How ecosystems recover from pulse perturbations: A theory of short- to long-term responses

Abstract

Quantifying stability properties of ecosystems is an important problem in ecology. A common approach is based on the recovery from pulse perturbations, and posits that the faster an ecosystem return to its pre-perturbation state, the more stable it is. Theoretical studies often collapse the recovery dynamics into a single quantity: the long-term rate of return, called asymptotic resilience. However, empirical studies typically measure the recovery dynamics at much shorter time scales. In this paper we explain why asymptotic resilience is rarely representative of the short-term recovery. First, we show that, in contrast to asymptotic resilience, short-term return rates depend on features of the perturbation, in particular on the way its intensity is distributed over species. We argue that empirically relevant predictions can be obtained by considering the median response over a set of perturbations, for which we provide explicit formulas. Next, we show that the recovery dynamics are controlled through time by different species: abundant species tend to govern the short-term recovery, while rare species often dominate the long-term recovery. This shift from abundant to rare species typically causes short-term return rates to be unrelated to asymptotic resilience. We illustrate that asymptotic resilience can be determined by rare species that have almost no effect on the observable part of the recovery dynamics. Finally, we discuss how these findings can help to better connect empirical observations and theoretical predictions.

The inherent multidimensionality of temporal variability: how common and rare species shape stability patterns

“…While asymptotic resilience is sometimes considered as a measure representative of collective recovery dynamics, we previously explained why that this is seldom the case (Arnoldi et al . ). The asymptotic rate of return to equilibrium generally reflects properties of rare ‘satellite' species, pushed at the edge of local extinction by abundant ‘core' species.…”

The three regimes of spatial recovery

“…Stability is a central notion in ecology, and it can be defined in various ways, which are typically context dependent (Grimm and Wissel 1997). Nevertheless, the concept of stability comes down fundamentally to the ability of the system to recover from a perturbation (Arnoldi et al 2018), which may be affected by the timing of the perturbation (e.g., constant or single event), the dynamical aspect considered (e.g., rate of convergence or disturbance strength withstood), or the central measure recovered (e.g., biodiversity or overall biomass).…”

How to find simple nonlocal stability and resilience measures

“…They demonstrate their measures on several examples and discuss also disadvantages of local methods for calculating stability and resilience measures. Extensions of the work of Neubert and Caswell have been done by, e.g., Arnoldi et al [11,13]. These papers consider small perturbations and put focus on local measures.…”

“…Doing so lead us into the resilience of a system and construction of resilience measures, an important concept increasingly used in ecology (see, e.g., [8][9][10][11][12][13]). There are at least two different definitions of resilience of a system in the literature.…”