vegan (version 1.6-7)

metaMDS: Nonmetric Multidimensional Scaling with Stable Solution from Random Starts, Axis Scaling and Species Scores

Description

Function metaMDS uses isoMDS to perform Nonmetric Multidimensional Scaling (NMDS), but tries to find a stable solution using several random starts (function initMDS). In addition, it standardizes the scaling in the result, so that the configurations are easier to interpret (function postMDS), and adds species scores to the site ordination (function wascores).

Usage

metaMDS(comm, distance = "bray", k = 2, trymax = 20, autotransform =TRUE,
        noshare = 0.1, expand = TRUE, trace = 1, plot = FALSE,
        previous.best, ...)
## S3 method for class 'metaMDS':
plot(x, choices = c(1, 2), type = "p", ...)
## S3 method for class 'metaMDS':
points(x, display = c("sites", "species"),
        choices = c(1,2), ...)
## S3 method for class 'metaMDS':
text(x, display = c("sites", "species"),
        choices = c(1,2), ...)
initMDS(x, k=2)
postMDS(X, dist, pc=TRUE, center=TRUE, halfchange=TRUE, threshold=0.8,
        nthreshold=10, plot=FALSE)

Arguments

comm

Community data.

distance

Dissimilarity index used in vegdist.

k

Number of dimensions in isoMDS.

trymax

Maximum number of random starts in search of stable solution.

autotransform

Use simple heuristics for possible data transformation (see below).

noshare

Proportion of site pairs with no shared species to trigger stepacross to find flexible shortest paths among dissimilarities.

expand

Expand weighted averages of species in wascores.

trace

Trace the function; trace = 2 or higher will be more voluminous.

plot

Graphical tracing: plot interim results. You may want to set par(ask = TRUE) with this option.

previous.best

Start searches from a previous solutions. Otherwise use isoMDS default for the starting solution.

x

Dissimilarity matrix for isoMDS or plot object.

choices

Axes shown.

type

Plot type: "p" for points, "t" for text, and "n" for axes only.

display

Display "sites" or "species".

X

Configuration from multidimensional scaling.

dist

Dissimilarity matrix used in multidimensional scaling.

pc

Rotate to principal components.

center

Centre the configuration.

halfchange

Scale axes to half-change units.

threshold

Largest dissimilarity used in half-change scaling.

nthreshold

Minimum number of points in half-change scaling.

...

Other parameters passed to functions.

Value

• Function metaMDS returns an object of class metaMDS. The final site ordination is stored in the item points, and species ordination in the item species. The other items store the information on the steps taken by the function. The object has print, plot, points and text methods. Function initMDS returns a random configuration which is intended to be used within isoMDS only. Function postMDS returns the result of isoMDS with updated configuration.

Details

Non-metric Multidimensional Scaling (NMDS) is commonly regarded as the most robust unconstrained ordination method in community ecology (Minchin 1987). Functions initMDS and postMDS together with some other functions are intended to help run NMDS wit isoMDS like recommended by Minchin (1987). Function metaMDS combines all recommendations into one command for a shotgun style analysis. The steps in metaMDS are:

1. Transformation: If the data values are larger than common class scales, the function performs a Wisconsin double standardization usingwisconsin. If the values look very large, the function also performssqrttransformation. Both of these standardization are generally found to improve the results. However, the limits are completely arbitrary (at present, data maximum 50 triggerssqrtand >9 triggerswisconsin). If you want to have a full control of the analysis, you should setautotransform = FALSEand make explicit standardization in the command.
2. Choice of dissimilarity: For a good result, you should use dissimilarity indices that have a good rank order relation to ordering sites along gradients (Faith et al. 1987). The default is Bray dissimilarity, because it often is the test winner. However, any other dissimilarity index invegdistcan be used. Functionrankindexcan be used for finding the test winner for you data and gradients.
3. Step-across dissimilarities: Ordination may be very difficult if a large proportion of sites have no shared species. In this case, the results may be improved withstepacrossdissimilarities, or flexible shortest paths among all sites. Thestepacrossis triggered by optionnoshare. If you do not like manipulation of original distances, you should setnoshare = 1.
4. NMDS with random starts: NMDS easily gets trapped into local optima, and you must start NMDS several times from random start to be confident that you have found the global solution. The default inisoMDSis to start from metric scaling (withcmdscale) which typically is close to a local optimum. The strategy inmetaMDSis to first run a defaultisoMDS, or use theprevious.bestsolution if supplied, and take its solution as the standard (Run 0). ThenmetaMDSstartsisoMDSfrom several random starts (maximum number is given bytrymax). If a solution is better (has a lower stress) than the previous standard, it is taken as the new standard. If the solution is better or close to a standard,metaMDScompares two solutions using Procrustes analysis using functionprocrusteswith optionsymmetric = TRUE. If the two solutions are very similar in their Procrustesrmseand the largest residual is very small, the solutions are regarded as convergent and the best one is saved. Please note that the conditions are stringent, and you may have found good and relatively stable solutions although the function is not yet satisfied. Settingtrace = TRUEwill monitor the final stresses, andplot = TRUEwill display Procrustes overlay plots from each comparison.
5. Scaling of the results:metaMDSwill runpostMDSfor the final result. FunctionpostMDSprovides the following ways of ``fixing'' the indeterminacy of scaling and orientation of axes in NMDS: Centring moves the origin to the average of the axes. Principal components rotate the configuration so that the variance of points is maximized on first dimension. Half-change scaling scales the configuration so that one unit means halving of community similarity from replicate similarity. Half-change scaling is based on closer dissimilarities where the relation between ordination distance and community dissimilarity is rather linear; the limit is controlled by parameterthreshold. If there are enough points below this threshold (controlled by the the parameternthreshold), dissimilarities are regressed on distances. The intercept of this regression is taken as the replicate dissimilarity, and half-change is the distance where similarity halves according to linear regression. Obviously the method is applicable only for dissimilarity indices scaled to$0 \ldots 1$, such as Kulczynski, Bray-Curtis and Canberra indices.
6. Species scores: Function adds the species scores to the final solution as weighted averages using functionwascoreswith given value of parameterexpand.

References

Faith, D. P, Minchin, P. R. and Belbin, L. (1987). Compositional dissimilarity as a robust measure of ecological distance. Vegetatio 69, 57--68.

Minchin, P.R. (1987) An evaluation of relative robustness of techniques for ecological ordinations. Vegetatio 71, 145-156.

See Also

isoMDS, decostand, wisconsin, vegdist, rankindex, stepacross, procrustes, wascores, ordiplot.

Examples

## The recommended way of running NMDS (Minchin 1987)
##
data(dune)
library(MASS) ## isoMDS
# NMDS
sol <- metaMDS(dune)
sol
plot(sol, type="t")