Since in the case in question all of the values in equation (2.38) 

 are constant except for y and m, while the value of y is proportional to 

 1, it leads us to the following theoretical equation: 



m = cl'^, (2.39) 



Where c is a constant coefficient: for the case in question, c = 7. 



Therefore, together with m, according to equations (2.37) and (2.39), 



curve p becomes a theoretical function (a quadratic function) of 

 parameter l--the aggregation of the food. 



Experimental comparison of these values was not performed, due to 

 the difficulty of observing the aggregation of zooplankton. Therefore, 

 we could judge the spottiness of the plankton only indirectly, on the 

 basis of the spottiness of the distribution of phy topi ank ton. The 

 spottiness of phytoplankton in the region of interest to us was measured 

 by optical methods (based on the absorption of light by chlorophyll) in 

 two sessions of approximately one hour each (these data were kindly 

 provided to us by V. N. Pelevin). To estimate the number of spots, a 

 threshold of 40 units, located in the moddle of the spread of both 

 curves, was arbitrarily selected. Using this threshold, on the curve 

 obtained on 26 January 1964, 23 excursions were noted, on the curve 

 obtained on 27 January--16 excursions. Given the mean speed of the ship 

 of 30 km/hr, the mean distances between spots of phytoplankton (1) was 

 defined as 1.3 and 1.9 km, while the mean number of flying fish on these 

 days (m) was 12 and 23. A numerical count shows good agreement of the 

 values m and 1 obtained with the theoretical equation (2.39). 



The value c = m/1^ ^ 7 was defined for 26 January; for 27 January, 

 the "theoretical" value of m was 25.3, which differs only slightly from 

 the observed value (23). Thus, we can present the following theoretical 

 equation for the density of predators, given constant density p^ = const 

 of prey, as a function of the aggregation of the prey 1: 



P = c(l/X)2 



Where c is a constant related p^^, depending on the type of predator and 

 prey, 1 and X are the mean distances between schools of predators and 

 spots of prey. 



358 



