Standardization Methods for Community Ecology

Description

The function provides some popular (and effective) standardization methods for community ecologists.

Usage

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decostand(x, method, MARGIN, range.global, logbase = 2, na.rm=FALSE, ...)
wisconsin(x)

Arguments

x

Community data, a matrix-like object.

method

Standardization method. See Details for available options.

MARGIN

Margin, if default is not acceptable. 1 = rows, and 2 = columns of x.

range.global

Matrix from which the range is found in method = "range". This allows using same ranges across subsets of data. The dimensions of MARGIN must match with x.

logbase

The logarithm base used in method = "log".

na.rm

Ignore missing values in row or column standardizations.

...

Other arguments to the function (ignored).

Details

The function offers following standardization methods for community data:

  • total: divide by margin total (default MARGIN = 1).

  • max: divide by margin maximum (default MARGIN = 2).

  • freq: divide by margin maximum and multiply by the number of non-zero items, so that the average of non-zero entries is one (Oksanen 1983; default MARGIN = 2).

  • normalize: make margin sum of squares equal to one (default MARGIN = 1).

  • range: standardize values into range 0 ... 1 (default MARGIN = 2). If all values are constant, they will be transformed to 0.

  • standardize: scale x to zero mean and unit variance (default MARGIN = 2).

  • pa: scale x to presence/absence scale (0/1).

  • chi.square: divide by row sums and square root of column sums, and adjust for square root of matrix total (Legendre & Gallagher 2001). When used with the Euclidean distance, the distances should be similar to the Chi-square distance used in correspondence analysis. However, the results from cmdscale would still differ, since CA is a weighted ordination method (default MARGIN = 1).

  • hellinger: square root of method = "total" (Legendre & Gallagher 2001).

  • log: logarithmic transformation as suggested by Anderson et al. (2006): log_b (x) + 1 for x > 0, where b is the base of the logarithm; zeros are left as zeros. Higher bases give less weight to quantities and more to presences, and logbase = Inf gives the presence/absence scaling. Please note this is not log(x+1). Anderson et al. (2006) suggested this for their (strongly) modified Gower distance (implemented as method = "altGower" in vegdist), but the standardization can be used independently of distance indices.

Standardization, as contrasted to transformation, means that the entries are transformed relative to other entries.

All methods have a default margin. MARGIN=1 means rows (sites in a normal data set) and MARGIN=2 means columns (species in a normal data set).

Command wisconsin is a shortcut to common Wisconsin double standardization where species (MARGIN=2) are first standardized by maxima (max) and then sites (MARGIN=1) by site totals (tot).

Most standardization methods will give nonsense results with negative data entries that normally should not occur in the community data. If there are empty sites or species (or constant with method = "range"), many standardization will change these into NaN.

Value

Returns the standardized data frame, and adds an attribute "decostand" giving the name of applied standardization "method".

Note

Common transformations can be made with standard R functions.

Author(s)

Jari Oksanen, Etienne Laliberté (method = "log").

References

Anderson, M.J., Ellingsen, K.E. & McArdle, B.H. (2006) Multivariate dispersion as a measure of beta diversity. Ecology Letters 9, 683–693.

Legendre, P. & Gallagher, E.D. (2001) Ecologically meaningful transformations for ordination of species data. Oecologia 129, 271–280.

Oksanen, J. (1983) Ordination of boreal heath-like vegetation with principal component analysis, correspondence analysis and multidimensional scaling. Vegetatio 52, 181–189.

Examples

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data(varespec)
sptrans <- decostand(varespec, "max")
apply(sptrans, 2, max)
sptrans <- wisconsin(varespec)

## Chi-square: PCA similar but not identical to CA.
## Use wcmdscale for weighted analysis and identical results.
sptrans <- decostand(varespec, "chi.square")
plot(procrustes(rda(sptrans), cca(varespec)))

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