1 INDICES OF STAND STRUCTURAL DIVERSITY: MIXING DISCRETE, CONTINUOUS, AND SPATIAL VARIABLES VALERIE LEMAY 1 and CHRISTINA STAUDHAMMER 2 1 Associate Professor, Department of Forest Resources Management, University of British Columbia, 2045-2424 Main Mall, Vancouver, BC. Valerie.LeMay@ubc.ca , corresponding author 2 Assistant Professor, University of Florida, Gainesville, Florida, USA Email: staudham@ifas.ufl.edu Presented at the IUFRO Sustainable Forestry in Theory & Practice: Recent Advances in Inventory & Monitoring Conference, April 5 to 8, 2005, Edinburgh, UK ABSTRACT. Stand structural diversity, defined as the diversity of trees in stands, can be indicative of overall biodiversity and habitat suitability, useful in forecasting stand growth, and provide within stand detail for forest inventories. A number of authors have suggested which tree variables to use to indicate structural diversity, and have combined these variables into structural indices. Other authors have suggested indices of spatial arrangement. A limited number of authors have tried to combine tree variables and spatial position into structural indices. Central issues in developing structural indices are 1) what is considered a most diverse stand in terms of vertical and horizontal diversity; 2) how can distributions of continuous variables (e.g., diameter and height) be mixed with species distribution as a discrete variable into a structural diversity index (indices); and 3) how should spatial heterogeneity be reflected in a structural index (indices). For this paper, a brief presentation of indices found in literature is given. The definition of most heterogeneous (most structurally diverse) stand is proposed as a uniform distribution over each continuous and each discrete stand variable, and a Poisson distribution of trees in clumps of varying sizes for the spatial distribution. A discussion of this definition and how a previously described structural index might be expanded to incorporate spatial arrangement is given. Keywords: structural diversity indices; vertical and horizontal diversity; height and diameter distribution; species distribution; spatial heterogeneity 1 INTRODUCTION Stand structure is an important element of stand biodiversity (MacArthur and MacArthur 1961; Willson 1974; Franzreb 1978; Temple et al. 1979; Aber 1979; Ambuel and Temple 1983; Freemark and Merriam 1986). High biodiversity is associated with stands where there are multiple tree species and sizes (Buongiorno et al. 1994). For forested ecosystems, structural diversity can indicate overall species diversity (Kimmins 1997), as shown in research on avian and insect diversity (Whittaker 1972; Franzreb 1978; Aber 1979; Temple et al. 1979; Recher et al. 1996; Moen and Gutierrez 1997). Managing forests for biodiversity may be accomplished by managing for structural diversity (Önal 1997). In addition to being useful as a possible proxy for measuring stand biodiversity, measures of stand structural diversity are also important for predicting future stand growth and development (Pretzsch 1997). Oliver and Larson (1996) indicated that a variety of patterns of growth are related to structural complexity. As a measure of horizontal complexity, spatial indices can be useful for comparing point patterns (Goreaud and Pélissier 1999) and for interpreting the ecology of species (Goreaud and Pélissier 1999; Davis et al. 2000). Several indices of stand structure have been proposed based on tree attributes, particularly species and tree size. Indices of spatial arrangement have also been proposed. A limited number of authors have suggested ways to provide indices that represent a mixture of spatial diversity (arrangement) and tree attribute diversity into an overall structural index. Good reviews of indices are given by Pommerening (2002), who described indices without considering spatial arrangement as “distance-independent”, versus those with spatial arrangement as “distance-dependent”, and in Cressie (1993, Chapter 8) and Dale (1999, Chapter 7) for spatial and mixed spatial/variable indices. Related to structural diversity indices is the development of competition indices used to modify tree growth. Weigelt and Jolliffe (2003) provided a review of competition indices, including the benefits and problems of