Stability metrics are robust across data qualities but sensitive to community size.

Modern biodiversity monitoring is generating increasingly multidimensional representations of wildlife populations and ecosystems. It is therefore appealing for conservation and environmental governance to combine that information into single measure of ecosystem or population health. Stability represents a desirable feature of ecosystems that supports this aim, measured through resistance, recovery, and variability. In deterministic mathematical systems, the Jacobian matrix is a common characteristic used to quantify resistance and resilience and whilst historically it has been challenging to estimate from empirical data, recent work has proposed a suite of metrics capable of reconstructing it for a real-world community using time series data. Here we assess the robustness of three Jacobian metrics and two variability estimating stability metrics to varying time series lengths and data qualities based on that seen in real-world wildlife time series. Using Lotka-Volterra equations, we generate short time series (to match global biodiversity datasets such as the Living Planet Index and BIOTIME) and introduce sampling error corruptions (to mimic varying search efforts) to validate metric performance in empirical data. The robustness stability metrics generally improved with time series length and search effort in the anticipated manner. However, number of species dramatically altered metric capability, with larger communities decreasing the reliability of stability metric trends. Overall, stability metrics behave predictably across realistic data corruptions. Generic stability estimation is therefore possible from abundance time series alone, and we suggest that, given the increasing availability of multivariate community data, focussing on Jacobian estimates is a plausible ecosystem condition indicator.