Statistics of Merging Peaks of Random Gaussian Fluctuations: Skeleton Tree Formalism

In order to study the statistics of the objects with hierarchical merging, we propose the skeleton tree formalism, which can analytically distinguish the episodic merging and the continuous accretion in the mass growth processes. The distinction was not clear in extended Press-Schechter (PS) formalism. The skeleton tree formalism is a natural extension of the peak theory which is an alternative formalism for the statistics of the bound objects. The fluctuation field smoothing with Gaussian filter produces the landscape with adding the extra-dimension of the filter resolution scale to the spatial coordinate of the original fluctuation. In the landscape, some smoothing peaks are nesting into the neighboring peaks at a type of critical points called sloping saddles appears, which can be interpreted as merging events of the objects in the context of the hierarchical structure formation. The topological properties of the landscape can be abstracted in skeleton trees, which consist of line process of the smoothing peaks and the point process of the sloping saddles. According to this abstract topological picture, in this paper, we present the concept and the basic results of the skeleton tree formalism to describe (1) the distinction between the accretion and the merger in the hierarchical structure formation from various initial random Gaussian fields; (2) the instantaneous number density of the sloping saddles which gives the instantaneous scale function of the objects with the destruction and reformation in the mergers; (3) the rates of the destruction, the reformation, and the relative accretion growth; (4) the self-consistency of the formalism for the statistics of the mass growth processes of the objects; (5) the mean growth history of the objects at the fixed mass.Comment: 16 pages, 4 figures, submitted to MNRAS at 28th July, not yet refereed until 4th Oc

Molecular Level Comparison of Water Extractives of Maple and Oak with Negative and Positive Ion ESI FT-ICR Mass Spectrometry

Soluble extractives in wood function to protect living trees from destructive agents and also contribute to wood color and fragrance. Some extractive components have biological activities with medical applications. They also play important roles in wood processing and related applications. To increase the knowledge of wood chemistry, maple and oak were extracted by water. Ultraviolet/visible (UV/vis) spectroscopy indicated the presence of a phenolic compound, resorcinol, in maple extractives having higher molecular mass and more aromatic components than oak extractives. Negative and positive electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry (ESI FT-ICR-MS) identified thousands of formulas in the two samples in the m/z range of 200 to 800. They mainly fall into the lignin-like, carbohydrate-like, and tannin-like compound categories. The top 25 peaks (ie, formulas) with the highest relative magnitude in negative ESI represented nearly 50% of the summed total spectral magnitude of all formulas assigned in the maple and oak extractives. Furthermore, the base peak (ie, most abundant peak) accounted for about 14% of the total abundance in each wood sample. Literature comparisons identified 17 of 20 formulas in the top five peaks of the four spectra as specific bioactive compounds in trees and other plants, implying the potential to explore utilization of maple and oak extractives for functional and medicinal applications. The various profiling of the top 25 peaks from the two samples also suggested the possible application of FT-ICR-MS for detecting chemical markers useful in profiling and identification of wood types and sources

Forest Disturbance History and Stand Dynamics of the Coweeta Basin, Western North Carolina

Understanding the patterns of past disturbance allows further insight into the composition, structure, and function of today’s forests. Disturbance history may also influence how forests will react to future stresses and disturbances. The disturbance histories of the mixed-oak forests at the Coweeta Hydrologic Laboratory (a 2,185 ha long-term research site with some history of harvesting) and the Joyce Kilmer Wilderness (a 6,805 ha old-growth forest with no known harvesting) located in southwestern North Carolina were studied using dendroecology. Dendroecology uses increment cores to determine tree ages and patterns of radial growth. In addition to evaluating the history of these two areas to better understand disturbance dynamic in the southern Appalachians, we compared the radial growth patterns of old-growth trees at Joyce Kilmer to remnant old-growth trees at Coweeta to determine if the trees have similar responses to disturbances throughout time. We found average decadal disturbance rates (calculated as percent of plot area affected per decade back to the mid-1700s) at Coweeta and Joyce Kilmer (8.7% to 18.3%) were similar to rates common in eastern temperate forests (5% to 20%). The general disturbance history is one of low, but fluctuating, rates, indicating the importance of small canopy gaps in these forests. Among the typically low rates of disturbance present in all stands are occasional, and noticeably higher, peaks of disturbance. The dominating peak in disturbance occurred across all stands in the 1920s and 1930s, likely attributable to American chestnut (Castanea dentata (Marshall) Borkh.) mortality due to the chestnut blight. Logging created pulses of disturbance in the 1900s, 1910s, and 1920s. Natural disturbances, such as windthrow from hurricanes, drought, insect outbreaks, and ice storms likely contributed to both the peaks in disturbance across the stands (1840s and 1960s) as well as localized pulses unique to single stands. Disturbance rates and patterns over time were not random with respect to species composition. The more closely related stands were in species composition, the more similar they were in disturbance history. This is likely due to some of the disturbances being specific to one or a few species. However, despite stands similar in species composition also being similar in elevation and slope, disturbance patterns were not influenced by elevation or slope. The early harvests at Coweeta were most likely selective, favoring some trees over others on the basis of species, size, or form. Thus, the remaining trees from that era were biased, making it unclear as to whether their growth patterns were representative of the pre-harvest disturbance history. Thus, we compared old remnant trees at Coweeta to old-growth trees at Joyce Kilmer, asking if radial growth patterns from old trees surviving harvesting were comparable to those of trees growing in the same time period but free from harvesting. We found similar patterns in radial growth as well as similar disturbance histories, indicating that using remnant trees left behind after harvesting to determine disturbance histories is plausible, at least in these stands