No abstract

Ecological resilience is the magnitude of the largest perturbation from which a system can still recover to its original state. However, a transition into another state may often be invoked by a series of minor synergistic perturbations rather than a single big one. We show how resilience can be estimated in terms of average life expectancy, accounting for this natural regime of variability. We use time series to fit a model that captures the stochastic as well as the deterministic components. The model is then used to estimate the mean exit time from the basin of attraction. This approach offers a fresh angle to anticipating the chance of a critical transition at a time when high-resolution time series are becoming increasingly available.

Concentrations of phycocyanin, a pigment of Cyanobacteria, were measured at 1‐min intervals during the ice‐free seasons of 2008–2018 by automated sensors suspended from a buoy at a central station in Lake Mendota, Wisconsin, U.S.A. In each year, stochastic‐dynamic models fitted to time series of log‐transformed phycocyanin concentration revealed two alternative stable states and random factors that were much larger than the difference between the alternate stable states. Transitions between low and high states were abrupt and apparently driven by stochasticity. Variation in annual magnitudes of the alternate states and the stochastic factors were not correlated with annual phosphorus input to the lake. At daily time scales, however, phycocyanin concentration was correlated with phosphorus input, precipitation, and wind velocity for time lags of 1–15 d. Multiple years of high‐frequency data were needed to discern these patterns in the noise‐dominated dynamics of Cyanobacteria.

Eusocial insects-ants, bees, wasps, and termites-are being recognized as model organisms to unravel the evolutionary paradox of aging for two reasons: (1) queens (and kings, in termites) of social insects outlive similarly sized solitary insects by up to several orders of magnitude and (2) all eusocial taxa show a divergence of long queen and shorter worker life spans, despite their shared genomes and even under risk-free laboratory environments. Traditionally, these observations have been explained by invoking the classical evolutionary aging theory: well-protected inside their nests, queens are much less exposed to external hazards than foraging workers, and this provides natural selection the opportunity to favor queens that perform well at advanced ages. Although quite plausible, these verbal arguments have not been backed up by mathematical analysis. Here, for the first time, we provide quantitative models for the evolution of caste-specific aging patterns. We show that caste-specific mortality risks are in general neither sufficient nor necessary to explain the evolutionary divergence in life span between queens and workers and the extraordinary queen life spans. Reproductive monopolization and the delayed production of sexual offspring in highly social colonies lead natural selection to inherently favor queens that live much longer than workers, even when exposed to the same external hazards. Factors that reduce a colony's reproductive skew, such as polygyny and worker reproduction, tend to reduce the evolutionary divergence in life span between queens and workers. Caste-specific extrinsic hazards also affect life span divergence, but to a much smaller extent than reproductive monopolization.