The double representation (2.36) of the value of y^^ results from 

 the two possible modes of hunting of an active predator seeking passive 

 prey (we shall not consider the case of a passive filter-feeder, which 

 simply waits for food to "swim up" to it). We are concerned with the 

 mode of directed ("visual") search (r > 1), in which n-spots are always 

 located within the field of detection of m-school, and the school 

 sequentially consumes the spots, as well as the mode of blind search, in 

 which m-school finds n-spots by randomly encountering them (1 > r), or 

 more accurately, by randomly approaching them until the radius of 

 detection r^ is reached. 



The basic formula (2.35) and its various interpretations have been 

 used for analysis of materials of the 17th cruise of the research vessel 

 AKADEMIK KURCHATOV. On this cruise, a visual count was made of the 

 number of flying fish and schools of flying fish (groups of at least ten 

 fish) in a section along the equator in the eastern Pacific, and the 

 time intervals between sightings were recorded. Processing of a portion 

 of these materials (ignoring the individual fish) produced the data of 

 Fig. 10. These included X(km)--the mean distance between sightings, m-- 

 the mean number of fish in each school, and p(km"^)--the density of the 

 number of fish. This last quantity is calculated from the first two: 



p = m/x2. (2.37) 



All means were calculated for a single day. The schools of flying fish 

 were encountered only west of 120°W, with a clear maximum in their 

 density at about 135°W. It is probable that this maximum is explained 

 by an increase in the concentration (mg/meter^) of zooplankton near the 

 surface, the food of the flying fish. However, data kindly provided to 

 us by A. G. Timonin clearly show that the biomass of zooplankton in the 

 upper 100 meter and 10 meter layers is practically constant between 120° 

 and 155°W ( B = 75 mg/meter^), while the increase in the value of 3 east 

 of 120°W is located in a zone where the water temperatures are too low 

 for flying fish (< 21°C). Thus, we must assume that the abundance of 

 flying fish also depends on the aggregation of zooplankton for a fixed 

 density P3 = 3/b(meter"-^) , where P3 is the number of zooplankters per 

 meter^, b is the mean biomass of one zooplankter. 



To explain this effect, we applied the theoretical equation (2.35): 



2 



Rm = (t--2>> (2.38) 



Where R^(day"-^) is the mean specific ration of flying fish in a school 

 of m fish, y = min (1, r), 1 (meter) is the mean distance between 

 zooplankton spots, r = r^ + r^ (m) , r^ is the mean radius of detection 

 of a spot by a school, r^ = /P3/P3P 1 is the mean radius of a spot 

 ( P3p > P3 represents increased density of a spot), z(meter"-'-) are the 

 energy losses of the flying fish in "standard" zooplankters per meter of 

 travel distance, w(meter/day) is the mean speed of the school. 



356 



