Fuzzy Set Classification of Old-growth Southern Pine

I propose the development of a fuzzy set ordination (FSO) approach to old-growth classification of southern pines. A fuzzy systems approach differs from traditional old-growth classification in that it does not require a “crisp” classification where a stand is either “old-growth” or “not old-growth”, but allows for fractional membership in the set of old-growth stands. FSO produces a score ranging from 0.0 (highly different from old-growth) to 1.0 (completely residing in the set of old-growth stands). This value can also be interpreted as “apparent” age, or an approximation of stand age based on measured variables other than time. A FSO old-growth classification is less subjective than current regression or indexing procedures, most of which assign an arbitrary value to each classification variable. In this example highlighting southern pine, five characteristic features of old-growth (q-factor, maximum tree DBH, stand basal area, percent red heart infection, and large woody debris volume) are expressed as response functions to help differentiate between stands synthesized from historical descriptions of virgin timber in southern Arkansas. INTRODUCTION Southern forests have been dramatically impacted by centuries of human influence. Logging, agriculture, settlement, introduced pests and pathogens, pollution, and other unnatural disturbances have notably altered natural ecosystems. Old-growth forests have been the most dramatically impacted: Davis (1996) estimated that less than 1% of original primary forests remain. This rapid disappearance has placed modernday public resource managers in a bind. Though expected to simultaneously protect threatened and endangered species (many of which are old-growth dependent), preserve and enhance existing resources, and maintain recreation and commodity production from a restricted land base, their options to address these issues are limited. New strategies like managing-for-old-growth have been proposed and are being implemented in small-scale field studies (e.g., Morton et al. 1991, Vora 1994), but the effectiveness of this approach has yet to be documented. Management is further hindered by the lack of agreement on what constitutes old-growth (Hunter and White 1997). While the inherent differences between vegetation types precludes the development of a universal old-growth definition, there are also within-type issues. Different ecological thresholds such as minimum levels of woody debris or tree size are often considered, making it difficult to compare old-growth from one region (or study) to the next. Hunter and White (1997) noted that the arbitrariness of the current working definitions of old-growth did not improve management, as the thresholds used were often based on limited criteria poorly related to stand potential. Several researchers have cautioned against the single feature classification strategy (e.g., Franklin and Spies 1991, Rusterholz 1996, Hunter and White 1997), preferring instead an index of “old-growthedness” in which multiple factors are scored to produce an oldgrowth evaluation system. For example, Franklin and Spies (1991) proposed a continuous scaling strategy, thus allowing for various degrees of old-growthedness. By assuming these characteristics fit a “U” or “S” shaped curve, they employed an arbitrary scale to reflect different stand developmental stages. The resulting values could then be summed to produce an index of old-growthedness. Rusterholz (1996) described a similar approach that applied criteria based on cover type. Each candidate stand was given a value for each of these criteria based on predetermined thresholds, and then the cumulative score (to a maximum of 65 points) was used to determine its status. For example, pine forests were evaluated using the following criteria: stand age, size, and context; degree of human intervention; pine regeneration; tree size class diversity; maximum tree size; and large woody debris volume. Stands with scores of $ 40 were recommended for old-growth protection. Another old-growth classification scheme was described by Hale et al. (1999), who applied a logistic regression model to differentiate between managed mature hardwood forests and unmanaged old-growth. They evaluated seven parameters before settling on large woody debris (LWD) volume as the most