Spore Dispersal and Plant Disease Gradients; a Comparison between two Empirical Models

Abstract

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.

Spatial aggregation of pathotypes of barley powdery mildew

“…Because the dispersal gradient for mildew decreases with distance (Fitt et al, 1987), we can assume that the amount of aggregation decreases with increasing separation also. This enables us to use a sequential strategy to test for the distance over which spatial correlation in the distribution of mildew pathotypes can be observed.…”

“…Together, these two studies imply that clones of E. graminis form many foci of infection in a field, which merge early in the progress of the epidemic. Because windborne spores are dispersed over larger distances than splash-dispersed spores (Fitt et al, 1987), aggregation in mildew populations within fields may be seen over larger distances. However, this would also mean that foci would merge earlier in the epidemic, and hence the amount of aggregation might be less.…”

“…Soil-borne diseases have been the focus of most of this work (reviewed by Campbell & Noe, 1985), whereas much of the experimental work on the spatial aspects of epidemics of airborne pathogens has tended to concentrate on dispersal gradients (e.g. Fitt et al, 1987). How the dispersal process affects the population dynamics of the pathogen has been studied largely through simulation (e.g.…”

Ascospores as primary inoculum for epidemics of white leaf spot (Mycosphaerella capsellae) in winter oilseed rape in the UK

“…For the Rothamsted epidemic, the two empirical models used to describe the decrease in disease (y) with distance (x) were the inverse power-law model and the negative exponential model (Fitt et al, 1987). So that gradients could be compared more easily, the equations for both models were made linear by taking natural logarithms of both sides.…”

“…The exponential model has the property that the amount of disease decreases by half as the distance from the source increases by a constant increment, the half-distance (␣). The half-distance is related to the exponent d (Fitt et al, 1987) and was calculated for each gradient:…”