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United States Department of Agriculture

Agricultural Research Service

Title: Long Distance Dispersal and Accelerating Waves of Disease: Empirical Relationships

Authors
item Mundt, Christopher - OREGON STATE UNIVERSITY
item Sackett, Kathryn - OREGON STATE UNIVERSITY
item Wallace, Larae - OREGON STATE UNIVERSITY
item Cowger, Christina
item Dudley, Joseph - SCI APP INTERNATIONL CORP

Submitted to: The American Naturalist
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: September 30, 2008
Publication Date: February 27, 2009
Citation: Mundt, C.C., Sackett, K.E., Wallace, L.D., Cowger, C., Dudley, J.P. 2009. Long Distance Dispersal and Accelerating Waves of Disease: Empirical Relationships. The American Naturalist. 173:456-466.

Interpretive Summary: Biological invasions have substantial ecological and economic impacts. Classic approaches to modeling biological invasions predict "traveling waves" with invasion fronts of constant velocity that are determined by an organism's reproductive capacity and its dispersal ability. These approaches are based on random walk models in which movement occurs between adjacent positions and in random direction, and have been used successfully to describe the spatiotemporal spread of a range of organisms and diseases. For a traveling wave of disease, transmission would be expected to result from close or direct contact between adjacent hosts. Therefore, most of the dynamics of spread will occur close to the epidemic front. Such models may not be appropriate, however, for aerially-dispersed pathogens that exhibit considerable long distance dispersal (LDD). Indeed, the shape of the dispersal kernel is expected to have a substantial effect on the spread of invading organisms. We developed a simple model to describe accelerating spread of epidemics caused by pathogens with "fat-tailed" dispersal kernels. The model assumes decline of inoculum over distance via dilution as described by the inverse square law and predicts that location of the epidemic front will double per unit time used to measure initial velocity and that a plot of velocity versus distance will have a slope of 1/2. The model provided reasonable fits to experimental data for the wheat stripe rust disease. The scale-invariance of the inverse square law allowed us to scale-up by over five orders of magnitude to describe the continental-scale spread of both plant and animal diseases caused by pathogens that exhibit LDD. The model predicts accelerating epidemic wave fronts that can attain velocities substantially faster than suggested by the classic traveling wave model.

Technical Abstract: Biological invasions have substantial ecological and economic impacts. Classic approaches to modeling biological invasions predict "traveling waves" with invasion fronts of constant velocity that are determined by an organism's reproductive capacity and its dispersal ability. These approaches are based on random walk models in which movement occurs between adjacent positions and in random direction, and have been used successfully to describe the spatiotemporal spread of a range of organisms and diseases. For a traveling wave of disease, transmission would be expected to result from close or direct contact between adjacent hosts. Therefore, most of the dynamics of spread will occur close to the epidemic front. Such models may not be appropriate, however, for aerially-dispersed pathogens that exhibit considerable long distance dispersal (LDD). Indeed, the shape of the dispersal kernel is expected to have a substantial effect on the spread of invading organisms. We developed a simple model to describe accelerating spread of epidemics caused by pathogens with "fat-tailed" dispersal kernels. The model assumes decline of inoculum over distance via dilution as described by the inverse square law and predicts that location of the epidemic front will double per unit time used to measure initial velocity and that a plot of velocity versus distance will have a slope of 1/2. The model provided reasonable fits to experimental data for the wheat stripe rust disease. The scale-invariance of the inverse square law allowed us to scale-up by over five orders of magnitude to describe the continental-scale spread of both plant and animal diseases caused by pathogens that exhibit LDD. The model predicts accelerating epidemic wave fronts that can attain velocities substantially faster than suggested by the classic traveling wave model.

Last Modified: 4/18/2014
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