Understanding the state-dependent impact of species correlated responses on community sensitivity to perturbations

Understanding how communities respond to perturbations requires us to consider not only changes in the abundance of individual species but also correlated changes that can emerge through interspecific effects. However, our knowledge of this phenomenon is mostly constrained to situations where interspecific effects are fixed. Here, we introduce a framework to disentangle the impact of species correlated responses on community sensitivity to perturbations when interspecific effects change over time due to cyclic or chaotic population dynamics. We partition the volume expansion rate of perturbed abundances (community sensitivity) into contributions of individual species and of species correlated responses by converting the time-varying Jacobian matrix containing interspecific effects into a time-varying covariance matrix. Using population dynamics models, we demonstrate that species correlated responses change considerably across time and continuously alternate between reducing and having no impact on community sensitivity. Importantly, these alternating impacts depend on the abundance of particular species and can be detected even from noisy time series. We showcase our framework using two experimental predator-prey time series and find that the impact of species correlated responses is modulated by prey abundance-as theoretically expected. Our results provide new insights into how and when species interactions can dampen community sensitivity when abundances fluctuate over time.