DISPERSION OF THE SPORE-CLOUD It is still convenient to speak of clouds of spores—not, indeed, keeping together in the manner of locust swarms, but tending to become dispersed while suspended passively in the atmosphere. Sampling a region small enough in relation to the size of the cloud may then reveal a random distribution of particles.
Dispersion of the spore-cloud can be deduced from early observations on the distribution of rust on rye by Windt (18o6), who observed that rust was severe near barberry bushes which are now known to be the alternate hosts for the fungus: `the effects are striking and desolating in the distance of ten to twelve paces, I have also perceived them visibly at 50, too, iso paces and a final attack at above t,000 paces.' Similarly, dispersion of the pollen cloud made it possible for Blackley (1873) to advise his hay-fever patients to keep away from grass fields during the flowering season of the grasses. Attempts to formulate the process of spore dispersion through the atmosphere have been based on geometrical, empirical, or meteorological considerations.
The geometrical approach is suggested by analogy with the laws of radiation. Nageli (1877) stated that the amount of dust which comes on an air current from one place falls off with the inverse square of the distance, whereas E. Fischer & Gaumann (1929) stated that, with linear increase of the distance, the chance of infection by rust spores decreases in cubic progression. Kursanov (1933) stated that, in the absence of wind, the number of fungus spores would fall off inversely as the cube of the dis tance from the source. The ideas that underlie the geometrical approach are simple. Spores travel away from the point of liberation: at greater distances the volume of air which they can occupy increases as the cube of the distance or, alternatively, the surface of the ground on which they could fall increases as the square of the distance. A third possibility would be a simple inverse relationship with distance, as the areas of successive annuli around a point increase in arithmetical progression.
The geometrical method is unsatisfactory because, although in a general way it illustrates the features of dispersion, it is not clear why spores should travel and spread out in the manner predicted. The particles interesting to us here are passively borne and do not behave like radiations, because the air which carries them is not in process of being continuously generated at some point in the atmosphere; consequently some totally different concept is needed.
The approach by empirical curve-fitting has been based on field records of dispersal gradients, such as the scatter of seeds or seedlings on the ground, contamination of seed crops by foreign pollen, or the incidence of plant diseases. Using such data, a curve is fitted to the ob served points, either graphically or by the statistical method of least squares, and an attempt is made to find an empirical formula to fit the curve. These methods will be referred to in detail in Chapter XIII, after the subject of spore deposition has been discussed. In general the empirical method has the advantage that an equation can usually be obtained, containing at most three parameters, which gives a good fit to any one set of field data. On the other hand, it is difficult to compare results obtained by different workers. The parameters are calculated from the data and correspond to no obvious natural phenomena; consequently it is difficult to use empirical formulae to predict a dispersal pattern under conditions differing from the original one.
In the long run a more ambitious approach seems essential, with the aim of developing formulae whose parameters correspond to factors of the environment, and which take into account the total number of microbes liberated (if known), allow for variations in weather, and use a standard unit of distance.