A general theory of multimetric indices and their properties

Methods in Ecology and Evolution
By: , and 



1. Stewardship 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 multimetric indices (MMIs). These indices synthesize data, often from multiple levels of biological organization, with the goal of deriving a single index that reflects the overall effects of human disturbance. Despite the widespread use of MMIs, there is uncertainty about why this approach can be effective. An understanding of MMIs requires a quantitative theory that illustrates how the properties of candidate metrics relates to MMIs generated from those metrics. 2. We present the initial basis for such a theory by deriving the general mathematical characteristics of MMIs assembled from metrics. We then use the theory to derive quantitative answers to the following questions: Is there an optimal number of metrics to comprise an index? How does covariance among metrics affect the performance of the index derived from those metrics? And what are the criteria to decide whether a given metric will improve the performance of an index? 3. We find that the optimal number of metrics to be included in an index depends on the theoretical distribution of signal of the disturbance gradient contained in each metric. For example, if the rank-ordered parameters of a metric-disturbance regression can be described by a monotonically decreasing function, then an optimum number of metrics exists and can often be derived analytically. We derive the conditions by which adding a given metric can be expected to improve an index. 4. We find that the criterion defining such conditions depends nonlinearly of the signal of the disturbance gradient, the noise (error) of the metric and the correlation of the metric errors. Importantly, we find that correlation among metric errors increases the signal required for the metric to improve the index. 5. The theoretical framework presented in this study provides the basis for understanding the properties of MMIs. It can also 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 it can be used directly as a decision aid in effective index construction.
Publication type Article
Publication Subtype Journal Article
Title A general theory of multimetric indices and their properties
Series title Methods in Ecology and Evolution
DOI 10.1111/j.2041-210X.2012.00200.x
Volume 3
Issue 4
Year Published 2012
Language English
Publisher Wiley
Publisher location Hoboken, NJ
Contributing office(s) National Wetlands Research Center
Description 8 p.
Larger Work Type Article
Larger Work Subtype Journal Article
Larger Work Title Methods in Ecology and Evolution
First page 773
Last page 781
Country United States
Additional Online Files (Y/N) Y
Google Analytic Metrics Metrics page
Additional publication details