Emerging dynamic regimes and tipping points from finite empirical principles

The dynamics of biogeochemical, ecological, and astronomical systems are transient. Yet, predicting the occurrence of dynamical shifts remains a challenge due to inferential uncertainties from datasets and the limitations of asymptotic-dependent theories. To address this problem, we developed a theoretical framework that builds on the finite nature of observations. This framework assesses the relative importance of processes, defined as the mechanisms that contribute to the rate of change of the systems dynamic variables, and it predicts the critical values that would trigger a shift into a new regime. The number of observable dynamic regimes within the framework increases exponentially with the number of processes. Observers, however, only experience dynamic regimes associated with relevant processes-- those exceeding a tipping point--within their reference framework. A case study of the framework was tested for a classic predator-prey system with four processes parameterized for bacteria (prey) and lytic bacteriophages (predator). The analysis recovered the sixteen dynamic regimes predicted by the framework, including two non-trivial quasi-equilibrium dynamics. An adaptive Boolean model, which used only relevant observable processes, validated the accuracy of the framework, recovering the dynamics of the full model. The observational framework introduced here provides a strategy for identifying the processes and conditions that lead to tipping points, representing a conceptual paradigm shift in transient dynamics, placing the focus on the specific, finite context of the observer, rather than the intrinsic, asymptotic states of the system. SIGNIFICANCESudden shifts in ecological, climate, and biological systems--so-called tipping points or critical transitions--are notoriously difficult to predict. This study introduces a mathematical framework that redefines these transitions as outcomes shaped by the observers empirical limits. By accounting for finite observation time and resolution, the framework uncovers a rich spectrum of dynamic regimes that classical theories overlook. Its conceptual rigor and practical value are demonstrated in a predator-prey system. This new approach reframes how to forecast regime shifts in complex systems and offers a tool with broad relevance, from microbial ecosystems to planetary climate.