Long-living transients in ecological models: Recent progress, new challenges, and open questions.

Traditionally, mathematical models in ecology placed an emphasis on asymptotic, long-term dynamics. However, a large number of recent studies highlighted the importance of transient dynamics in ecological and eco-evolutionary systems, in particular 'long transients' that can last for hundreds of generations or even longer. Many models as well as empirical studies indicated that a system can function for a long time in a certain state or regime (a 'metastable regime') but later exhibits an abrupt transition to another regime not preceded by any parameter change (or following the change that occurred long before the transition). This scenario where tipping occurs without any apparent source of a regime shift is also referred to as 'metastability'. Despite considerable evidence of the presence of long transients in real-world systems as well as models, until recently research into long-living transients in ecology has remained in its infancy, largely lacking systematisation. Within the past decade, however, substantial progress has been made in creating a unifying theory of long transients in deterministic as well as stochastic systems. This has considerably accelerated further studies on long transients, in particular on those characterised by more complicated patterns and/or underlying mechanisms. The main goal of this review is to provide an overview of recent research on long transients and related regime shifts in models of ecological dynamics. We pay special attention to the role of environmental stochasticity, the effect of multiple timescales (slow-fast systems), transient spatial patterns, and relation between transients and spatial synchronisation. We also discuss current challenges and open questions in understanding transients with applications to ecosystems dynamics.