Brandon T. Bestelmeyer

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. (1992) Ecol. Monogr. 62, 447-502] or spatial connectivity and the spread of contagious processes without a consideration of cross-scale interactions and feedbacks [Zeng, N., Neeling, J. D., Lau, L. M. & Tucker, C. J. (1999) Science 286, 1537-1540]. These approaches rarely have ventured beyond traditional disciplinary boundaries. 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.

ABSTRACT 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.