
MINIMUM SPANNING TREES
Minimum Spanning Trees (MST) and the associated Minimum Spanning Networks/Forests (MSN) are a useful method of visually displaying relationships between samples, whether those samples are biogeographic or taxonomic in nature (Figure 1;
Gower and Ross 1969). The MST is closely related to the final product of a Single Linkage Cluster Analysis (SLCA;
Sneath 1957;
Gower and Ross 1969) and connects all the points in a sample with the minimum number of connections (n  1). The method used to find the tree—also the most common method—is to begin with a single point at random, and begin connecting to the closest point not already in the tree. When there is more than one equally close point, one will be chosen at random. The randomness aspect of the connections can be disabled in the options for the function, if so desired, such that the first listed point will be used as the start for the tree and if more than one point is equally close, the first listed will be chosen. Although there are other MST functions available for R (Oksanen et al. 2010), those other methods did not allow for a random start or random selection of equally minimal branches. The MSN is closely related to the MST; the MSN is a combination of all the possible MSTs. This could mean that if there was only one shortest MST that the MSN would be identical.
