Hierarchical clusters of vegetation types

In this paper, we examine possible sources of hierarchical (nested) structure in vegetation data. We then use the Minimum Message length principle to provide a rational means of comparing hierarchical and non-hierarchical clustering. The results indicate that, with the data used, a hierarchical solution was not as efficient as a nonhierarchical one. However, the hierarchical solution seems to provide a more comprehensible solution, separating first isolated types, probably caused from unusual contingent events, then subdividing the more diverse areas before finally subdividing the less diverse. By presenting this in 3 stages, the complexity of the non-hierarchical result is avoided. The result also suggests that a hierarchical analysis may be useful in determining ‘homogeneous’ areas. Abbreviatons: MML Minimum Message Length; MUAP Modifiable unit area problem. which provides a preferable model of the variation we have observed. Hierarchies and ecology Ecologically hierarchies have attracted much attention, with studies like those of Allen and Starr (1982) and Ahl and Allen (1996), but they have been most employed in providing classifications of vegetation, often for bureaucratic purposes. As an example of one such classification we use an example from the California Vegetation Classification (Californian Department of Fish and Game, 2003). A single vegetation community is described by a code such as [6 1 . 3 1 1 . 0 2]. Here there are 4 levels in the hierarchy and the key to the code is presented in Table 1. The reason for this example is to illustrate that, in practice, ecological hierarchies may be a composite of habitat, physiognomic and floristic attributes. In contrast, our study will use only floristic data. If we cluster both species and sites we can arrange our data as a two-way table. The intersections of the 2 cluster sets can be used in a nodal analysis (Lambert and Williams 1962), and this makes any hierarchical structure much easier to identify visually. A node represents a block where a subset of species is represented strongly in a subset of sites. Quantitatively the definition can be more subtle, depending on the permissible form of variation within clusters (cf. Dale and Anderson 1973). An idealised nested structure is presented in Table 2 But do real data display such patterns? In Table 3, we show structures abstracted from Doherty and Coops (1995) concerning Eucalyptus species in South-eastern New South Wales. These were sorted using a numerical agglomerative clustering and a Bray-Curtis similarity measure. The concentration of entries in each nodal call was visually assessed. The results from qualitative and quantitative data differ, and neither shows any marked nested structure. Both do show a general gradient pattern although in neither case is a single gradient sufficient. A more complex situation is shown in Table 4, which is adapted from Dale and Quadraccia (1973) after Lang (1970). The organisation here was obtained by manual sorting and encompasses all species, not just the trees. While there is certainly some nesting, the patterns of nodes are clearly quite complex, with a reticulate pattern more likely than any binary tree structure. The final example is taken from Webb et al. (1967) and records the vegetation in 10 plots for 12 years (Table 5). As with all the other examples, it is possible to obtain a hierarchy from the relationships between the groups. However, it is not obvious that the nesting could be easily described monothetically, and in several cases a common substructure would be repeated, complicating the tree structure. These examples show us that, while a hierarchy can be used to organise data, it will often suffer from defects as a representation of the nodal pattern. One particular problem is that of duplication where a similar subtree recurs at several places in the tree. In supervised clustering this has been addressed by introducing decision graphs, but such a reticulate pattern has not been commonly sought in unsupervised clustering. Similarly, insistence on a hierarchical structure could result in fragmentation of the data into numerous small clusters. It seems that vegetation hovers tantalising between hierarchy and other structure, so that a means of determining which is the ‘better’ model is highly desirable. It is this task that the MML principle permits us to accomplish.