Climbing Escher's stairs: a way to approximate stability landscapes in multidimensional systems

Stability landscapes are useful for understanding the properties of dynamical systems. These landscapes can be calculated from the system's dynamical equations using the physical concept of scalar potential. Unfortunately, for most biological systems with two or more state variables such potentials do not exist. Here we use an analogy with art to provide an accessible explanation of why this happens. Additionally, we introduce a numerical method for decomposing differential equations into two terms: the gradient term that has an associated potential, and the non-gradient term that lacks it. In regions of the state space where the magnitude of the non-gradient term is small compared to the gradient part, we use the gradient term to approximate the potential as quasi-potential. The non-gradient to gradient ratio can be used to estimate the local error introduced by our approximation. Both the algorithm and a ready-to-use implementation in the form of an R package are provided

Five fundamental ways in which complex food webs may spiral out of control

Theory suggests that increasingly long, negative feedback loops of many interacting species may destabilize food webs as complexity increases. Less attention has, however, been paid to the specific ways in which these ‘delayed negative feedbacks’ may affect the response of complex ecosystems to global environmental change. Here, we describe five fundamental ways in which these feedbacks might pave the way for abrupt, large‐scale transitions and species losses. By combining topological and bioenergetic models, we then proceed by showing that the likelihood of such transitions increases with the number of interacting species and/or when the combined effects of stabilizing network patterns approach the minimum required for stable coexistence. Our findings thus shift the question from the classical question of what makes complex, unaltered ecosystems stable to whether the effects of, known and unknown, stabilizing food‐web patterns are sufficient to prevent abrupt, large‐scale transitions under global environmental change

Some species flourish when many do not: a pattern in data on ecological communities

Patterns in species × sample tables of communities depend above all on the organisms of the data sets and the conditions involved. Patterns that surpass individual sets are of special interest. Our question, looking for a shared pattern in 12 sets, is if relative abundances among species are independent of the sample, or formulated alternatively, if species have abundances that are correlated with total abundances over samples. For exploration we study the overdispersion/aggregation of the data. A relatively high variation in the total abundances of samples is noticed, indicating an effect of environmental variation. Overdispersion imposes constraints on the accommodation of relatively high abundance values to samples with a relatively low total abundance. The null hypothesis of ‘no association’ is modelled by permutation/resampling of the data at the level of the individual. A correlation study of actual and permuted sets is performed. All actual sets contain a significant number of species that defy our question. These species flourish when many do not. The relation of our question with issues in theoretical ecology, such as the assumption of a neutral effect of environmental conditions and/or of neutral characteristics of species, is discussed

Exit time as a measure of ecological resilience

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.</p

Hysteresis of tropical forests in the 21st century

Tropical forests modify the conditions they depend on through feedbacks at different spatial scales. These feedbacks shape the hysteresis (history-dependence) of tropical forests, thus controlling their resilience to deforestation and response to climate change. Here, we determine the emergent hysteresis from local-scale tipping points and regional-scale forest-rainfall feedbacks across the tropics under the recent climate and a severe climate-change scenario. By integrating remote sensing, a global hydrological model, and detailed atmospheric moisture tracking simulations, we find that forest-rainfall feedback expands the geographic range of possible forest distributions, especially in the Amazon. The Amazon forest could partially recover from complete deforestation, but may lose that resilience later this century. The Congo forest currently lacks resilience, but is predicted to gain it under climate change, whereas forests in Australasia are resilient under both current and future climates. Our results show how tropical forests shape their own distributions and create the climatic conditions that enable them

A global climate niche for giant trees

Rainforests are among the most charismatic as well as the most endangered ecosystems of the world. However, although the effects of climate change on tropical forests resilience is a focus of intense research, the conditions for their equally impressive temperate counterparts remain poorly understood, and it remains unclear whether tropical and temperate rainforests have fundamental similarities or not. Here we use new global data from high precision laser altimetry equipment on satellites to reveal for the first time that across climate zones \u27giant forests\u27 are a distinct and universal phenomenon, reflected in a separate mode of canopy height (~40 m) worldwide. Occurrence of these giant forests (cutoff height > 25 m) is negatively correlated with variability in rainfall and temperature. We also demonstrate that their distribution is sharply limited to situations with a mean annual precipitation above a threshold of 1,500 mm that is surprisingly universal across tropical and temperate climates. The total area with such precipitation levels is projected to increase by ~4 million km2 globally. Our results thus imply that strategic management could in principle facilitate the expansion of giant forests, securing critically endangered biodiversity as well as carbon storage in selected regions

Early Warning Signals of Ecological Transitions: Methods for Spatial Patterns

A number of ecosystems can exhibit abrupt shifts between alternative stable states. Because of their important ecological and economic consequences, recent research has focused on devising early warning signals for anticipating such abrupt ecological transitions. In particular, theoretical studies show that changes in spatial characteristics of the system could provide early warnings of approaching transitions. However, the empirical validation of these indicators lag behind their theoretical developments. Here, we summarize a range of currently available spatial early warning signals, suggest potential null models to interpret their trends, and apply them to three simulated spatial data sets of systems undergoing an abrupt transition. In addition to providing a step-by-step methodology for applying these signals to spatial data sets, we propose a statistical toolbox that may be used to help detect approaching transitions in a wide range of spatial data. We hope that our methodology together with the computer codes will stimulate the application and testing of spatial early warning signals on real spatial data