dissimilarity index used for community data in `vegdist`. `upto` Maximum number of parameters in studied subsets. `formula, data` Model `formula` and data. `trace` Trace the advance of calculations `partial` Dissimilarities partialled out when inspecting variables in `env`. `...` Other arguments passed to `cor`.

### Details

The function calculates a community dissimilarity matrix using `vegdist`. Then it selects all possible subsets of environmental variables, `scale`s the variables, and calculates Euclidean distances for this subset using `dist`. Then it finds the correlation between community dissimilarities and environmental distances, and for each size of subsets, saves the best result. There are 2^p-1 subsets of p variables, and an exhaustive search may take a very, very, very long time (parameter `upto` offers a partial relief).

The function can be called with a model `formula` where the LHS is the data matrix and RHS lists the environmental variables. The formula interface is practical in selecting or transforming environmental variables.

With argument `partial` you can perform “partial” analysis. The partializing item must be a dissimilarity object of class `dist`. The `partial` item can be used with any correlation `method`, but it is strictly correct only for Pearson.

Clarke & Ainsworth (1993) suggested this method to be used for selecting the best subset of environmental variables in interpreting results of nonmetric multidimensional scaling (NMDS). They recommended a parallel display of NMDS of community dissimilarities and NMDS of Euclidean distances from the best subset of scaled environmental variables. They warned against the use of Procrustes analysis, but to me this looks like a good way of comparing these two ordinations.

Clarke & Ainsworth wrote a computer program BIO-ENV giving the name to the current function. Presumably BIO-ENV was later incorporated in Clarke's PRIMER software (available for Windows). In addition, Clarke & Ainsworth suggested a novel method of rank correlation which is not available in the current function.

### Value

The function returns an object of class `bioenv` with a `summary` method.

### Note

If you want to study the ‘significance’ of `bioenv` results, you can use function `mantel` or `mantel.partial` which use the same definition of correlation. However, `bioenv` standardizes environmental variables to unit standard deviation using function `scale` and you must do the same in `mantel` for comparable results. Further, `bioenv` selects variables to maximize the Mantel correlation, and significance tests based on a priori selection of variables are biased.

Jari Oksanen

### References

Clarke, K. R & Ainsworth, M. 1993. A method of linking multivariate community structure to environmental variables. Marine Ecology Progress Series, 92, 205–219.

`vegdist`, `dist`, `cor` for underlying routines, `isoMDS` for ordination, `procrustes` for Procrustes analysis, `protest` for an alternative, and `rankindex` for studying alternatives to the default Bray-Curtis index.

### Examples

```# The method is very slow for large number of possible subsets.
# Therefore only 6 variables in this example.
data(varespec)
data(varechem)
sol <- bioenv(wisconsin(varespec) ~ log(N) + P + K + Ca + pH + Al, varechem)
sol
summary(sol)
```

[Package vegan version 1.16-32 Index]