spantree {vegan} | R Documentation

## Minimum Spanning Tree

### Description

Function `spantree` finds a minimum spanning tree connecting all points, but disregarding dissimilarities that are at or above the threshold or `NA`.

### Usage

    spantree(dis, toolong = 0)
    ## S3 method for class 'spantree':
    cophenetic(x)
    ## S3 method for class 'spantree':
    plot(x, ord, cex = 0.7, type = "p", labels, dlim,
         FUN = sammon,  ...)
    ## S3 method for class 'spantree':
    lines(x, ord, display="sites", ...)

### Arguments

`dis` | Dissimilarity data inheriting from class `dist` or a an object, such as a matrix, that can be converted to a dissimilarity matrix. Functions `vegdist` and `dist` are some functions producing suitable dissimilarity data.
`toolong` | Shortest dissimilarity regarded as `NA`. The function uses a fuzz factor, so that dissimilarities close to the limit will be made `NA`, too. If `toolong = 0` (or negative), no dissimmilarity is regarded as too long.
`x` | A `spantree` result object.
`ord` | An ordination configuration, or an ordination result known by `scores`.
`cex` | Character expansion factor.
`type` | Observations are plotted as points with `type="p"` or `type="b"`, or as text with `type="t"`. The tree (lines) will always be plotted.
`labels` | Text used with `type="t"` or row names if this is missing.
`dlim` | A ceiling value used to highest `cophenetic` dissimilarity.
`FUN` | Ordination function to find the configuration from cophenetic dissimilarities.
`display` | Type of `scores` used for `ord`.
`...` | Other parameters passed to functions.

### Details

Function `spantree` finds a minimum spanning tree for dissimilarities (there may be several minimum spanning trees, but the function finds only one). Dissimilarities at or above the threshold `toolong` and `NA`s are disregarded, and the spanning tree is found through other dissimilarities. If the data are disconnected, the function will return a disconnected tree (or a forest), and the corresponding link is `NA`. Connected subtrees can be identified using `distconnected`.

Function `cophenetic` finds distances between all points along the tree segments. Function `plot` displays the tree over a supplied ordination configuration, and `lines` adds a spanning tree to an ordination graph. If configuration is not supplied for `plot`, the function ordinates the the cophenetic dissimilarities of the spanning tree and overlays the tree on this result. The default ordination function is `sammon` (package MASS), because Sammon scaling emphasizes structure in the neighbourhood of nodes and may be able to beautifully represent the tree (you may need to set `dlim`, and sometimes the results will remain twisted). These ordination methods do not work with disconnected trees, but you must supply the ordination configuration. Function `lines` will overlay the tree in an existing plot.

Function `spantree` uses Prim's method implemented as priority-first search for dense graphs (Sedgewick 1990). Function `cophenetic` uses function `stepacross` with option `path = "extended"`. The `spantree` is very fast, but `cophenetic` is slow in very large data sets.

### Value

Function `spantree` returns an object of class `spantree` which is a list with two vectors, each of length n-1. The number of links in a tree is one less the number of observations, and the first item is omitted. The items are

`kid` | The child node of the parent, starting from parent number two. If there is no link from the parent, value will be `NA` and tree is disconnected at the node.
`dist` | Corresponding distance. If `kid = NA`, then `dist = 0`.

### Note

In principle, minimum spanning tree is equivalent to single linkage clustering that can be performed using `hclust` or `agnes`. However, these functions combine clusters to each other and the information of the actually connected points (the ``single link'') cannot be recovered from the result. The graphical output of a single linkage clustering plotted with `ordicluster` will look very different from an equivalent spanning tree plotted with `ordispantree`.

### Author(s)

Jari Oksanen

### References

Sedgewick, R. (1990). Algorithms in C. Addison Wesley.

### See Also

`vegdist` or `dist` for getting dissimilarities, and `hclust` or `agnes` for single linkage clustering.

### Examples

    data(dune)
    dis <- vegdist(dune)
    tr <- spantree(dis)
    ## Add tree to a metric scaling
    plot(tr, cmdscale(dis))
    ## Find a configuration to display the tree neatly
    plot(tr)

[Package vegan version 1.8-6 Index]