Our approach to validating and revising a priori state-and-transition models it to conduct cluster analysis of vegetation community composition and biological crust cover. Some authors have argued that, to focus on functional properties of plant communities such analyses should be conducted based primarily on functional rather than structural indicators. Functional groups of plants (e.g. perrennial grasses, exotic annual grasses, native palatable shrubs) rather than species-level data, are proposed as one way to describe function but would optimally be used in addition to other pertinent indicators of ecosystem function. There are two problems with ascribing state or phase membership based solely on plant functional groups: 1. Some key transitions might involve a shift in dominance among two plants in the same functional group. Despite membership in the same functional group, this represents a stark structural transformation and could represent an unmeasured functional transformation. 2. When working with existing data, rather than collecting a dataset, plant community structure data are the most commonly available detailed data, other more directly functional data are often lacking or incomplete. Therefore, we pragmatically chose to use the richest data we had, plant community structure, in addition to biological crust cover, a structural and functional indicator.
We based our analysis on the NCPN integrated dataset. To standardize the various datasets collected by different observers using different techniques, we applied two steps. 1. Removal of rare species was conducted, because these species are so infrequent they primarily introduce noise. We removed all species with fewer than 10 occurrences in EITHER desert or semi-desert shallow sandy loam. We further removed all species with fewer than 5 occurrences in semi-desert shallow sandy loam, prior to clustering. Finally we removed all species with fewer than 3 occurrences in the desert shallow sandy loam. 2. We applied a double relativization transformation. First each column (a species) is rescaled form 0 - 1. Second, each row is rescaled from 0-1. This equalizes the influence of each column, then purges the influence of total abudance in the sample.
We chose a hierarchical clustering method rather than a fuzzy clustering method because community structure data contain many zeros. In such situations, methods compatible with the Bray-Curtis distance (hierarchical clustering) are preferred over those requiring Euclidean distance (fuzzy clustering), because they do not interpret shared absences as a source of similarity among samples. We used a flexible beta linkage method with beta = - 0.25.
Based on the number of clusters in our a priori models (4), we examined results for 2 - 8 cluster solutions. Cluster analyses are subjective descriptive tools and should not be viewed as strict hypothesis tests. We used the following guidelines to select the best number of clusters: 1) Based on threshold theory, that intermediates between states are unstable and would be uncommonly observed, we chose a number of clusters which displayed a low degree of overlap in ordination space, 2) Acknowledging that we may not observe all of the clusters in our a priori model (and that their absence does not prove they do not exist), and that additional clusters may exist that we did not anticipate, we selected a solution with a number of clusters reasonably close to our a priori expectations, 3) we accepted clusters which were a good match with our a priori expectations if they existed, 4) we accepted unanticipated clusters when they were consistent with a mechanistic explanation as to how they could arise (e.g. dictated by abiotic factors, or a likeley otucome of a given disturbance). We selected the solution that best satisfied all of the above criteria. To help us define the characteristics of our clusters we applied indicator species analysis (Dufrene & Legendre 1997), and viewed NMDS ordinations.
Results
Semi-desert shallow sandy loam
Due to it's much better replication, we analyzed semi-desert sandy loam first. We selected a 5-cluster solution (Fig.1 & 2). One of the hypothesized states (annualized) was confirmed and retained as a state in the final model. One hypothesized state (severely eroded) was never observed, but its absence does not prove that it cannot exist, only that it was not observed, thus it is retained in the final state-and-transition model. The other two hypothesized states (crusted wooded shrublands and uncrusted wooded shrublands) were revised as follows. Three unanticipated clusters were observed (grassy shrublands, rocky shrublands). These were interpreted as spatial phases of the reference state which appear to be dictated by differences in soil depth and degree of surface rock cover. One hypothesized state (crusted wooded shrublands) proved to be two distinct clusters (wooded shrublands, blackbrush shrublands), apparently dictated by precipitation. These were reinterpreted as distinct spatial phases of the reference state. Another hypothesized state was the uncrusted wooded shrubland, a hypothesized outcome of surface disturbance in crusted wooded shrublands. In both the wooded shrublands and blackbrush shrublands clusters, there is a gradient of crust cover, corresponding to time since grazing, however these do not sort into distinct clusters. Therefore we reinterpreted the crusted and uncrusted counterparts of wooded shrublands and blackbrush shrublands as four distinct phases within the reference state.
Fig. 1. NMDS ordination of a 5 cluster solution in 3 dimensions. a. most clusters separate well when viewing the two strongest axes (the horizontal axis is rotated to maximize correlation with time since grazing), with the exception of a wooded shrubland cluster; The annualized cluster is best correlated with current or recent grazing. b. A view of the third axis demonstrates that the wooded shrublands also separate from the other clusters (click to enlarge image).
Fig. 2. Six versions of the above NMDS ordination, illustrating indicator species of the various clusters. In each panel, the symbols are resized based on the abundance of a single species or biotic component. It is clear that particular species correlate well with particular clusters. a. Biological crust cover, an indicator of blackbrush and wooded shrublands. b. C. viscidiflorus, an indicator of rocky shrublands. c. C. ramosissima, an indicator and namesake of blackbrush shrublands. d. P. edulis, an indicator of wooded shrublands. e. Opuntia, an indicator of annualized. f. A. hymendoides, an indicator of grassy shrublands (click to enlarge image).
These revisions result in a 3 state state-and-transition model with 6 phases of the reference state. Three of these phases are at-risk and potentially subject to transition out of the reference state. Transitions are modeled and discussed in a separate exercise.
Desert shallow sandy loam
Using our a priori model and knowledge gained from our analysis of semi-desert sandy loam we conducted a similar exercise for desert shallow sandy loam. We selected a three cluster solution (Fig. 3 & 4). As above, one state (annualized) was observed and confirmed, and another (severely eroded) was not observed but retained as a possibility in the final model. Because this ecological site is drier there was no distinction between wooded shrublands and blackbrush shrublands, only blackbrush shrublands occurred. We also observed a cluster strongly reminiscent of the rocky shrublands identified in semi-desert shallow sandy loam. Finally, we did not observe a phase corresponding to grassy shrublands, but we infer its existence as a precursor to annualized states. The sample size was considerably lower (40), only about half of which were not currently disturbed, thus it is entirely reasonable that such a phase exists but was not detected.
Fig. 3. NMDS ordination of a 3 cluster solution (click to enlarge image).
Fig. 4. Three versions of the above NMDS ordination, illustrating indicator species of the 3 clusters. In each panel, the symbols are resized based on the abundance of a single species or biotic component. It is clear that particular species correlate well with particular clusters. a. C. ramosissima, an indicator and namesake of blackbrush shrublands. b. C. viscidiflorus, an indicator of rocky shrublands. c. G. sarothrae, an indicator of annualized. (click to enlarge image).
Our final 3 state state-and-transition model closely resembled that developed for semi-desert shallow sandy loam, except that phases with tree overstories were omitted. Transitions are modeled and discussed in a separate exercise.
