Estimating thresholds for semi-desert shallow sandy loam (JUOS-CORA) and desert shallow loam (CORA)

Semidesert shallow sandy loam
Transition 9: S1P1 Grassy Shrublands to S2 Annualized

There was only a single state transition for which we had sufficient data to model a state transition. Transition 9 from S1P1 Grassy Shrublands to S2 Annualized was the only case where both the initial state/phase and the final state were documented in the dataset. A previous cluster analysis was used to assign samples to clusters corresponding to these designations. We used the NCPN integrated dataset to extract 46 samples representing either S1P1 or S2. We focused our efforts on the following data: 1. currently grazed (binary) as an indication of recent disturbance regime, 2. crust cover as an indicator of recent disturbance regime and resistance of soil surface to exotic annual establishment, 3. total plant cover as an index of recent consumption of forage and competitive barriers to the establishment of exotic annuals, 4. Relative cover of exotic annuals as an index of the degree of invasion, standardized by the site productivity, 5. State membership (S1P1 or S2). We developed the following path model to articulate our hypothesis about how transition 9 may occur. Using linear regressions we established the mathematical relationships expressed in the path model. Total plant cover and crust cover were well predicted by simple linear regressions using grazing as a predictor, after data transformation. Relative cover of exotic annuals was well predicted by a full-factorial regression model of all three of these variables. The second order interaction was particularly important in this predictive equation. State membership was well predicted particularly by relative cover of exotic annuals, with contributions from BSC cover and total plant cover.

The equations were as follows

1. log total plant cover = 1.56 – 0.27 (grazing)

2. √crust = 2.67 – 2.35 (grazing)

3. exotic annual rel. cover =
5.93 + 0.30 (grazing)
- 4.10 (log total plant cover)
+ 0.05 (√crust)
- 8.85 (grazing × log total plant cover)
2.45 (√crust × log total plant cover)
+ 0.21 (√crust × grazing)
-5.93 (√crust × grazing × log total plant cover)

4. probability of transition =
1/1 +e -(-0.0797 – 1.15(log total plant cover) – 1.96(√crust) + 2.69( exotic annual rel. cover))

Fig. 1. A path model illustrating the hypothesized mechanism underlying T9. Boxes represent measured variables, darkly filled ones being binary. The oval represents interaction terms. Directed arrows are causal dependencies. Black arrows represent linear regression relationships, arrow width indicates the strength of the relationship. Gray arrows represent information flow form predictors in a logistic regression equation (Click image to enlarge).
















This system of equations, applied in the sequence illustrated in the path model formed the basis of the simulation of data with the correlative structure of the real data. Each linear regession was modeled with an appropriate amount of random error (based on the RMSE, the standard deviation around the regression line). In order to simulate a wide variety of combinations of the predictors of probability of transition, we solved the system of equations, with error, for continuous grazing values ranging from zero to one, at a resolution of two decimal places. Although in the real data, grazing is a binary variable, it is easy to envision a continuous grazing intensity underlying this coarse indicator. We solved this 100 separate times, and calculated a mean probability and 95% confidence interval for each level of grazing (Fig 2). We determined the lowest grazing level at which probability of transition was 25% and 50% (normally we would do so for 5% and 95%, but a grazing intensity of 0 resulted in probability greater than 5%, and and a grazing intensity of 1 resulted in probability < style="font-weight: bold;" size="2">

Fig. 2. Modeled probabilities of transition from S1P1 to S2, given a range of grazing scenarios. Dashed lines represent critical probabilities (5%, 25%, 50%). The right panels indicate values of monitored indicator variables corresponding to grazed and ungrazed scenarios, and transition probabilities of 25% and 50% (Click to enlarge image).










Interpretation:
This ecological site is relatively resistant to transition to an annualized state, as the greatest probabilities of transition observed were only about 50%. However, even if grazing is ceased there is still a small probability (~5%) that transition will occur. This may be because of past grazing induced transitions that persisted after grazing ceased, or that despite low grazing disturbance, invasion occurred anyway, perhaps aided by climate events.

This modeling exercise provides real values which can trigger management actions. Our critical probablitities are: 5% the threshold beyond which transitions are a reasonable possibility, 95% the threshold beyond which transitions are almost certain, 50% the threshold at which transition or lack therof are equiprobable, and 25% the threshold beyond which transitions are becoming a common event. For sites in the S1P1 state our analyses indicate that when relative exotic annual cover reaches about 0.70, and/or its predecessors, crust cover and total plant cover, are reduced to 3.7 and 31.4, respectively, an assessment of the necessity of management actions (e.g. modifications of grazing regime) may occur. When relative exotic annual cover reaches about 1.0, crusts are reduced to 1.2% and total plant cover is reduced to 24.3%, a management action is needed(e.g. cessation of grazing or active restoration). If a management response is not undertaken, a transition will become reasonably likely, though not certain. Although we lacked the data to test the assumption, we suspect that a similar mechanism underlies the corresponding Transition 3 in the ecological site Desert shallow sandy loam (CORA), and that a similar management recommendation can be made regarding this site.

Semidesert shallow sandy loam Transition 1 & 2: S1P2 Wooded shrublands - crusted to S1P3 Wooded shrublands (and vice-versa) Transition 3 & 4: S1P5 Blackbrush shrublands - crusted to S1P6 Blackbrush shrublands (and vice-versa) Desert shallow sandy loam Transition 1 & 2: S1P1 Blackbrush shrublands - crusted to S1P2 Blackbrush shrublands (and vice-versa)
These 6 transitions were considered together because they are within-state transitions among phases, they all involve a very similar dependency of soil stability upon biological crust cover. They are also presumed to be reversible, if the stressor generating surface disturbance is removed. In both of the ecological sites (Semidesert shallow sandy loam, Desert sandy loam) we hypothesize shrubland or woodland states with the potential to support a high cover of biological crusts. In both we also hypothesize another state, a severely eroded state, which might eventually arise from the crusted woodlands or shrublands. The severely eroded state was not directly observed. We hypothesize the existence of intermediate phases lying along these degradation sequences, woodlands and shrublands lacking crusts, but otherwise similar to their crusted counterparts. This is because in response to livestock grazing, the most common stressor, the condition of the soil surface is likely to be impacted faster than the predominantly woody, unpalatable vegetation, due to the inherent fragility of the soil surface. This phase transition is expected to increase erodibility, which may or may not lead to enhanced erosion. Under further pressure we hypothesize that the stature and spatial patterning of the woody vegetation chnages in such a way that the ability of the vegetation to buffer erosivity of wind and water is reduced. When both erodibility and erosivity are increased, a highly eroded state is possible. We acknowledge that a surface disturbance which both disturbs the soil surface and degrades vegetation (e.g. off road vehicles, seismic exploration) could conceivably lead to a state transition to an eroded states without the intervening phase.

Within the sites falling within blackbrush shrubland or wooded shrubland clusters (Semidesert Desert shallow sandy loam cluster analysis) we used the NCPN database to plot regressions of soil stability by biological soil crust cover. In the database there were 7 cases of blackbrush shrublands with soil stability and biological crust measurements for the desert shallow sandy loam ecological site. There were 21 cases of blackbrush shrublands . There were 18 cases of wooded shrublands in the semidesert shallow sandy loam ecological site with the appropriate data. We used the square of the soil stability value because the data generated by the Herrick soil stability test (Herrick et al. 2001) is curvilinearly related to continuous measures of aggregate stability; the transformation helps linearize the scale. As hypothesized above spatial pattern of vegetation did not appear to be strongly dependent on recent grazing history, and was not considered a useful predictor of these transitions. We prepared 4 different regressions (Fig. 3: 1) Semi-desert shallow sandy loam wooded shrublands 2) Semi-desert shallow sandy loam blackbrush shrublands, 3) Semi-desert and desert shallow sandy loam blackbrush shrublands, 4) All of the above, combined. The desert shallow sandy loam blackbrush shrublands were not replicated well enough to be considered on their own, thus we pooled them with similar sites from semidesert shallow sandy loam to generate 3 above. Since regressions 1-3 were strikingly similar we also pooled all data and generated a regression for all simultaneously.

Fig. 3. Linear regressions of soil stability as a function of biological crust cover in: a. Wooded shrublands, b. Semidesert blackbrush shrublands, c. Desert and semidesert blackbrush shrublnds, and d. Pooled data (click image to enlarge)
















Because these are not transition among states we were not expecting threshold-like behavior, rather we expected and saw very strong linear dependencies. Nevertheless, we use the regression equations to estimate the biological crust cover at which soil stability was 5%, 25%, 50%, and 95% reduced to provide benchmarks for managing these ecosystems (Table 1).

Table 1. Biological crust cover at critical points in the degradation of soil stability (click image to enlarge). Percentages are based upon a maximal value of 36, the square of the maximal value of the Herrick soil stability test (Herrick 2001).












Interpretation:
All of the regression equations, regardless of which input data was used, resulted in very similar values. Therefore the pooled regression may be the most useful because it pertains to all of the data. This regression suggests that to maintain the potential soil stability, biological crust cover ought to be maintained at 38.9%.

If land is being managed for uses which require surface disturbance, degradation of soil stability can be maintained at 25% or less if crust cover is maintained at at least 28.3%. Likewise degradation can be maintained at 50% of less if at least 15.1% crust cover is retained. Beyond this point, a site is increasingly likely to have passed into an at-risk phase. The at-risk phases, if further damaged, are susceptible to transition to severely eroded states

References
Herrick, J.E., W.G. Whitford, A.G. de Soyza, J.W. Van Zee, K.M. Havstad, C.A. Seybold, M. Walton. 2001. Soil aggregate stability kit for field-based soil quality and rangeland health evaluations. Catena 44:27-35.

Desert and semidesert shallow sandy loam- Validating existence of states and phases

Methods
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.