Measuring stability in ecological systems without static equilibria

Ecological stability refers to a range of concepts used quantify how species and environments change over time in response disturbances. Most empirically tractable ecological metrics assume that systems have simple dynamics static equilibria. However, are typically complex often lack equilibria (e.g., predator–prey oscillations, transient dynamics, chaos). Failing account for these factors can lead biased estimates stability, particular, by conflating effects observation error, process noise, underlying deterministic dynamics. To distinguish among processes, we combine three existing approaches: state space models; delay embedding methods; particle filtering. Jointly, provide something akin deterministically “detrended” version the coefficient variation, separately tracking variability due versus stochastic perturbations. Moreover, be forecast classify sources estimate “exit time” before takes place local extinction events). Importantly, time-delay methods employ make very few assumptions about functions governing which facilitates applications with limited data priori biological knowledge. demonstrate without bias estimates, analyze simulated series abundance system time-varying carrying capacity observed green algae Chlamydomonas terricola grown diverse microcosm mixture under variable temperature conditions. We show based on raw observations greatly overestimate temporal fail accurately extinction. In contrast, joint application modeling, embedding, filters were able to: (1) correctly contributions variability; (2) successfully “true” dynamics; (3) Our results therefore importance accounting complex, nonstatic studies an flexible toolkit conducting measurements.