Our logistic regressions provided the values of several of these predictors at which transition form reference state to the coppiced state are 25%, 50% and 100% probable (Table 2). The solutions for mean gap length and k failed to converge, likely because of the large magnitude of the difference between reference and coppiced samples. However they did produce reasonable values which should be interpreted cautiously.
[Stay tuned for results later today]
Methods:
There was no single, well-replicated dataset which purposefully measured numerous relevant indicators regarding ecosystem dynamics in Desert Sand (Sand Sagebrush) ecosites. However we did identify a total of 42 data points, 24 of which are currently mapped as Desert Sand, while the remainder are close analogs, e.g. Semi-desert sand (fourwing saltbush). Semi-desert sand analog sites were carefully pruned to remove sites that poorly matched the characteristic vegetation of Desert Sand. Replication of various indicators varied, as did methodology. Most data sources contained some form of plant community composition data, usually cover, although some range assessments estimated above ground biomass instead. All told seven different data sources were used (Table 1).
To calibrate our apriori state-and transition model, we conducted a cluster analysis based upon plant community structure data. We acknowledge that structure alone is often not the best technique for designation of states and phases, but in this data-sparse case it was the best replicated form of data and represented our best option. A series of data standardization steps were necessary to merge the various datasets because of differing methodologies. First we reduced the number of species considered to those which are known to be important in processes (e.g. Ephedra spp. and coppicing), dominate at least one site, or were frequent occurrences in multiple sites. Native annuals and perennials which annually die back were excluded because their detection rate likely varies based on time of year. Some species which were identified to varying levels of precision were lumped, including Ephedra spp., and Sporobolus spp. To account for different quantification procedures, we converted the perennial species abundances to proportional abundance of the total cover. We included two non-native annuals Bromus tectorum and Salsola spp. as presence and absence data, because detection rate varies from year to year, and within years, and some data measured frequency rather than cover.
Our cluster analysis used a flexible beta group linkage method to form clusters from a Bray-Curtis distance matrix (McCune and Grace 2002). We obtained 2, 3, 4 and 5 group clusters and selected the 4 cluster option because it provided enough detail to distinguish among multiple states and phases, was most consistent with our apriori conception of this ecosite, was easily interpretable, and was least strongly driven by disproportionate weighting of the invasive annuals (an artifact created by our data standardization protocol). To help define the characteristics of the four groups we applied Indicator Species analysis (Dufrene & Legendre 1997). As a visualization of our clusters we used a non-metric multi-dimensional scaling ordination, using a Monte-Carlo test to determine optional dimensionality (McCune and Grace 2002).
Using cluster analysis-defined state and phase memberships we applied one way ANOVA to describe the degree to which the various groups differed from one another in the following key structural and functional indicators: total plant cover, total crust cover, soil aggregate stability, gap size distribution (detailed below), and perennial shrub:grass ratio. Gap size distribution was characterized by four separate but related variables: the mean gap length and mean number of gaps per meter, and the scale (k) and shape (θ) parameters of the gamma distribution. The large majority of the available samples fit a gamma distribution reasonably well because it is useful for modeling positively skewed data. This is a very flexible distribution which resembles an exponential distribution when the shape parameter is low and the scale parameter is high, but grades from log-normal-like to normal-like when the shape parameter is high, and the scale parameter is low. To improve normality, or heterogeneity of variance, we applied logarithmic transformations in some case prior to ANOVA.
We used logistic regression equations to estimate critical values in these functional indicators in the transition sequence form the reference state to the coppiced state. Because of the heterogeneous nature of data collection protocols in the various studies it was impossible to conduct a multiple logistic regression without severely compromising sample size due to missing values. As an alternative, we used separate simple logistic regressions for each of seven functional indicators which we felt were most directly linked to the processes underlying the coppicing phenomenon, to estimate the indicator values at which state transition was 25%, 50%, and 100% probable. The first two values can be thought of as a conservative and liberal preventative threshold, whereas the third value is a restoration threshold. We focused on the transition from the reference state to the coppiced state, because of availability of multiple relevant predictors. Transition to the invaded shrub state may be driven by different processes less related to sand redistribution, and which are less well represented in our data.
This is the latest incarnation of the Limy uplands model. I am not soliciting additional edits to the model structure. The only thing that will be updated are confidence estimates, and threshold estimates will be added. Think about if you'd like to do any simplifying for the book chapter.
