Tipping points in Complex Coupled Life-Environment Systems

Abstract

Simple models of complex phenomena provide powerful insights and suggest low-level mechanistic descriptions. The Earth system arises from the interaction of subsystems with multi-scale temporal and spatial variability; from the microbial to continental scales, operating over the course of days to geological time. System-level homeostasis has been demonstrated in a number of conceptual, artificial life, models which share the advantage of a thorough and transparent analysis. We reintroduce a general model for a coupled life-environment model, concentrating on a minimal set of assumptions, and explore the consequences of interaction between simple life elements and their shared, multidimensional environment. In particular stability, criticality and transitions are of great relevance to understanding the history, and future of the Earth system. The model is shown to share salient features with other abstract systems such as Ashby's Homeostat and Watson and Lovelock's Daisyworld. Our generic description is free to explore high-dimensional, complex environments, and in doing so we show that even a small increase in the environmental complexity gives rise to very complex attractor landscapes which require a much richer conception of critical transitions and hysteresis.

Early warning signals in complex ecosystems

“…2, and explained in detail in this section. The model builds upon previous work (Weaver and Dyke, 2012;Dyke and Weaver, 2013;Weaver and Dyke, 2013), extending the model with the inclusion of feedback mechanisms within the biotic and environmental components, not just between them. In doing so, we further extend the generality of the model without sacrificing any of the appealing tractability.…”

“…The linear time evolution of α ensures this system has a 2N-dimensional phase space (Weaver and Dyke, 2013) though this can be reduced to N-dimensions if the time scales of processes associated with changes in the biota, α and the environment, E may be assumed separated, such that changes to the ecology occur on very much shorter time scales than those to the environment, or τ α τ E .…”