Standardization Methods for Community Ecology

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

Usage

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

Arguments

x: Community data, a matrix-like object. For decobackstand standardized data.
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. The NA values remain as NA, but they are ignored in standardization of other values.
zap: Make near-zero values exact zeros to avoid negative values and exaggerated estimates of species richness.
...: 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).
frequency: divide by margin total 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.
rank, rrank: rank replaces abundance values by their increasing ranks leaving zeros unchanged, and rrank is similar but uses relative ranks with maximum 1 (default MARGIN = 1). Average ranks are used for tied values.
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.
alr: Additive log ratio ("alr") transformation (Aitchison 1986) reduces data skewness and compositionality bias. The transformation assumes positive values, pseudocounts can be added with the argument pseudocount. One of the rows/columns is a reference that can be given by reference (name of index). The first row/column is used by default (reference = 1). Note that this transformation drops one row or column from the transformed output data. The alr transformation is defined formally as follows: $$alr = [log\frac{x_1}{x_D}, ..., log\frac{x_{D-1}}{x_D}]$$ where the denominator sample $x_D$ can be chosen arbitrarily. This transformation is often used with pH and other chemistry measurenments. It is also commonly used as multinomial logistic regression. Default MARGIN = 1 uses row as the reference.
clr: centered log ratio ("clr") transformation proposed by Aitchison (1986) and it is used to reduce data skewness and compositionality bias. This transformation has frequent applications in microbial ecology (see e.g. Gloor et al., 2017). The clr transformation is defined as: $$clr = log\frac{x}{g(x)} = log x - log g(x)$$ where $x$ is a single value, and g(x) is the geometric mean of $x$. The method can operate only with positive data; a common way to deal with zeroes is to add pseudocount (e.g. the smallest positive value in the data), either by adding it manually to the input data, or by using the argument pseudocount as in decostand(x, method = "clr", pseudocount = 1). Adding pseudocount will inevitably introduce some bias; see the rclr method for one available solution.
rclr: robust clr ("rclr") is similar to regular clr (see above) but allows data that contains zeroes. This method does not use pseudocounts, unlike the standard clr. The robust clr (rclr) divides the values by geometric mean of the observed features; zero values are kept as zeroes, and not taken into account. In high dimensional data, the geometric mean of rclr approximates the true geometric mean; see e.g. Martino et al. (2019) The rclr transformation is defined formally as follows: $$rclr = log\frac{x}{g(x > 0)}$$ where $x$ is a single value, and $g(x > 0)$ is the geometric mean of sample-wide values $x$ that are positive (> 0).

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.

Function decobackstand can be used to transform standardized data back to original. This is not possible for all standardization and may not be implemented to all cases where it would be possible. There are round-off errors and back-transformation is not exact, and it is wise not to overwrite the original data. With zap=TRUE original zeros should be exact.

Value

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

Author

Jari Oksanen, Etienne Laliberté (method = "log"), Leo Lahti (alr, "clr" and "rclr").

Note

Common transformations can be made with standard R functions.

References

Aitchison, J. The Statistical Analysis of Compositional Data (1986). London, UK: Chapman & Hall.

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

Egozcue, J.J., Pawlowsky-Glahn, V., Mateu-Figueras, G., Barcel'o-Vidal, C. (2003) Isometric logratio transformations for compositional data analysis. Mathematical Geology 35, 279–300.

Gloor, G.B., Macklaim, J.M., Pawlowsky-Glahn, V. & Egozcue, J.J. (2017) Microbiome Datasets Are Compositional: And This Is Not Optional. Frontiers in Microbiology 8, 2224.

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

Martino, C., Morton, J.T., Marotz, C.A., Thompson, L.R., Tripathi, A., Knight, R. & Zengler, K. (2019) A novel sparse compositional technique reveals microbial perturbations. mSystems 4, 1.

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

Examples

data(varespec)
sptrans <- decostand(varespec, "max")
apply(sptrans, 2, max)
#> Callvulg Empenigr Rhodtome Vaccmyrt Vaccviti Pinusylv Descflex Betupube 
#>        1        1        1        1        1        1        1        1 
#> Vacculig Diphcomp   Dicrsp Dicrfusc Dicrpoly Hylosple Pleuschr Polypili 
#>        1        1        1        1        1        1        1        1 
#> Polyjuni Polycomm Pohlnuta Ptilcili Barbhatc Cladarbu Cladrang Cladstel 
#>        1        1        1        1        1        1        1        1 
#> Cladunci Cladcocc Cladcorn Cladgrac Cladfimb Cladcris Cladchlo Cladbotr 
#>        1        1        1        1        1        1        1        1 
#> Cladamau   Cladsp Cetreric Cetrisla Flavniva Nepharct   Stersp Peltapht 
#>        1        1        1        1        1        1        1        1 
#> Icmaeric Cladcerv Claddefo Cladphyl 
#>        1        1        1        1 
sptrans <- wisconsin(varespec)

# CLR transformation for rows, with pseudocount
varespec.clr <- decostand(varespec, "clr", pseudocount=1)

# ALR transformation for rows, with pseudocount and reference sample
varespec.alr <- decostand(varespec, "alr", pseudocount=1, reference=1)

## 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)))