Merging dynamical and structural indicators to measure resilience in multispecies systems

Abstract

Resilience is broadly understood as the ability of a system to recover and resist perturbations coming in abundance from the environment. However, one of the main problems in assessing resilience has been linked to its measurement and the interconnection among its components, which may not be complementary (i.e., respond to the same types of perturbations) or even possible to quantify. While recovery has a strong tradition under the mathematical analysis of asymptotic dynamical stability (i.e., return to a reference equilibrium state after infinitesimal perturbations acting on state variables), it is unclear whether this same formalism can be used to measure resistance and whether it is independent from recovery. Importantly, resilience and, in particular, resistance can also be linked to structural stability (i.e., the response of a system to structural perturbations). Formally, this structure can be represented by a model describing the governing laws of a system and its parameters. Furthermore, it has already been shown that stochastic perturbations of state variables in the vicinity of the equilibrium are equivalent to fluctuations of model parameters within the same infinitesimal border. Here, we extend the link between dynamical and structural stability beyond the vicinity of an equilibrium point to provide a framework to measure the resilience of the species composition of an ecological system to perturbations in species abundances and model parameters. We show that the return rate of the slowest-recovered species (what we call full recovery) is negatively associated with the largest random parameter perturbation that a system can withstand before losing any species (what we call full resistance). Next, we show that the return rate of the second slowest-recovered species (what we call partial recovery) is negatively associated with the largest random parameter perturbation that a system can withstand before losing all but one species (what we call partial resistance). Then, using random and experimental systems with different types of ecological interactions, we show that full and partial indicators of resilience are complimentary measurements. Because it is expected that non-infinitesimal perturbations in abundances and model parameters happen simultaneously in nature, our findings reveal that recovery (dynamical indicator) and resistance (structural indicator) are interdependent. Therefore, our results suggest that merging full and partial indicators of resilience, whether dynamical or structural, can allow a more complimentary assessment of risk in ecological systems under model-driven and data-driven applications.

Chuliang Song

PostDoc

I am a quantitative ecologist driven by the curiosity of how biodiversity is generated and maintained.