Abstract:
There has been an increased interest in the
quantification of pattern in ecological systems over the past
years. This interest is motivated by the desire to construct
valid models which extend across many scales. Spatial methods
must quantify pattern, discriminate types of pattern, and
relate hierarchical phenomena across scales. Wavelet analysis
is introduced as a method to identify spatial structure in
ecological transect data. The main advantage of the wavelet
transform over other methods is its ability to preserve and
display hierarchical information while allowing for pattern
decomposition.
Two applications of wavelet analysis are illustrated, as
a means to: 1) quantify known spatial patterns in Douglas-fir
forests at hypotheses regarding pattern generating mechanisms.
Application of the wavelet variance, derived from the wavelet
transform, is developed for forest ecosystem analysis to
obtain additional insight into spatially-explicit data.
Specifically, the resolution capabilities of the wavelet
variance are compared to the semi-variogram and Fourier power
spectra for the description of spatial data using a set of
one-dimensional stationary and non-stationary processes. The
wavelet cross-covariance function is derived from the wavelet
transform and introduced as an alternative method for the
analysis of multivariate spatial data of understory vegetation
and canopy in Douglas-fir forests of the western Cascades of
Oregon.
