Semi-desert stony loan (ATCO) - modeling transitions

We considered all five transitions proposed in our state-and-transition model for semi-desert stony loam. We found that a complex model was not required to provide a mechanistic model of transition among these states and phases, based on the small amount of data we had available. Rather, univariate logistic regression models based on three different, functionally significant predictors were constructed. Transitions 1 and 2 follow the same model based upon the ratio of grazing decreaser plants to increaser plants (summed cover) as defined by the NRCS ecological site description. Transition 2 is simply a reversal of transition 1. Transitions 3 and 4 follow the same model based upon the ratio of the summed cover of perrennial grasses to the summed cover of shrubs.Transition 4 is simply a reversal of transition 3. Transition 5 was based upon the summed cover of exotic annuals.

Transition 1 (and 2)
Transition 1 can be modeled by the logistic function, with a pseudo R2 of 0.56:

probability of transition =
1/1 +e -(1.6089 - 8.9706(decreasers/increasers))

Transition 2 can be modeled by using the negatives of the slope and intercept parameters like so:

probability of transition =
1/1 +e -(-1.6089 + 8.9706(decreasers/increasers))

Transition 3 (and 4)
Transition 3 can be modeled by the logistic function, with a pseudo R2 of 0.82:

probability of transition =
1/1 +e -(15.86395 - 31.3721(grass/shrub))

Transition 4 can be modeled by using the negatives of the slope and intercept parameters like so:

probability of transition =
1/1 +e -(-15.86395 + 31.3721(grass/shrub))

Transition 5
Transition 5 can be modeled by the following logistic function. (This function, based upon the available data was "perfect" in the sense that the two groups of data (S2 and S3) did not overlap at all, leading to a pseudo R2 of 1.0. Thus, multiple parameters are possible solutions and the solution provided below is unstable. In practice this is not terribly important because the boundary between the two states is in the range between 27 and 28% exotic annual cover):

probability of transition =
1/1 +e -(198.2512 - 720.8806(exotic annual cover))

Simulations
We solved the above equations for all reasonable values of each of these predictors. The results are plotted in Figure 1.

Fig. 1. Logistic equations of Transitions 1,3, and 5, predicitng the probability of transition. Dashed horizontal lines depict critical probabilities (5%, 25%, 50%, 95%) (click to enlarge image)










This modeling exercise provides real values which can trigger management actions. Our critical probabilities 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 thereof are equiprobable, and 25% the threshold beyond which transitions are becoming a common event. The values corresponding to all 5 transitions are tabulated below (Table 1).

Table 1. Critical probabilities of transition given values of monitorable predictors for 5 transitions (click to enlarge).






















Interpretation:
Unlike many semi-arid ecosystems, grazing pressures primarily take the form of shifts in vegetation composition and do not degrade soil surfaces. All of the transitions are assumed to be driven at least partially by grazing pressure. If Decreasers/Increasers is used as an index of the grazing pressure on community composition, a negligible probability of transition from S1P1 to S1P2 exists is decreasers compose 51% or more of the community. If grazing is allowed to decrease this ratio to 30% a transition would not be an uncommon event, and if the ratio decreases to 18% transition is just as probable as no transition. If these probabilities of transition are too high given management priorities, relaxation of grazing might be prescribed. Using this predictor, near certainty (95% transition probability) of transition is not observed even if all decreasers are eliminated. This implies that there is another unmeasured driver of transition that is not incorporated into the model.

If transition does occur to S1P2, the ecosystem is then at-risk for transition to a new state with an increase in prevalence of grazing tolerant grasses (State 2). Whether this constitutes degradation depends upon management goals. Again, grazing pressure is assumed to underly this transition. Grasses may compose up to 41% of the community without a transition being possible. If, however grasses (primarily Pleuraphis jamesii) are allowed to increase to 51% a transition is about as probably as not. Transition becomes nearly certain as grasses compose 60% of the community. Again, if these probabilities of transition are too high given management priorities, relaxation of grazing might be prescribed.

The primary management concern with State 2 is that it may be susceptible to annualization. The best measure of annualization is the intra- and interannual variation in vegetation cover. We did not have this data to work with, thus we used exotic annual cover as our predictor. Regardless of land use preferences, annualization by exotics is never desired. Our data indicate a very sharp boundary between S2 and S3. Below 27 % exotic annual cover, transition is highly improbable. Above 28% exotic annual cover, transition is nearly certain. Thus if 27% exotic annual cover is close to being attained management intervention should occur to increase perrenial species or reduce exotic annuals.

Semi-desert stony loam (ATCO) - Validation of ecosystem states

Data
We analyzed 15 cases from 3 sources in the NCPN database, primarily in and around Capitol Reef National Park. Shane Green of the NRCS kindly provided some vegetative composition data from an additional 14 sites that were on file, the location of these was not documented in the data files.

Caveats and alternative explanations
In general, our observed clusters seem to provide a reasonable validation of the NRCS ecological site description. We see a gradient of communities dominated by putative decreaser species identified in the description, grade into ones dominated by increaser species, which in turn grades into states dominated by exotic invasive grasses. Tp our knowledge, all of our sites are currently in active grazing allotments and have likely been impacted by livestock in recent years; from these results we would infer that the more strongly impacted cluster had experienced more grazing activity.

We cannot rule out observer bias in generating these differences. The annualized cluster is exclusively from data provided by the NRCS. The less impacted cluster are primarily sites sampled by the NPS Inventory and Monitoring Program, whereas the other cluster consists of a mixture of sites from the Capitol Reef vegetation mapping project, and from the Grand Staircase-Escalante National Monument Rangeland Health Assessment. Biases could be present resulting from different personnel collecting data, or the more southerly distribution of the samples in the more impacted cluster.

Cluster analysis
We subjected all available data on plant community composition to hierarchical cluster analysis to determine if clusters could validate the existence of a priori states and phases. All species with fewer than 3 occurrences were excluded from the analysis. We applied to relativization by row maximum transformation to focus the analysis on relative species abundance. A double relativization to further standardize data was not appropriate, because the NRCS data did not provide absolute abundance of species, only relative abundance. Based on a rather simple apriori concept of a state with 2 phases (one dominated by grazing decreasers, and one dominated by grazing increasers), and an additional devegetated state subject to erosion, we examined 2,3 and 4 cluster solutions. All of these were "clean" clusters with little overlap and all could be potentially be explained by a hypothesized unquantified grazing gradient (from lower right to upper left in Fig. 1).

Fig. 1. NMDS ordination diagram depicting results of cluster analysis. Clusters do not overlap, and seem to correspond to a plausible degradation sequence (Click image to enlarge).



















Based upon the four cluster solution, we determined the degree of correlation of various species with the clusters. We found that there were clusters indicated by: 1. Atriplex canescens, 2. Atriplex confertifolia, 3. Pleuraphis jamesii, and Bromus tectorum (Fig 2).

Fig. 2. Image of the same ordination as above, with symbols resized to reflect the relative abundance of key species (click image to enlarge).
















The clusters depicted in panels a - c seem to correspond well to NRCS concepts of vegetation changes under grazing pressure (loss of decreasers, expansion of increasers). All three of these could be interpreted as different phases of the same state; because of the shift in growth form dominance we interpreted the perrenial grass rich cluster (open circles) as its own state. We were surprised to also detect a Bromus tectorum-dominated cluster, which we deemed functionally distinct enough to be its own state, and due to floristic similarities and closeness in ordination space hypothesized that it can arise from the P. jamesii-dominated cluster. The resultant state-and-transition model can be viewed here.

Semi-desert stony loam (ATCO)

Background
Semidesert stony loam (shadscale) ecological sites, are situated on stony, often cobbley alluvial and colluvial soils. They are deep and well drained, and typically on mild to moderate slopes. They are at least slightly calcareous. A large proportion of the soil surface is covered by rock, making the soil well-armored against wind erosion, but these soils may be susceptible to water erosion. The current draft ecological site description does not provide a state-and-transition model, but does mention some ecosystem dynamics in response to grazing and fire. In the description, grazing decreasers included Hesperostipa comata, Achnatherum hymenoides, Artemisia bigelovii and Ephedra torreyana (all palatable except for Ephedra). Grazing increasers include Artemisia tridentata, Gutierrezia sarothrae, Pleuraphis jamesii, and Atriplex confertifolia. Although fire dynamics were mentioned, our a priori state and transition model did not include fire-related transitions because these communities are characterized by low cover (usually Helianthus, Juniperus, Pinus, or Bromus tectorum.

With these assertions in mind we developed the following state-and-transition model:

Fig. 1. State-and-transition diagram for Semi-desert stony loam (shadscale). Solid boxes refer to ecosystem states, and dashed boxes represent phases within those states (red being at-risk of state transition). Click image to enlarge.

















State 1. REFERENCE SHRUBLANDS.
State one consists of sparse shrublands over growing shallow soils with a large amount of surface rock. Atriplex confertifolia is a common species, which may co-occur with Atriplex canescens, Artemisia spp., Ephedra torreyana. There may be a grass component such as Hesperostipa comata, Achnatherum hymenoides, Pleuraphis jamesii or Elymus elymoides. Rock cover is 35% on average, ranging from 9 - 75%. Biological soil crusts may be present but habitat is constrained by rock cover. Plant cover averages 18%, with most sites having less cover, and some extremely productive sites with cover up to 45%. Basal gaps average 1.25 m. Shrubs are usually about twice as abundant as grasses. A large proportion of the soil that is armored by rock, but soil aggregate stability of exposed soil surface may be low, averaging 2-3 using the Herrick soil stability kit. Like many ecological sites surface soil stability is controlled largely by biological crust cover, which explain around 60% of the variation in aggregate stability.

Fig. 2. Photograph of Semidesert stony loam (ATCO) from Witwicki et al. 2009. Click to enlarge image.
















SIPhase1: PALATABLE SHRUBLANDS
Total plant cover is about 15%, and a typical shrub to grass ratio is ~ 5:1. These sites are more likely to contain cool season bunchgrasses such as Achnatherum hymenoides and Hesperostipa comata, the palatable shrubs Artemisia bigelovii and Atriplex canescens, and the unpalatable Ephedra torreyana. Biological crust cover is usually sparse.

S2Phase2: LESS PALATABLE SHRUBLANDS
Total plant cover is about 8 %, and a typical shrub to grass ratio is ~ 3.3:1. These sites are most likely to contain higher relative abundance of Atriplex confertifolia, along with unpalatable shrubs Guttierezia sarothrae. The warm season perrennial grass Pleuraphis jamesii may increase in importance. Biological soil crust cover is usually sparse. Juniperus osteosperma may occasionally be an important species.

State 2. GRAZING IMPACTED GRASSY SHRUBLAND
Total plant cover is about 28%, though smaller statured species are dominant, suggesting that standing biomass may be lower than the previous state. A typical shrub to grass ratio is ~ 1. This state is dominated by the grazing tolerant grass, Pleuraphis jamesii, and the palatable shrubs are greatly reduced. Guttierrezia sarothrae is a common sub-dominant and Bromus tectorum may have invaded.

State 3. ANNUALIZED
Information on total plant cover is lacking, Palatable shrubs have largely been replaced by unpalatable ones such as Coleogyne ramosissima and G. sarothrae. Grasses typically account for more cover than shrubs by a ratio of ~3.5:1. This is driven by annual grasses which account for ~70% of the grass cover; the perrennial grass to shrub ratio is close to 1. Bromus tectorum dominates and as a result, vegetative cover fluctuates within and among years. The exposed soil surface is erodible, especially in highly erosive thunderstorms.


Proceed to this link to read a summary of a data-derived validation of the phases of state 1, and this link to read a summary of a data-derived effort at modeling transitions.

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.