An information theory-based approach to assessing the sustainability and stability of an island system

It is well documented that a sustainable system is based on environmental stewardship, economic viability, and social equity. What is often overlooked is the need for continuity such that desirable system behavior is maintained with mechanisms in place that facilitate the ability of core system functions to endure or adapt (in the face of perturbations), and ensure that future generations are able to meet their needs. Assessing regional systems poses unique challenges in that they are interlinked with larger- and smaller-scale dynamics that may dramatically affect trends in key system variables. From 1970-2009, Puerto Rico experienced a 140% increase in urban population which may have amplified impacts related to resource demands, waste production, and natural habitats. Because such changes can have strong implications for sustainability, the dynamics of Puerto Rico provide a great opportunity to explore methods for assessing the sustainability of a complex geographic region. In this work, we employ Fisher information, an information theory-based approach, to evaluate changes in system dynamics and examine the effect of regionalization impacts on trends in variables characterizing social, environmental, and economic aspects of the system. Results indicate dramatic change from 1981-1999, after which the system dynamics remained steady until 2005. While there was no indication that a regime shift occurred, system trends corresponded with variations in non-yield economic variables. To determine whether Fisher information provides warning signals of critical change, consecutive declines in the index were explored and demonstrated as a possible leading indicator of impending regime shifts.