Alan Hastings

Transient dynamics pose unique challenges when dealing with predictions and management of ecological systems yet little headway has been made on understanding when an ecological system might be in a transient state. As a start we consider a specific model, here focusing on a canonical model for anaerobic digestion. Through a series of simplifications, we analyse the potential of the model for transient dynamics, and the driving mechanisms. Using a stochastic analogue of this model, we create synthetic ecological data. Thus, combining our understanding of the deterministic transient dynamics with the use of empirical dynamical modelling, we propose several new metrics to indicate when the synthetic time series is leaving a transient state.

Compartmental models play an important role to describe the dynamics of systems that involve mass movements between different types of pools. We develop a theory to analyse the average ages of mass in different pools in a linear compartmental system with time-dependent (i.e. non-autonomous) transfer rates, which involves transit times that characterize the average time a particle has spent in a particular pool. We apply our theoretical results to investigate a nine-dimensional compartmental system with time-dependent fluxes between pools modelling the carbon cycle which is a modification of the Carnegie–Ames–Stanford approach model. Knowledge of transit time and mean age allows calculation of carbon storage in a pool as a function of time. The general result that has important implications for understanding and managing carbon storage is that the change in storage in different pools does not change monotonically through time: as rates change monotonically a pool which initially shows a decrease may then show an increase in storage or vice versa. Thus caution is needed in extrapolating even the direction of future changes in storage in carbon storage in different pools with global change.