Estimating temporal trend in the presence of spatial complexity: a Bayesian hierarchical model for a wetland plant population undergoing restoration

Monitoring programs that evaluate restoration and inform adaptive management are important for addressing environmental degradation. These efforts may be well served by spatially explicit hierarchical approaches to modeling because of unavoidable spatial structure inherited from past land use patterns and other factors. We developed bayesian hierarchical models to estimate trends from annual density counts observed in a spatially structured wetland forb (Camassia quamash [camas]) population following the cessation of grazing and mowing on the study area, and in a separate reference population of camas. The restoration site was bisected by roads and drainage ditches, resulting in distinct subpopulations ("zones") with different land use histories. We modeled this spatial structure by fitting zone-specific intercepts and slopes. We allowed spatial covariance parameters in the model to vary by zone, as in stratified kriging, accommodating anisotropy and improving computation and biological interpretation. Trend estimates provided evidence of a positive effect of passive restoration, and the strength of evidence was influenced by the amount of spatial structure in the model. Allowing trends to vary among zones and accounting for topographic heterogeneity increased precision of trend estimates. Accounting for spatial autocorrelation shifted parameter coefficients in ways that varied among zones depending on strength of statistical shrinkage, autocorrelation and topographic heterogeneity--a phenomenon not widely described. Spatially explicit estimates of trend from hierarchical models will generally be more useful to land managers than pooled regional estimates and provide more realistic assessments of uncertainty. The ability to grapple with historical contingency is an appealing benefit of this approach.     

A new algorithm for computational image analysis of deformable motion at high spatial and temporal resolution applied to root growth. Roughly uniform elongation in the meristem and also,after an abrupt acceleration,in the elongation zone

A requirement for understanding morphogenesis is being able to quantify expansion at the cellular scale. Here, we present new software (RootflowRT) for measuring the expansion profile of a growing root at high spatial and temporal resolution. The software implements an image processing algorithm using a novel combination of optical flow methods for deformable motion. The algorithm operates on a stack of nine images with a given time interval between each (usually 10 s) and quantifies velocity confidently at most pixels of the image. The root does not need to be marked. The software calculates components of motion parallel and perpendicular to the local tangent of the root's midline. A variation of the software has been developed that reports the overall root growth rate versus time. Using this software, we find that the growth zone of the root can be divided into two distinct regions, an apical region where the rate of motion, i.e. velocity, rises gradually with position and a subapical region where velocity rises steeply with position. In both zones, velocity increases almost linearly with position, and the transition between zones is abrupt. We observed this pattern for roots of Arabidopsis, tomato (Lycopersicon lycopersicum), lettuce (Lactuca sativa), alyssum (Aurinia saxatilis), and timothy (Phleum pratense). These velocity profiles imply that relative elongation rate is regulated in a step-wise fashion, being low but roughly uniform within the meristem and then becoming high, but again roughly uniform, within the zone of elongation. The executable code for RootflowRT is available from the corresponding author on request.