Sonia Kéfi

Spatial vegetation patterns and imminent desertification in Mediterranean arid ecosystems

Humans and climate affect ecosystems and their services, which may involve continuous and discontinuous transitions from one stable state to another. Discontinuous transitions are abrupt, irreversible and among the most catastrophic changes of ecosystems identified. For terrestrial ecosystems, it has been hypothesized that vegetation patchiness could be used as a signature of imminent transitions. Here, we analyse how vegetation patchiness changes in arid ecosystems with different grazing pressures, using both field data and a modelling approach. In the modelling approach, we extrapolated our analysis to even higher grazing pressures to investigate the vegetation patchiness when desertification is imminent. In three arid Mediterranean ecosystems in Spain, Greece and Morocco, we found that the patch-size distribution of the vegetation follows a power law. Using a stochastic cellular automaton model, we show that local positive interactions among plants can explain such power-law distributions. Furthermore, with increasing grazing pressure, the field data revealed consistent deviations from power laws. Increased grazing pressure leads to similar deviations in the model. When grazing was further increased in the model, we found that these deviations always and only occurred close to transition to desert, independent of the type of transition, and regardless of the vegetation cover. Therefore, we propose that patch-size distributions may be a warning signal for the onset of desertification.

Methods for Detecting Early Warnings of Critical Transitions in Time Series Illustrated Using Simulated Ecological Data

Many dynamical systems, including lakes, organisms, ocean circulation patterns, or financial markets, are now thought to have tipping points where critical transitions to a contrasting state can happen. Because critical transitions can occur unexpectedly and are difficult to manage, there is a need for methods that can be used to identify when a critical transition is approaching. Recent theory shows that we can identify the proximity of a system to a critical transition using a variety of so-called ‘early warning signals’, and successful empirical examples suggest a potential for practical applicability. However, while the range of proposed methods for predicting critical transitions is rapidly expanding, opinions on their practical use differ widely, and there is no comparative study that tests the limitations of the different methods to identify approaching critical transitions using time-series data. Here, we summarize a range of currently available early warning methods and apply them to two simulated time series that are typical of systems undergoing a critical transition. In addition to a methodological guide, our work offers a practical toolbox that may be used in a wide range of fields to help detect early warning signals of critical transitions in time series data.

The ecological and evolutionary implications of merging different types of networks.

Interactions among species drive the ecological and evolutionary processes in ecological communities. These interactions are effectively key components of biodiversity. Studies that use a network approach to study the structure and dynamics of communities of interacting species have revealed many patterns and associated processes. Historically these studies were restricted to trophic interactions, although network approaches are now used to study a wide range of interactions, including for example the reproductive mutualisms. However, each interaction type remains studied largely in isolation from others. Merging the various interaction types within a single integrative framework is necessary if we want to further our understanding of the ecological and evolutionary dynamics of communities. Dividing the networks up is a methodological convenience as in the field the networks occur together in space and time and will be linked by shared species. Herein, we outline a conceptual framework for studying networks composed of more than one type of interaction, highlighting key questions and research areas that would benefit from their study.

More than a meal… integrating non‐feeding interactions into food webs

Organisms eating each other are only one of many types of well documented and important interactions among species. Other such types include habitat modification, predator interference and facilitation. However, ecological network research has been typically limited to either pure food webs or to networks of only a few (<3) interaction types. The great diversity of non-trophic interactions observed in nature has been poorly addressed by ecologists and largely excluded from network theory. Herein, we propose a conceptual framework that organises this diversity into three main functional classes defined by how they modify specific parameters in a dynamic food web model. This approach provides a path forward for incorporating non-trophic interactions in traditional food web models and offers a new perspective on tackling ecological complexity that should stimulate both theoretical and empirical approaches to understanding the patterns and dynamics of diverse species interactions in nature.

Slowing down in spatially patterned ecosystems at the brink of collapse.

Predicting the risk of critical transitions, such as the collapse of a population, is important in order to direct management efforts. In any system that is close to a critical transition, recovery upon small perturbations becomes slow, a phenomenon known as critical slowing down. It has been suggested that such slowing down may be detected indirectly through an increase in spatial and temporal correlation and variance. Here, we tested this idea in arid ecosystems, where vegetation may collapse to desert as a result of increasing water limitation. We used three models that describe desertification but differ in the spatial vegetation patterns they produce. In all models, recovery rate upon perturbation decreased before vegetation collapsed. However, in one of the models, slowing down failed to translate into rising variance and correlation. This is caused by the regular self-organized vegetation patterns produced by this model. This finding implies an important limitation of variance and correlation as indicators of critical transitions. However, changes in such self-organized patterns themselves are a reliable indicator of an upcoming transition. Our results illustrate that while critical slowing down may be a universal phenomenon at critical transitions, its detection through indirect indicators may have limitations in particular systems.

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.

The ecological forecast horizon, and examples of its uses and determinants

Forecasts of ecological dynamics in changing environments are increasingly important, and are available for a plethora of variables, such as species abundance and distribution, community structure and ecosystem processes. There is, however, a general absence of knowledge about how far into the future, or other dimensions (space, temperature, phylogenetic distance), useful ecological forecasts can be made, and about how features of ecological systems relate to these distances. The ecological forecast horizon is the dimensional distance for which useful forecasts can be made. Five case studies illustrate the influence of various sources of uncertainty (e.g. parameter uncertainty, environmental variation, demographic stochasticity and evolution), level of ecological organisation (e.g. population or community), and organismal properties (e.g. body size or number of trophic links) on temporal, spatial and phylogenetic forecast horizons. Insights from these case studies demonstrate that the ecological forecast horizon is a flexible and powerful tool for researching and communicating ecological predictability. It also has potential for motivating and guiding agenda setting for ecological forecasting research and development.

REVIEW: Predictive ecology in a changing world

1. In a rapidly changing world, ecology has the potential to move from empirical and conceptual stages to application and management issues. It is now possible to make large-scale predictions up to continental or global scales, ranging from the future distribution of biological diversity to changes in ecosystem functioning and services. With these recent developments, ecology has a historical opportunity to become a major actor in the development of a sustainable human society. With this opportunity, however, also comes an important responsibility in developing appropriate predictive models, correctly interpreting their outcomes and communicating their limitations. There is also a danger that predictions grow faster than our understanding of ecological systems, resulting in a gap between the scientists generating the predictions and stakeholders using them (conservation biologists, environmental managers, journalists, policymakers). 2. Here, we use the context provided by the current surge of ecological predictions on the future of biodiversity to clarify what prediction means, and to pinpoint the challenges that should be addressed in order to improve predictive ecological models and the way they are understood and used. 3. Synthesis and applications. Ecologists face several challenges to ensure the healthy development of an operational predictive ecological science: (i) clarity on the distinction between explanatory and anticipatory predictions; (ii) developing new theories at the interface between explanatory and anticipatory predictions; (iii) open data to test and validate predictions; (iv) making predictions operational; and (v) developing a genuine ethics of prediction.

Robust scaling in ecosystems and the meltdown of patch size distributions before extinction.

Robust critical systems are characterized by power laws which occur over a broad range of conditions. Their robust behaviour has been explained by local interactions. While such systems could be widespread in nature, their properties are not well understood. Here, we study three robust critical ecosystem models and a null model that lacks spatial interactions. In all these models, individuals aggregate in patches whose size distributions follow power laws which melt down under increasing external stress. We propose that this power-law decay associated with the connectivity of the system can be used to evaluate the level of stress exerted on the ecosystem. We identify several indicators along the transition to extinction. These indicators give us a relative measure of the distance to extinction, and have therefore potential application to conservation biology, especially for ecosystems with self-organization and critical transitions.

The multilayer nature of ecological networks

Although networks provide a powerful approach to study a large variety of ecological systems, their formulation does not typically account for multiple interaction types, interactions that vary in space and time, and interconnected systems such as networks of networks. The emergent field of ‘multilayer networks’ provides a natural framework for extending analyses of ecological systems to include such multiple layers of complexity, as it specifically allows one to differentiate and model ‘intralayer’ and ‘interlayer’ connectivity. The framework provides a set of concepts and tools that can be adapted and applied to ecology, facilitating research on high-dimensional, heterogeneous systems in nature. Here, we formally define ecological multilayer networks based on a review of previous, related approaches; illustrate their application and potential with analyses of existing data; and discuss limitations, challenges, and future applications. The integration of multilayer network theory into ecology offers largely untapped potential to investigate ecological complexity and provide new theoretical and empirical insights into the architecture and dynamics of ecological systems.