Abstract: Transient dynamics are population dynamics that happen on ecologically relevant timescales, in which classical modelling techniques often fail to capture. Due to the ever changing environments and ecosystems, increased interest has been placed on the study of transient dynamics. Although studies have been done on understanding ecological tipping points via changes in ecological parameters, the goal of this study is to understand similar tipping points that stem from non-typical approaches to steady state when the underlying ecological parameters are not changing. To study this, we first propose a dynamical model for anaerobic digestion, which is a process commonly used in wastewater treatment and production of biogas, that readily exhibits transient dynamics before settling to its steady state. We use this model to produce synthetic ecological data and show how, using the underlying theory of dynamical attractors, empirical dynamical modelling, and the qualitative aspects of the anaerobic digestion model, we can classify when an ecological system is in a transient state based solely on ecological time series data. In particular, we use empirical dynamical modelling to reconstruct dynamical attractors and based on the relative position of the system from the attractor we can gain insight towards its future dynamics. That is, to aid in control and timing of management interventions we present a new quantitative method that accurately predicts the point in time the anaerobic digestion system will transition between transient behavior and steady state behavior. We further present several new metrics that forecast with high accuracy (Pearson's r >0.9) when the anaerobic digestion systems transient event will end using only synthetic ecological data. We further find that our method does better at predicting the end of the transient using historical monitoring data, as opposed to the use of a control time series and can thus be useful for real-time management and control of anaerobic digesters. This work connects the mathematical literature on transient dynamics to the real-world ecological applications of monitoring systems and appropriate timing of ecological interventions to prevent undesired outcomes.
