THE MICROBIOLOGY OF THE ATMOSPHERE 



to occur around the primary lesions. Examples of this effect are found in 

 Pape & Rademacher (1934), Zogg (1949, Figs. 10 and 11), Waggoner 

 (1952, Fig. 2), and Cammack (1958). 



(vii) Sampling. At low levels of infection, the size of samples must be 

 increased, as otherwise the sampling error becomes large {see Finney, 



1947)- 



Empirical Methods 



As noted in Chapter V, gradients can be represented by either an 

 empirical or a theoretical model. In the empirical method we make the 

 curve to fit the data, but in the theoretical method we test the fit of the 

 data to the curve. 



Frampton et al. (1942) concluded that incidence of some insect- 

 transmitted virus diseases decreased logarithmically with distance. 

 Zentmeyer et al. (1944) studied the spread of the Dutch elm-disease 

 pathogen, CeratostomeUa tilmi, which is transmitted from tree to tree by 

 the elm-bark beetle, Scolytus niulthtriatus. Their data, to distances 

 of about 84 metres, indicated that the probability of infection decreased 

 with the logarithm of the distance. Most subsequent curve-fitters agree 

 that such decrease is logarithmic. 



Wolfenbarger (1946, 1959; see also Wadley & Wolfenbarger, 1944), 

 in valuable surveys of literature on the dispersal of bacteria, spores, seeds, 

 pollen, and insects, concluded that the observed data could be fitted by 

 one of the two following equations : 



E = a + b (log x), or 



E = a + b (log x) + c (i/x), 



where E = the expected value, x = distance from source, and a, b, 

 and c are parameters derived from the observed data. Values of the para- 

 meters a, b, and c, obtained by Wolfenbarger, showed enormous variation 

 between the numerous sets of published results, and it is not possible to 

 make any kind of generalization using this method, or to use the para- 

 meters, as given, to predict gradients. 



E. E. Wilson & Baker (1946, 1946^^) made field observations in 

 California on the dispersion pattern of apricot brown-rot {Sclcrotmia laxa 

 on Primus armeniaca), and they also liberated Lycopodium spores experi- 

 mentally. They fitted the following equations to their data : 



(i) y = loo/x^ for the gradient of aerial spore concentration (con- 

 centration at distance X2 and at subsequent distances being expressed as 

 a percentage of the concentration at x^). 



(2) y = 100 (i + a)2 / (x + a)^, for the gradient of infection by 

 airborne spores, where a is a parameter for the experiment. 



Dispersal by insect vectors is usually fitted by a logarithmic expression. 

 Bateman (1947^) found that the proportion (F) of contamination of 



166 



