Predicting regime shifts - drastic changes in dynamic behaviour - is a key challenge in ecology and other fields. Here we show that the class of ecological systems that will exhibit leading indicators of regime shifts is limited, and that there is a set of ecological models and, therefore, also likely to be a class of natural systems for which there will be no forewarning of a regime change. We first describe how nonlinearities in combination with environmental variability lead to model descriptions that will not have smooth potentials, concluding that many ecological systems are described by systems without smooth potentials and thus will not show typical leading indicators of regime shifts. We then illustrate the impact of these general arguments by numerically examining the dynamics of several model ecological systems under slowly changing conditions. Our results offer a cautionary note about the generality of forecasting sudden changes in ecosystems.

Nuclear-associated oscillations in calcium act as a secondary messenger in the symbiotic signaling pathway of legumes. These are decoded by a nuclear-localized calcium and calmodulin-dependent protein kinase, the activation of which is sufficient to drive downstream responses. This implies that the calcium oscillations within the nucleus are the predominant signals for legume symbiosis. However, the mechanisms that allow targeted release of calcium in the nuclear region have not been defined. Here we show that symbiosis-induced calcium changes occur in both the nucleoplasm and the perinuclear cytoplasm and seem to originate from the nuclear membranes. Reaction diffusion simulations suggest that spike generation within the nucleoplasm is not possible through transmission of a calcium wave from the cytoplasm alone and that calcium is likely to be released across the inner nuclear membrane to allow nuclear calcium changes. In agreement with this, we found that the cation channel DMI1, which is essential for symbiotic calcium oscillations, is preferentially located on the inner nuclear membrane, implying an essential function for the inner nuclear membrane in symbiotic calcium signaling. Furthermore, a sarco/endoplasmic reticulum calcium ATPase (SERCA) essential for symbiotic calcium oscillations is targeted to the inner nuclear membrane, as well as the outer nuclear membrane and endoplasmic reticulum (ER). We propose that release of calcium across the inner nuclear membrane allows targeted release of the ER calcium store, and efficient reloading of this calcium store necessitates the capture of calcium from the nucleoplasm and nuclear-associated cytoplasm.L egumes form mutualistic symbiotic interactions with mycorrhizal fungi and with rhizobial bacteria that aid in the uptake of nutrients (1, 2). Establishment of both symbioses requires the common symbiosis (Sym) signaling pathway (1, 2) that involves calcium oscillations after perception of diffusible signals from the symbionts (3, 4): Nod factors from rhizobia and Myc factors from mycorrhizal fungi (4-7). The calcium oscillations are concentrated in the perinuclear region (3), and a nuclear-targeted calcium reporter showed that part of these oscillations occurs in the nucleoplasm (8). The decoder of the calcium oscillations, a calcium and calmodulin-dependent protein kinase (CCaMK), is localized to the nucleoplasm (9, 10), implying that intranuclear calcium changes are paramount. Furthermore, some of the components of the Sym pathway required for the induction of calcium oscillations are localized to the nuclear envelope: two cation channels and three components of the nuclear pore (11-14). All of this points to the nuclear membrane as playing a central role in symbiotic calcium oscillations.The question of whether calcium changes can derive from the nucleus has been a contentious point for many years (15, 16). In animals, it is widely accepted that calcium events in and around the nucleus have significant effects on signaling pathways in the nucleus (15). Depend...

Legumes form symbioses with rhizobial bacteria and arbuscular mycorrhizal fungi that aid plant nutrition. A critical component in the establishment of these symbioses is nuclear-localized calcium (Ca 2+ ) oscillations. Different components on the nuclear envelope have been identified as being required for the generation of the Ca 2+ oscillations. Among these an ion channel, Doesn't Make Infections1, is preferentially localized on the inner nuclear envelope and a Ca 2+ ATPase is localized on both the inner and outer nuclear envelopes. Doesn't Make Infections1 is conserved across plants and has a weak but broad similarity to bacterial potassium channels. A possible role for this cation channel could be hyperpolarization of the nuclear envelope to counterbalance the charge caused by the influx of Ca 2+ into the nucleus. Ca 2+ channels and Ca 2+ pumps are needed for the release and reuptake of Ca 2+ from the internal store, which is hypothesized to be the nuclear envelope lumen and endoplasmic reticulum, but the release mechanism of Ca 2+ remains to be identified and characterized. Here, we develop a mathematical model based on these components to describe the observed symbiotic Ca 2+ oscillations. This model can recapitulate Ca 2+ oscillations, and with the inclusion of Ca 2+ -binding proteins it offers a simple explanation for several previously unexplained phenomena. These include long periods of frequency variation, changes in spike shape, and the initiation and termination of oscillations. The model also predicts that an increase in buffering capacity in the nucleoplasm would cause a period of rapid oscillations. This phenomenon was observed experimentally by adding more of the inducing signal.