Identifying and explaining resilience in ecological networks.

Resilient ecological systems are more likely to persist and function in the Anthropocene. Current methods for estimating an ecosystem's resilience rely on accurately parameterized ecosystem models, which is a significant empirical challenge. In this paper, we adapt tools from biochemical kinetics to identify ecological networks that exhibit 'structural resilience', a strong form of resilience that is solely a property of the network structure and is independent of model parameters. We undertake an exhaustive search for structural resilience across all three-species ecological networks, under a generalized Lotka-Volterra modelling framework. Out of 20,000 possible network structures, approximately 2% display structural resilience. The properties of these networks provide important insights into the mechanisms that could promote resilience in ecosystems, provide new theoretical avenues for qualitative modelling approaches and provide a foundation for identifying robust forms of ecological resilience in large, realistic ecological networks.

Ultrasensitivity and bistability in covalent-modification cycles with positive autoregulation.

Switch-like behaviours in biochemical networks are of fundamental significance in biological signal processing, and exist as two distinct types: ultra-sensitivity and bistability. Here we propose two new models of a reversible covalent-modification cycle with positive autoregulation (PAR), a motif structure that is thought to be capable of both ultrasensitivity and bistability in different parameter regimes. These new models appeal to a modelling framework that we call complex-complete, which accounts fully for the molecular complexities of the underlying signalling mechanisms. Each of the two new models encodes a specific molecular mechanism for PAR. We demonstrate that the modelling simplifications for PAR models that have been used in previous work, which rely on Michaelian approximations, are unable to accurately recapitulate the qualitative signalling responses supported by our detailed models. Strikingly, we show that complex-complete PAR models are capable of new qualitative responses such as one-way switches and a 'prozone' effect, depending on the specific PAR-encoding mechanism, which are not supported by Michaelian simplifications. Our results highlight the critical importance of accurately representing the molecular details of biochemical signalling mechanisms, and strongly suggest that the Michaelian approximation is inadequate for predictive models of enzyme-mediated chemical reactions with added regulations such as PAR.