DEPOSITION GRADIENTS AND ISOLATION 



applanatum will emit spores continuously and copiously for months, and 

 the spores will be diffused and deposited; yet the occurrence ofGanoderma 

 fruit-bodies remains erratic throughout a forest, their occurrence being 

 limited by what may be expressed in the ignorance-blanketing phrase — 

 'availability of sites'. An infection gradient can only develop when sites 

 such as trap surfaces, nutrient medium, susceptible host-plants, ripe 

 stigmas, or burnt soil, are freely available. The deposition gradient is a 

 regular phenomenon: an infection gradient follows when the deposition 

 gradient is superimposed on unoccupied sites. Ecologically, an infection 

 gradient is a stage in succession, not a characteristic of a balanced state. 



(iv) Multiple infections. As long as the number of available sites is 

 large, the slope of the infection gradient will be parallel to that of the 

 deposition gradient. But as soon as available sites begin to be used up, the 

 infection gradient will be flattened, the flattening beginning nearest 

 the source, and the relation between the two gradients under simple 

 conditions is given by the multiple-infection transformation (Gregory, 



'948)- 



When disease incidence is recorded as the number or percentage of 



plants attacked, irrespective of whether the plant has one or many lesions, 



aphid punctures, etc., the percentage will have to be suitably transformed 



before the formula for deposition can be applied. 



The need for the transformation may be illustrated by considering a 

 hypothetical example of lOO potato plants, uniformly susceptible and 

 exposed to infection by Phytophthora infestans from a distant source. 

 The first spore that causes an infection must obviously infect i per cent 

 of the plants. A second infecting spore, so long as it falls at random 

 among the lOO plants, will have one chance in loo of alighting on the 

 one plant already infected, instead of infecting a second plant. As the 

 percentage of infected plants increases, the probability that each additional 

 infection falls on a plant already infected (thus producing no increase in 

 the percentage of plants infected) increases greatly. When 99 per cent of 

 the plants are infected, another infection will have only one chance in 100 

 of falling on the single remaining healthy plant. Different parts of the 

 percentage range, therefore, correspond to very different spore densities 

 per unit area, and the transformation can be neglected only in the lower- 

 percentage categories. 



Thompson (1924) applied the Poisson distribution to the problem of 

 multiple infection and showed that if N = number of hosts available, and 

 y = average number of hosts infected after the deposition at random among 

 the hosts of x parasites, then 



y = N (i - e-'^/^), 



Table XXVI gives x calculated for values of y varying from i to 99-9 

 per cent; it shows that whereas only one infection is required to bring 

 about an increase from i to 2 per cent, the increase from 98 to 99 per cent 



163 



