Optimality of early warning signals for critical transitions: Distribution moment approaches and transition to higher dimensions

Critical transitions are abrupt transitions between distinct states in time varying systems, and early warning signals are leading indicators of such transitions. They occur in natural systems ranging from climate and ecology to financial markets and physiology. Here we propose a new framework for optimality of such early warning signals, and then demonstrate some ways of calculating them. In particular we focus on the utility of distribution moment approximation for this purpose, and in particular the extension of distribution moment approximation to higher-dimensional systems and where useful closed-form expressions can be extracted by perturbation approaches, in contrast to approaches where numerical integration or simulation are required. One consequence of this framework is that the notion of a single ‘optimal’ early warning signal may in general be ill-posed: competing objectives (such as signal strength and lead time) produce inherent trade-offs (and thus a Pareto front), and any particular choice of signal represents an implicit resolution of those trade-offs based on context-specific priorities.