Location: Emerging Pests and Pathogens ResearchTitle: Theory of advection-driven long range biotic transport
|KOGAN, OLEG - Cornell University - New York|
|O'KEEFFE, KEVIN - Stinger Ghaffarian Technologies, Inc (SGT, INC)|
|MYERS, CHRISTOPHER - Cornell University - New York|
Submitted to: USDA-ARS Research Notes
Publication Type: Research Notes
Publication Acceptance Date: 1/6/2016
Publication Date: 1/6/2016
Citation: Kogan, O., O'Keeffe, K., Schneider, D.J., Myers, C.R. 2016. Theory of advection-driven long range biotic transport. USDA-ARS Research Notes. http://arxiv.org/abs/1510.08987v4.
Interpretive Summary: Many devastating fungal pathogens of plants have been spread by means of wind-blown spores. Various classes of statistical and dynamical models have been proposed over the years for the general phenomena or for the spread of specific diseases. Statistical models describe the net effect of all relevant processes but fail to provide useful insight into the role of the separate physical processes of transport, deposition and growth. Most dynamical models are based on complex weather simulations to predict wind patterns. Again, it is extremely difficult to assess the role of specific processes. We propose a simple two-layer model that includes: a) growth and local spread on the ground; b) advective flow in an atmospheric layer; c) exchange of spores between the ground and atmospheric layers characterized by density-dependent rates of uptake and deposition. Unlike dynamical models based on detailed weather predictions, it is possible to obtain important qualitative insights regarding the importance of specific processes, as well as quantitative results on the rate of spread. In particular, we show that sharp density fronts in both the atmospheric and ground layers develop from localized initial inoculations. These fronts propagate together at fixed speeds that can be computed in terms of the basic parameters used in the model. If diffusion in the ground layer is slow then the effects of the advective layer cannot be ignored for all non-zero uptake and deposition rates. If the rate of diffusive spread on the ground is larger, then the two transport processes function cooperatively. Estimates for the parameters appropriate for the spread of wheat stem rust suggest slow diffusion in the ground layer and rapid transport in the atmospheric layer, hence a need to explicitly include advective transport terms in dynamical models.
Technical Abstract: We propose a simple mechanistic model to examine the effects of advective flow on the spread of fungal diseases spread by wind-blown spores. The model is defined by a set of two coupled non-linear partial differential equations for spore densities. One equation describes the long-distance advective transport of spores in the atmosphere and the other describes growth and local spread by diffusive processes within the ground layer. These equations are coupled by density-dependent rates for spore uptake and deposition. The non-linearity of the system arises from the growth term. In the absence of diffusion, the model reduces to a set of strictly hyperbolic quasi-linear balance laws that are analyzed in detail. It is shown that sharp propagating fronts in both the ground and atmospheric layers develop from realistic initial conditions. The speed and shape of these fronts are computed in terms of the basic parameters of the model. Including the local diffusion term within the ground layer changes the qualitative structure of the model from hyperbolic to parabolic. However, we show that the numerical solution to the full parabolic model smoothly maps into the results for the limiting hyperbolic model as the diffusion constant approaches zero. If diffusion in the ground layer is slow then the effects of the advective layer cannot be ignored unless the uptake and deposition rates are strictly zero. If the rate of diffusive spread on the ground is larger, then the two transport processes function cooperatively. Estimates for the parameters appropriate for the spread of wheat stem rust suggest slow diffusion in the ground layer and rapid transport in the atmospheric layer, hence a need to explicitly include advective transport terms in dynamical models.