Mathematical models in ecology have traditionally focused on asymptotic or long-term dynamics, such as the study of equilibrium states. However, a significant amount of recent research has shown the importance of studying the dynamics of transient processes in ecological systems, in particular the consideration of long-term transient processes that may last for hundreds of generations or even longer. Many models, as well as empirical studies, have shown that an ecosystem can function for a long time in a certain state or regime (we can call it metastable), but later it exhibits an abrupt transition to another regime of functioning without any prior change in parameters (or after a change that occurred long before the transition). This scenario, where the collapse of the studied population occurs without any obvious cause for the regime change, is also called 'metastability'.
Despite considerable evidence for the existence of long transitions in real natural ecosystems as well as in theoretical models, until recently the study of long-term transitions in ecology remained in its infancy and was largely unsystematized. However, over the last decade, significant progress has been made in developing a unifying theory of long transitions in both deterministic (i.e., systems whose functioning is predetermined and completely determined) and stochastic (i.e., systems with external and internal random factors) systems. This has greatly accelerated further research on long transitions in ecological systems, particularly as the complexity of the models under consideration increases.
This paper provides a detailed critical analysis of recent research on long transitions and associated regime changes in models of ecological dynamics. Particular attention in the work is paid to such factors as ecological stochasticity (the presence of noise in the system), the effect of multiple time scales (consideration of slow-fast systems, with periods of fast and slow changes), the influence of heterogeneity of the distribution of organisms over the area, as well as issues of spatial synchronization of fluctuations in population numbers. The predicted ubiquity of long-term transient processes emphasizes the need to take them into account in programs for the conservation of species diversity. The paper describes how such scenarios can be modeled and predicted.
The paper also highlights the importance of using machine learning elements to study long-living transients. For example, one potential application of machine learning is to search for long-living transients in complex ecological models that include a large number of interacting species and, as a result, a large number of model parameters.
The results are published in the journal Physics of Life Reviews. Morozov, A., Feudel, U., Hastings, A., Abbott, K.C., Cuddington, K., Heggerud, C.M. and Petrovskii, S., 2024. Physics of Life Reviews Long-living transients in ecological models: Recent progress, new challenges, and open questions. // Physics of Life Reviews, Vol., 51, pp.423-441.