University of Washington - Department of Statistics
Analysis of the patterns of entities and their attributes in space is a common and useful endeavor in ecology. Often, the end of a statistical analysis is a general characterization of the observed pattern or series of patterns. However, a good description of the outcome may be somewhat dissatisfying to the practicing scientist or resources manager in that the mechanisms and processes that led to the outcomes remain unknown. While a precise description of all relevant processes in an ecological context â€“ and in most other contexts â€“ is not possible, the development and testing of hypothetical mechanisms, though incomplete or general, is essential to understanding what we have observed and expect to observe.
Specifically, we are motivated by an even-aged stand of Abies amabilis (Pacific Silver Fir) partially described by Sorrensen-Cothern, Ford, and Sprugel (1993). Several observations of size (diameter) and death were collected over several years, with tree identified by location. Of interest is describing the intraspecific competition (within species) and subsequent effects on growth and mortality, if any. Following SÃ¤rkkÃ¤ and Renshaw (2006), approximate mechanisms take the form of ordinary differential equations (ODEâ€™s) where differential growth of each tree is a function of the (spatially) local subset of the entire stand. Ultimately there are many other proposed models for growth and mortality that may be examined, as well as other data sets.