Field data on disease gradients are essential for understanding the spread of plant diseases. In particular, dispersal far from an inoculum source can drive the behavior of an expanding focal epidemic. In this study, primary disease gradients of wheat stripe rust, caused by the aerially dispersed fungal pathogen Puccinia striiformis, were measured in Madras and Hermiston, OR, in the spring of 2002 and 2003. Plots were 6.1 m wide by 128 to 171 m long, and inoculated with urediniospores in an area of 1.52 by 1.52 m. Gradients were measured as far as 79.2 m downwind and 12.2 m upwind of the focus. Four gradient models—the power law, the modified power law, the exponential model, and the Lambert's general model—were fit to the data. Five of eight gradients were better fit by the power law, modified power law, and Lambert model than by the exponential, revealing the non-exponentially bound nature of the gradient tails. The other three data sets, which comprised fewer data points, were fit equally well by all the models. By truncating the largest data sets (maximum distances 79.2, 48.8, and 30.5 m) to within 30.5, 18.3, and 6.1 m of the focus, it was shown how the relative suitability of dispersal models can be obscured when data are available only at a short distance from the focus. The truncated data sets were also used to examine the danger associated with extrapolating gradients to distances beyond available data. The power law and modified power law predicted dispersal at large distances well relative to the Lambert and exponential models, which consistently and sometimes severely underestimated dispersal at large distances.
A computational analysis of natural convection in a vertical channel with a modified power law non-Newtonian fluid
