An algorithmic and information-theoretic approach to multimetric index construction

The use of multimetric indices (MMIs), such as the widely used index of biological integrity (IBI), to measure, track, summarize and infer the overall impact of human disturbance on biological communities has been steadily growing in recent years. Initially, MMIs were developed for aquatic communities using pre-selected biological metrics as indicators of system integrity. As interest in these bioassessment tools has grown, so have the types of biological systems to which they are applied. For many ecosystem types the appropriate biological metrics to use as measures of biological integrity are not known a priori. As a result, a variety of ad hoc protocols for selecting metrics empirically has developed. However, the assumptions made by proposed protocols have not be explicitly described or justified, causing many investigators to call for a clear, repeatable methodology for developing empirically derived metrics and indices that can be applied to any biological system. An issue of particular importance that has not been sufficiently addressed is the way that individual metrics combine to produce an MMI that is a sensitive composite indicator of human disturbance. In this paper, we present and demonstrate an algorithm for constructing MMIs given a set of candidate metrics and a measure of human disturbance. The algorithm uses each metric to inform a candidate MMI, and then uses information-theoretic principles to select MMIs that capture the information in the multidimensional system response from among possible MMIs. Such an approach can be used to create purely empirical (data-based) MMIs or can, optionally, be influenced by expert opinion or biological theory through the use of a weighting vector to create value-weighted MMIs. We demonstrate the algorithm with simulated data to demonstrate the predictive capacity of the final MMIs and with real data from wetlands from Acadia and Rocky Mountain National Parks. For the Acadia wetland data, the algorithm identified 4 metrics that combined to produce a -0.88 correlation with the human disturbance index. When compared to other methods, we find this algorithmic approach resulted in MMIs that were more predictive and comprise fewer metrics.