Hierarchical analysis of pattern and processes of Douglas-fir forests

There has been an increased interest in thequantification of pattern in ecological systems over the pastyears. This interest is motivated by the desire to constructvalid models which extend across many scales. Spatial methodsmust quantify pattern, discriminate types of pattern, andrelate hierarchical phenomena across scales. Wavelet analysis is introduced as a method to identify spatial structure inecological transect data. The main advantage of the wavelettransform over other methods is its ability to preserve anddisplay hierarchical information while allowing for patterndecomposition.
Two applications of wavelet analysis are illustrated, asa means to: 1) quantify known spatial patterns in Douglas-firforests at several scales, and 2) construct spatially-explicit hypotheses regarding pattern generating mechanisms.Application of the wavelet variance, derived from the wavelettransform, is developed for forest ecosystem analysis toobtain additional insight into spatially-explicit data.Specifically, the resolution capabilities of the waveletvariance are compared to the semi-variogram and Fourier powerspectra for the description of spatial data using a set ofone-dimensional stationary and non-stationary processes. Thewavelet cross-covariance function is derived from the wavelettransform and introduced as an alternative method for theanalysis of multivariate spatial data of understory vegetationand canopy in Douglas-fir forests of the western Cascades ofOregon.