Eluding catastrophic shifts

Abstract

Transitions between regimes with radically different properties are ubiquitous in nature. Such transitions can occur either smoothly or in an abrupt and catastrophic fashion. Important examples of the latter can be found in ecology, climate sciences, and economics, to name a few, where regime shifts have catastrophic consequences that are mostly irreversible (e.g., desertification, coral reef collapses, and market crashes). Predicting and preventing these abrupt transitions remains a challenging and important task. Usually, simple deterministic equations are used to model and rationalize these complex situations. However, stochastic effects might have a profound effect. Here we use 1D and 2D spatially explicit models to show that intrinsic (demographic) stochasticity can alter deterministic predictions dramatically, especially in the presence of other realistic features such as limited mobility or spatial heterogeneity. In particular, these ingredients can alter the possibility of catastrophic shifts by giving rise to much smoother and easily reversible continuous ones. The ideas presented here can help further understand catastrophic shifts and contribute to the discussion about the possibility of preventing such shifts to minimize their disruptive ecological, economic, and societal consequences.catastrophic shifts | critical transitions | demographic stochasticity | nonequilibrium phase transitions | renormalization group

Landau–Ginzburg theory of cortex dynamics: Scale-free avalanches emerge at the edge of synchronization

“…The resulting Landau-Ginzburg theory, including fluctuations and spatial dependence is regarded as a meta-model of phase transitions and constitutes a firm ground on top of which the standard theory of phases of matter rests (9). Similar coarse-grained theories are nowadays used in interdisciplinary contexts -such as collective motion (52), population dynamics (53), and neuroscience (54)(55)(56)-where * This theory, developed three decades ago aims at explaining the seemingly ubiquitous presence of criticality in natural systems as the result of auto-organization to the critical point of a quiescent/active phase transition by means of diverse mechanisms, including the presence of two dynamical processes occurring at infinitely separated timescales (34,35). diverse collective phases stem out of the interactions among many elementary constituents.…”

Allee dynamics: Growth, extinction and range expansion

“…The RD model studied in the paper could be generalized to higher dimensions, say, d = 2 and a stochastic component included in the model. A recent study [24] indicates that in a 2d system, discontinuous transitions are of the type shown in Fig. 1 could be replaced by continuous transitions under the conditions of limited diffusion, enhanced noise and quenched spatial heterogeneity.…”

Land-use regime shifts: an analytical framework and agenda for future land-use research

“…Thus, although the existence of alternate stable states is a key indicator of regime shifts, it may be challenging, in practice, to empirically identify these. Further, a recent paper showed that intrinsic stochasticity could dramatically alter the nature of the phase transitions (Villa Martín et al 2015), further exacerbating the challenge. The development and analysis of a land-use regime shift database, discussed earlier, would be a first step in identifying land-use regime shifts in practice.…”