bioenv.RdFunction finds the best subset of environmental variables, so that the Euclidean distances of scaled environmental variables have the maximum (rank) correlation with community dissimilarities.
# S3 method for default bioenv(comm, env, method = "spearman", index = "bray", upto = ncol(env), trace = FALSE, partial = NULL, metric = c("euclidean", "mahalanobis", "manhattan", "gower"), parallel = getOption("mc.cores"), ...) # S3 method for formula bioenv(formula, data, ...) bioenvdist(x, which = "best")
| comm | Community data frame or a dissimilarity object or a square matrix that can be interpreted as dissimilarities. |
|---|---|
| env | Data frame of continuous environmental variables. |
| method | The correlation method used in |
| index | The dissimilarity index used for community data ( |
| upto | Maximum number of parameters in studied subsets. |
| formula, data | Model |
| trace | Trace the calculations |
| partial | Dissimilarities partialled out when inspecting
variables in |
| metric | Metric used for distances of environmental distances. See Details. |
| parallel | Number of parallel processes or a predefined socket
cluster. With |
| x |
|
| which | The number of the model for which the environmental
distances are evaluated, or the |
| ... | Other arguments passed to |
The function calculates a community dissimilarity matrix using
vegdist. Then it selects all possible subsets of
environmental variables, scales the variables, and
calculates Euclidean distances for this subset using
dist. The function 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 argument metric defines distances in the given set of
environmental variables. With metric = "euclidean", the
variables are scaled to unit variance and Euclidean distances are
calculated. With metric = "mahalanobis", the Mahalanobis
distances are calculated: in addition to scaling to unit variance,
the matrix of the current set of environmental variables is also
made orthogonal (uncorrelated). With metric = "manhanttan",
the variables are scaled to unit range and Manhattan distances are
calculated, so that the distances are sums of differences of
environmental variables. With metric = "gower", the Gower
distances are calculated using function
daisy. This allows also using factor
variables, but with continuous variables the results are equal to
metric = "manhattan".
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.
Function bioenvdist recalculates the environmental distances
used within the function. The default is to calculate distances for
the best model, but the number of any model can be given.
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.
The function returns an object of class bioenv with a
summary method.
Clarke, K. R & Ainsworth, M. 1993. A method of linking multivariate community structure to environmental variables. Marine Ecology Progress Series, 92, 205--219.
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 depending on the used metric, and you must do the same in
mantel for comparable results (the standardized data are
returned as item x in the result object). It is safest to use
bioenvdist to extract the environmental distances that really
were used within bioenv. NB., bioenv selects variables
to maximize the Mantel correlation, and significance tests based on
a priori selection of variables are biased.
vegdist, dist, cor
for underlying routines, monoMDS and
metaMDS for ordination, procrustes for
Procrustes analysis, protest for an alternative, and
rankindex for studying alternatives to the default
Bray-Curtis index.
# 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#> #> Call: #> bioenv(formula = wisconsin(varespec) ~ log(N) + P + K + Ca + pH + Al, data = varechem) #> #> Subset of environmental variables with best correlation to community data. #> #> Correlations: spearman #> Dissimilarities: bray #> Metric: euclidean #> #> Best model has 3 parameters (max. 6 allowed): #> P Ca Al #> with correlation 0.4004806 #>summary(sol)#> size correlation #> P 1 0.2513 #> P Al 2 0.4004 #> P Ca Al 3 0.4005 #> P Ca pH Al 4 0.3619 #> log(N) P Ca pH Al 5 0.3216 #> log(N) P K Ca pH Al 6 0.2822