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AbstractEcological stability refers to a family of concepts used to describe how systems of interacting species vary through time and respond to disturbances. Because observed ecological stability depends on sampling scales and environmental context, it is notoriously difficult to compare measurements across sites and systems. Here, we apply stochastic dynamical systems theory to derive general statistical scaling relationships across time, space, and ecological level of organisation for three fundamental stability aspects: resilience, resistance, and invariance. These relationships can be calibrated using random or representative samples measured at individual scales, and projected to predict average stability at other scales across a wide range of contexts. Moreover deviations between observed vs. extrapolated scaling relationships can reveal information about unobserved heterogeneity across time, space, or species. We anticipate that these methods will be useful for cross‐study synthesis of stability data, extrapolating measurements to unobserved scales, and identifying underlying causes and consequences of heterogeneity.

Ecological stability refers to a family of concepts used to describe how systems of interacting species vary through time and respond to disturbances. Because observed ecological stability depends on sampling scales and environmental context, it is notoriously difficult to compare measurements across sites and systems. Here, we apply stochastic dynamical systems theory to derive general statistical scaling relationships across time, space, and ecological level of organisation for three fundamental stability aspects: resilience, resistance, and invariance. These relationships can be calibrated using random or representative samples measured at individual scales, and projected to predict average stability at other scales across a wide range of contexts. Moreover deviations between observed vs. extrapolated scaling relationships can reveal information about unobserved heterogeneity across time, space, or species. We anticipate that these methods will be useful for cross-study synthesis of stability data, extrapolating measurements to unobserved scales, and identifying underlying causes and consequences of heterogeneity., Funding Agencies|TULIP French Laboratory of Excellence [ANR-10-LABX-41, ANR-11-IDEX-0002-02]; Swedish Research CouncilSwedish Research CouncilEuropean Commission [VR 2017-05245]; Deutsche ForschungsgemeinschaftGerman Research Foundation (DFG) [FZT 118]; NSFNational Science Foundation (NSF) [EPS-1655726]; Horizon 2020 Framework Programme [666971]

Estimates of biodiversity change are essential for the management and conservation of ecosystems. Accurate estimates rely on selecting representative sites, but monitoring often focuses on sites of special interest. How such site‐selection biases influence estimates of biodiversity change is largely unknown. Site‐selection bias potentially occurs across four major sources of biodiversity data, decreasing in likelihood from citizen science, museums, national park monitoring, and academic research. We defined site‐selection bias as a preference for sites that are either densely populated (i.e., abundance bias) or species rich (i.e., richness bias). We simulated biodiversity change in a virtual landscape and tracked the observed biodiversity at a sampled site. The site was selected either randomly or with a site‐selection bias. We used a simple spatially resolved, individual‐based model to predict the movement or dispersal of individuals in and out of the chosen sampling site. Site‐selection bias exaggerated estimates of biodiversity loss in sites selected with a bias by on average 300–400% compared with randomly selected sites. Based on our simulations, site‐selection bias resulted in positive trends being estimated as negative trends: richness increase was estimated as 0.1 in randomly selected sites, whereas sites selected with a bias showed a richness change of −0.1 to −0.2 on average. Thus, site‐selection bias may falsely indicate decreases in biodiversity. We varied sampling design and characteristics of the species and found that site‐selection biases were strongest in short time series, for small grains, organisms with low dispersal ability, large regional species pools, and strong spatial aggregation. Based on these findings, to minimize site‐selection bias, we recommend use of systematic site‐selection schemes; maximizing sampling area; calculating biodiversity measures cumulatively across plots; and use of biodiversity measures that are less sensitive to rare

Dissolved organic carbon (DOC) is the main energy source for marine heterotrophic microorganisms, but a small fraction of DOC resists microbial degradation and accumulates in the ocean. The reason behind this recalcitrance is unknown. We test whether the long-term stability of DOC requires the existence of structurally refractory molecules, using a mechanistic model comprising a diverse network of microbe-substrate interactions. Model experiments reproduce three salient observations, even when all DOC compounds are equally degradable: (i) >15% of an initial DOC pulse resists degradation, but is consumed by microbes if concentrated, (ii) the modelled deep-sea DOC reaches stable concentrations of 30–40 mmolC/m3, and (iii) the mean age of deep-sea DOC is several times the age of deep water with a wide range from <100 to >10,000 years. We conclude that while structurally-recalcitrant molecules exist, they are not required in the model to explain either the amount or longevity of DOC.