metaMDS {vegan} | R Documentation

## 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, display = c("sites", "species"), choices = c(1, 2),
         type = "p", shrink = FALSE,  ...)
    ## S3 method for class 'metaMDS':
    points(x, display = c("sites", "species"),
            choices = c(1,2), shrink = FALSE, select, ...)
    ## S3 method for class 'metaMDS':
    text(x, display = c("sites", "species"), labels,
            choices = c(1,2), shrink = FALSE, select, ...)
    ## S3 method for class 'metaMDS':
    scores(x, display = c("sites", "species"), shrink = FALSE,
            choices, ...)
    metaMDSdist(comm, distance = "bray", autotransform = TRUE, noshare = 0.1,
        trace = 1, commname, zerodist = "fail", distfun = vegdist, ...)
    metaMDSiter(dist, k = 2, trymax = 20, trace = 1, plot = FALSE, previous.best,
        ...)
    initMDS(x, k=2)
    postMDS(X, dist, pc=TRUE, center=TRUE, halfchange=TRUE, threshold=0.8,
            nthreshold=10, plot=FALSE, ...)
    metaMDSredist(object, ...)

### 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"`.
`shrink` | Shrink back species scores if they were expanded originally.
`labels` | Optional test to be used instead of row names.
`select` | Items to be displayed. This can either be a logical vector which is `TRUE` for displayed items or a vector of indices of displayed items.
`X` | Configuration from multidimensional scaling.
`commname` | The name of `comm`: should not be given if the function is called directly.
`zerodist` | Handling of zero dissimilarities: either `"fail"` or `"add"` a small positive value.
`distfun` | Dissimilarity function. Any function returning a `dist` object and accepting argument `method` can be used (but some extra arguments may cause name conflicts).
`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.
`object` | A result object from `metaMDS`.
`...` | Other parameters passed to functions.

### 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 using `wisconsin`. If the values look very large, the function also performs `sqrt` transformation. Both of these standardization are generally found to improve the results. However, the limits are completely arbitrary (at present, data maximum 50 triggers `sqrt` and >9 triggers `wisconsin`). If you want to have a full control of the analysis, you should set `autotransform = FALSE` and 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 in `vegdist` can be used. Function `rankindex` can 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 with `stepacross` dissimilarities, or flexible shortest paths among all sites. The `stepacross` is triggered by option `noshare`. If you do not like manipulation of original distances, you should set `noshare = 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 in `isoMDS` is to start from metric scaling (with `cmdscale`) which typically is close to a local optimum. The strategy in `metaMDS` is to first run a default `isoMDS`, or use the `previous.best` solution if supplied, and take its solution as the standard (`Run 0`). Then `metaMDS` starts `isoMDS` from several random starts (maximum number is given by `trymax`). 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, `metaMDS` compares two solutions using Procrustes analysis using function `procrustes` with option `symmetric = TRUE`. If the two solutions are very similar in their Procrustes `rmse` and 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. Setting `trace = TRUE` will monitor the final stresses, and `plot = TRUE` will display Procrustes overlay plots from each comparison.
5. Scaling of the results: `metaMDS` will run `postMDS` for the final result. Function `postMDS` provides 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 parameter `threshold`. If there are enough points below this threshold (controlled by the the parameter `nthreshold`), 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 ... 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 function `wascores` with given value of parameter `expand`. The expansion of weighted averages can be undone with `shrink = TRUE` in `plot` or `scores` 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. Functions `metaMDSdist` and `metaMDSredist` return `vegdist` objects. Function `initMDS` returns a random configuration which is intended to be used within `isoMDS` only. Functions `metaMDSiter` and `postMDS` returns the result of `isoMDS` with updated configuration.

### Note

Function `metaMDS` is a simple wrapper for `isoMDS` and some support functions. You can call these support functions separately for better control of results. Data transformation, dissmilarities and possible `stepacross` are made in function `metaMDSdist` which returns a dissimilarity result. Iterative search (with starting values from `initMDS`) is made in `metaMDSiter`. Processing of result configuration is done in `postMDS`, and species scores added by `wascores`. If you want to be more certain of reaching a global solution, you can compare results from several independent runs. You can also continue analysis from previous results or from your own configuration. Function does not save the used dissimilarity matrix, but `metaMDSredist` tries to reconstruct the used dissimilarities with original data transformation and possible `stepacross`.

### Author(s)

Jari Oksanen

### 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")

[Package vegan version 1.8-8 Index]