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Catastrophic events share characteristic nonlinear behaviors that are often generated by cross-scale interactions and feedbacks among system elements. These events result in surprises that cannot easily be predicted based on information obtained at a single scale. Progress on catastrophic events has focused on one of the following two areas: nonlinear dynamics through time without an explicit consideration of spatial connectivity [Holling, C. S. We provide an interdisciplinary, conceptual, and general mathematical framework for understanding and forecasting nonlinear dynamics through time and across space. We illustrate the generality and usefulness of our approach by using new data and recasting published data from ecology (wildfires and desertification), epidemiology (infectious diseases), and engineering (structural failures). We show that decisions that minimize the likelihood of catastrophic events must be based on cross-scale interactions, and such decisions will often be counterintuitive. Given the continuing challenges associated with global change, approaches that cross disciplinary boundaries to include interactions and feedbacks at multiple scales are needed to increase our ability to predict catastrophic events and develop strategies for minimizing their occurrence and impacts. Our framework is an important step in developing predictive tools and designing experiments to examine cross-scale interactions. N onlinear interactions and feedbacks across spatial scales and their associated thresholds are common features of biological, physical, and materials systems (1-3). These spatial nonlinearities and emergent behaviors challenge the ability of scientists and engineers to understand and predict system behavior at one scale based on information obtained at finer or broader scales (3, 4). Cross-scale interactions often result in ''surprises'' with severe consequences for the environment and human welfare (5). For example, wildfire initiated by a single lightning strike can spread nonlinearly across large forested landscapes as a result of positive feedbacks between weather, fire behavior, and vegetation pattern, with significant impacts on ecosystem function, local and regional economies, and human health (6). Similarly, the devastating impact of a relatively small piece of foam (Ͻ0.3 m 2 ) initiated a series of reactions that cascaded very rapidly and nonlinearly to result in the break up of the Columbia space shuttle within minutes after the initial temperature increase (7).In this article, we introduce a general framework for understanding the occurrence and consequences of system interactions that cross scales in space and time (Fig. 1). Our goal is to identify the conditions leading to catastrophic events to minimize the impacts of these events on ecosystem services, atmospheric conditions, and human welfare. The significance of thresholds and feedbacks is gaining recognition in various disciplines (3, 8, 9). However, the key to understanding threshold behavior through time necessitates the incorpor...

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Many arid grasslands around the world are affected by woody plant encroachment and by the replacement of a relatively continuous grass cover with shrub patches bordered by bare soil. This shift in plant community composition is often abrupt in space and time, suggesting that it is likely sustained by positive feedbacks between vegetation and environmental conditions (e.g. resource availability) or disturbance regime (e.g. fire or freeze). These feedbacks amplify the effects of drivers of shrub encroachment, i.e. of conditions favouring a shift from grass to shrub dominance (e.g. overgrazing, climate change). Here, we review some major drivers and feedbacks and identify the basic stages in the transition from grassland to shrubland. We discuss some possible scenarios of interactions between drivers and feedbacks that could explain the transition from a stage to the next and the potential irreversibility of the shift from grass to shrub dominance. We introduce a simplistic modelling framework that can integrate the various drivers to explain the emergence of bistability for shrub‐encroached grassland systems. Published 2011. This article is a U.S. Government work and is in the public domain in the USA.

We examined the responses of a ground‐foraging ant community to a gradient of land‐use intensity in a grazing agroecosystem in the Chaco of northern Argentina. The gradient extended from a highly degraded condition characteristic of traditional grazing practices, through an area of less severe disturbance where grazing was less concentrated, to two areas in which grazing had been managed for 3 and 18 yr, respectively. Ground cover changed along this gradient from bare to litter‐covered, ground‐layer vegetation changed from sparse to a structurally complex mixture of grasses and forbs, and canopy cover increased in areas of intermediate grazing intensity and then decreased. Community diversity varied among the sites depending on both season and scale of analysis. Site‐scale ant species richness was slightly higher in sites of intermediate disturbance in the summer‐wet season but was much greater in the least disturbed site in the winter‐dry season. The same dry‐season pattern was evident in both species richness and diversity at the scale of transects within sites, whereas species richness at the scale of individual traps within transects was significantly lower at sites of intermediate disturbance than at either highly restored or highly degraded sites. Abundances of individual ant species and functional groups also changed along the land‐use gradient. Litter‐inhabiting cryptic species and specialized predators responded positively to grazing management, whereas opportunists and the hot‐climate specialist Forelius nigriventris were prevalent in highly disturbed areas. Other functional groups exhibited redundancy and species turnover along the gradient. Detrended correspondence analysis (DCA) revealed that the ant faunas at the extremes of the land‐use gradient were more similar than expected. We hypothesize that the interaction of local‐scale habitat features with historical and biogeographic influences may determine the responses of this ant community to land use, and that highly degraded areas may have conservation value because they are regional sources of arid‐adapted ants.

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The objective of this paper is to recommend conceptual modifications for incorporation in state-and-transition models (STMs) to link this framework explicitly to the concept of ecological resilience. Ecological resilience describes the amount of change or disruption that is required to transform a system from being maintained by one set of mutually reinforcing processes and structures to a different set of processes and structures (e.g., an alternative stable state). In light of this concept, effective ecosystem management must focus on the adoption of management practices and policies that maintain or enhance ecological resilience to prevent stable states from exceeding thresholds. Resilience management does not exclusively focus on identifying thresholds per se, but rather on within-state dynamics that influence state vulnerability or proximity to thresholds. Resiliencebased ecosystem management provides greater opportunities to incorporate adaptive management than does threshold-based management because thresholds emphasize limits of state resilience, rather than conditions that determine the probability that these limits will be surpassed. In an effort to further promote resilience-based management, we recommend that the STM framework explicitly describe triggers, at-risk communities, feedback mechanisms, and restoration pathways and develop process-specific indicators that enable managers to identify at-risk plant communities and potential restoration pathways. Two STMs representing different ecological conditions and geographic locations are presented to illustrate the incorporation and application of these recommendations. We anticipate that these recommendations will enable STMs to capture additional ecological information and contribute to improved ecosystem management by focusing attention on the maintenance of state resilience in addition to the anticipation of thresholds. Adoption of these recommendations may promote valuable dialogue between researchers and ecosystem managers regarding the general nature of ecosystem dynamics. Resumen El objetivo de este documento es recomendar las modificaciones conceptuales para la incorporación en los modelos estado-ytransición (STMs) para ligar explícitamente este marco con el concepto de resistencia ecológica. La resistencia ecológica describe la cantidad de cambio o de interrupción que se requiere para transformar un sistema mantenido con sus procesos y estructuras mutuas a un sistema diferente (ej. un estado estable alternativo). Basándose en esta idea, el manejo eficaz del ecosistema debe centrarse en la adopción de prácticas de manejo y reglamentos que mantengan o promuevan la resistencia ecológica para evitar que los estados estables excedan los umbrales. El manejo de la resistencia no se centra exclusivamente en la identificación de umbrales por sí mismo, sino en las dinámicas dentro del-estado que influencian vulnerabilidad o proximidad del estado a los umbrales. El manejo del ecosistema basado en la resistencia proporciona mayores oportunidades de incorp...