Stochastic regimes can hide the attractors in data, reconstruction algorithms can reveal them

Tipping points and alternative attractors have become an important focus of research and public discussions about the future of climate, ecosystems and societies. However, empirical evidence for the existence of alternative attractors remains scarce. For example, bimodal frequency distributions of state variables may suggest bistability, but can also be due to bimodality in external conditions. Here, we bring a new dimension to the classical arguments on alternative stable states and their resilience showing that the stochastic regime can distort the relationship between the probability distribution of states and the underlying attractors. Simple additive Gaussian white noise produces a one-to-one correspondence between the modes of frequency distributions and alternative stable states. However, for more realistic types of noise, the number and position of modes of the frequency distribution do not necessarily match the equilibria of the underlying deterministic system. We show that data must represent the stochastic regime as thoroughly as possible. When data are adequate then existing methods can be used to determine the nature of the underlying deterministic system and noise simultaneously. This may help resolve the question of whether there are tipping points, but also how realized states of a system are shaped by stochastic forcing vs internal stability properties. ### Competing Interest Statement The authors have declared no competing interest.