Spore dispersal and plant disease gradients: a comparison between two empirical models

Power law and exponential models were fitted to 325 sets of observations which described decreases with distance in deposition of air-borne or splash-borne spores, or pollen, or in amounts of plant disease caused by fungi, bacteria or viruses. There, was generally little difference between the models in the goodness of fit to these data, although deposition gradients for spores borne in splash droplets were fitted better by exponential models and gradients for fungi with air-borne spores less than 10 μm in diameter were fitted better by power law models. The exponential model has the property that the observed variable decreases by half as the distance from the source increases by a constant increment (the half-distance); this provides a measureof the gradient that is more easy to visualize than the exponent in power law model. The half-distances of gradients for air-borne pathogens were greater than those for splash-borne or soil-borne pathogens. The exponential model is easier to incorporate into models of disease development than the power law model because the boundary condition at the source (the estimated number of spores or amount of disease at the source) is finite rather than infinite. However, both these empirical models have limitations and should not be extrapolated to distances outside the observed range.