Figure 1.
A photograph of camas growing in the restoration study site, Weippe Prairie, Idaho, USA.
Camas is a bulb-forming geophyte (upper inset) with limited dispersal capabilities. This attribute and its propensity for prairie swales that experience longer periods of inundation and elevated soil moisture during the growing season creates dense but patchily distributed colonies, as illustrated here. This patchy distribution also leads to highly skewed density counts (lower inset). Upper inset illustration by Andrea Foust Carlson, reproduced with permission. Photo courtesy of the National Park Service.
Figure 2.
The restoration site, Weippe Prairie, Idaho, USA.
The stratified sampling frame identifies 5 zones labeled A–E. A narrow ditch between zone A and B overlaps with the sampling frame boundary and is not readily visible. A paved road separates zone C and D. Elevations were obtained from high-resolution laser altimetry (LiDAR).
Figure 3.
Semivariograms of camas density in the restoration site.
In panels a and b, parametric exponential semivariogram models were fit to a) pooled and year-specific and b) pooled and zone-specific empirical models from model 3 residuals for the restoration site. In panel c, zone-specific posterior median estimates for partial sill and range covariance parameters (, φk) obtained from model 4 were used.
Table 1.
Parameter estimates based on 12,000 MCMC samples from posterior densities obtained from a fully spatial hierarchical model (model 4) fit to camas lily monitoring data collected in Weippe Prairie, Idaho, USA and to a reference site in Big Hole National Battlefield, Montana, USA, during 2005–2010.
Figure 4.
Posterior medians and 95% Bayesian credible intervals for a) trend and b) elevation parameters.
Results are for the restoration study site from a series of 4 models of camas density each with successive amounts of spatial structure included. Model 1 represents a spatially “naïve” approach with estimates obtained from independent simple regression models for each zone. Note that no overall restoration site estimate (i.e. µyear) is generated from model 1. Model 2 is a hierarchical model that allows for zone-specific slopes and intercepts as well as an estimate of µyear for the restoration site (labeled “site”). Model 3 is an extension of model 2 with elevation included. Model 4 adds further spatial structure by including zone-specific exponential spatial covariance models that account for residual spatial autocorrelation.