Print PageStewardship of biological and ecological resources requires the ability to make integrative assessments of ecological integrity. One of the emerging methods for making such integrative assessments is through the use of multi-metric indices (MMIs) such as Indices of Biotic Integrity or Indices of Ecological Integrity. These indices assemble data, often from multiple levels of biological organization (e.g., abundance, diversity, conservation value) with the goal of deriving a single index to capture the effects of human disturbance. Such indices can then be used to provide decision makers with a synopsis of condition of the natural resources for which they are responsible. Despite the widespread use of MMIs, there is uncertainty about whether, how, or why this approach is effective, and how to best assemble an index from a pool of candidate metrics. Such understanding must come from a quantitative theory of index construction. We present the initial basis for such a theory. We use the theory to derive quantitative answers to questions such as: Is there an optimal number of metrics to comprise an index? How does covariance among metrics affect the performance of an index? And what are the criteria to decide whether given metric will improve the performance of an index.
Results/Conclusions
Assuming linearity between metrics and disturbance gradient, we find that the optimal number of metrics to be included in an index depends on the theoretical distribution of the parameters that describe the amount of information about the disturbance gradient contained in each metric (i.e. the betas in a regression context). For example, if the rank-ordered betas can be described by a monotonically decreasing function, then an optimum number of metrics exists and can be derived analytically. We derive conditions by which adding a given metric can be expected to improve an index. We find that the criterion depends non-linearly on the signal of the disturbance gradient and noise (error) of the metric. Importantly, we find that covariance among metrics increases the degree of non-linearity of the criteria in such a way that increases the required signal required for the metric to be included. We believe that this theoretical framework for index construction can be useful throughout the index construction process. Specifically, it can be used to aid understanding of the benefits and limitations of combining metrics into indices; it can inform selection/collection of candidate metrics and can be used directly as a decision aid in effective index construction.
