A scalar measure tracing tree species composition in space or time

Abstract The tree species composition of a forest ecosystem is commonly represented with weights that measure the importance of one species with respect to the other species. Inclusion of weight in practical applications is difficult because of the inherent multidimensional perspective on composition. Scalar indices overcome the multidimensional challenges, and, consequently, are commonly present in complex ecosystem modeling. However, scalar indices face two major issues, namely non-uniqueness and non-measurability, which limit their ability to be generalized. The objective of this study is to identify the conditions for developing a univariate true measure of composition from weights. We argue that six conditions define a scalar measure of species mixture: (1) usefulness, (2) all species have equal importance, (3) all individuals have the same importance, (4) the measurements expressing importance of an individual are consistent and appropriate, (5) the function measuring composition is invertible, and (6) the function is a true-measure. We support our argument by formally proving all the conditions. To illustrate the applicability of the scalar measure we develop a rectilinear-based measure, and apply it in yield modeling and assessment of ecosystem dynamics.