Obviously, similar estimates can be performed to predict the 

 results of other strong effects, related to pollution, catastrophes and 

 other harmful influences on a community. 



2.3 Static Model of a Community Considering Aggregation . 



The construction of a dynamic stochastic model considering 

 aggregation is quite difficult. Therefore, let us analyze a static case 

 of this model or a 2-component community (a=2) consisting of a predator 

 and its prey, referring to the aggregations of the predator as schools , 

 of the prey as spots . 



A set consisting of N objects will be referred to as a N-set. In a 

 single biotope with the volume V„(q = 2 for area, q = 3 for volume), we 

 analyze the N-field of food particles and the M-accumulation of 

 individual predators. The aggregation of food particles is determined 

 by the v n-spots (N = v.n), the aggregation of the latter by the u m- 

 schools. Furthermore, the former aggregation can be described by the 

 two parameters r^ and 1, where r^ is the radius of a sphere equal in 

 volume to n-spot or a half-side of an equivalent cube, while 1 is the 

 distance between their centers. With the distribution of n-spots stable 

 in the probabilistic sense, rp and 1 act as constant means. From the 

 standpoint of the m-school , tne value of r^ is replaced by the quantity 

 r = Tf^ + r^, where r^ is the distance from the edge of n-spot to the 

 point where m-school will reliably detect n-spot (this quantity has a 

 precise statistical sense. 



It can be shown (Fleishman, 1974), that the mean specific ration Rj^ 

 of individuals within m-school is 



P y*^"^ 

 R = (l5fil! z)w particles per day (2.35) 



m 



m 



where yn,( meter) is 



1, if 1 < r (directed catching) 

 y^, = min r, 1 = 2.36 



■" r, if r < 1 (blind search); 



z (in particles/meter) is the energy cost expressed in individuals, 

 equivalent to the loss of z food particles in one meter of travel path, 

 w (meter/day) is the mean speed of movement of m-school. 



The expression R_ will now be analyzed given the constant value: 



N .particles, 

 ^ 'q meters^ 



Of the mean construction of food and the variable aggregation of food, 

 defined by the parameter 1 or v = V-/l^. 



355 



