Potential Pitfalls in Visual Models of Tipping Points -- And How to Fix Them

Abstract

Visual models play a crucial role in both science and science communication. However, the distinction between mere analogies and mathematically sound graphical representations is not easy and can be misunderstood not only by laypeople but also within academic literature itself. Moreover, even when the graphical representation exactly corresponds to the mathematical model, its interpretation is often far from obvious. In this paper we discuss the potential landscape visualization commonly used for tipping points in the context of nonlinear dynamics and reveal potential pitfalls, in particular when distinguishing bifurcation induced tipping (B-tipping) from noise-induced tipping (N-tipping). We propose new visualization techniques for tipping dynamics, carefully distinguishing between B- and N-tipping as well as between single systems and ensembles of systems. Explicitly, we apply these visualizations both to molecular cell biology and to climate science in order to reveal the crucial differences in the interpretation of the visual models. We find that it is crucial to explicitly discuss the assumptions made within the visual model and to be aware of the risk of misinterpretation. These findings apply to a wide range of readership, from graduate students - as some general knowledge of nonlinear systems is required - to research professionals working in the field of nonlinear sciences. This paper provides the theoretical groundwork for these new visualizations. As a next step, we propose to investigate the individual mental models that might be induced by these visualizations using empirical research that builds upon these findings.