Abstract
Spatial scale is of great importance to understanding the spread of organisms exhibiting long-distance dispersal (LDD). We tested whether epidemics spread in direct proportion to the size of the host population and size of the initial disease focus. This was done through analysis of a previous study of the effects of landscape heterogeneity variables on the spread of accelerating epidemics of wheat (Triticum aestivum) stripe rust, caused by the fungus Puccinia striiformis f. sp. tritici. End-of-season disease gradients were constructed by estimating disease prevalence at regular distances from artificially inoculated foci of different sizes, in field plots of different dimensions. In one set of comparisons, all linear dimensions (plot width and length, focus width and length, and distance between observation points) differed by a factor of four. Disease spread was substantially greater in large plot/large focus treatments than in small plot/small focus treatments. However, when disease gradients were plotted using focus width as the unit distance, they were found to be highly similar, suggesting a proportional relationship between focus or plot size and disease spread. A similar relationship held when comparing same-size plots inoculated with different-sized foci, an indication that focus size is the driver of this proportionality. Our results suggest that power law dispersal of LDD organisms results in scale-invariant relationships, which are useful for better understanding spatial spread of biological invasions, extrapolating results from small-scale experiments to invasions spreading over larger scales, and predicting speed and pattern of spread as an invasion expands.