Cross-scale interactions, nonlinearities, and forecasting catastrophic events.
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.
U.S. Department of Agriculture Agricultural Research Service, Jornada Experimental Range, New Mexico State University, Las Cruces, NM 88003, USA. debpeter@nmsu.edu
Debra P C
DP
Peters
Roger A
RA
Pielke
Brandon T
BT
Bestelmeyer
Craig D
CD
Allen
Stuart
S
Munson-McGee
Kris M
KM
Havstad
D000818:Animals; D002388:Catastrophic Illness / Q000453:epidemiology; D003141:Communicable Diseases / Q000635:transmission; D003889:Desert Climate; D004189:Disaster Planning / Q000706:statistics & numerical data; D004190:Disasters / Q000706:statistics & numerical data; D017753:Ecosystem; D004738:Engineering; D005390:Fires / Q000706:statistics & numerical data; D005544:Forecasting; D006801:Humans; D007303:Insect Vectors; D017711:Nonlinear Dynamics; D010935:Plant Diseases / Q000209:etiology / Q000706:statistics & numerical data; D014197:Trees