Powers: Recruitment as an evolving random process of aggregation and mortality 



357 



o f= 

 + t=5t 



a f= 2f 



School size 



0002 

 [ 



Figure 4 



Simulated dynamics of school-size distributions using m JX as the mortal- 

 ity model and w as the aggregation model. This simulation started with 

 aggregated initial conditions (S=2xl0 6 ). The aggregation parameter was 

 o=1.5x 10" 6 . The top panel shows school-size distributions (in log-log scale) 

 at selected times (t). The lower panel gives the mean school size (kbar) and 

 school abundance (N) versus time. 



Albert (1999) was that scaling of the aggregate-size dis- 

 tribution was dependent on the type of aggregation, spe- 

 cifically preferential attachment. Bonabeau and Dagorn 

 noted the generic occurrence of scaling of aggregation 

 distributions in nature (Bonabeau and Dagorn, 1995) and 

 this scaling of aggregation distributions motivated the 

 development of the models presented here. 



The emphasis of the aggregation models was on prefer- 

 ential attachment and on comparison of model results with 

 results for models with random attachment strategies. The 

 preferential attachment rule used in the simulations was 

 that aggregation rates were proportional to the size of the 

 school encountered. But, what is meant by preferential 



attachment and does preferential attachment occur in 

 nature? Clearly, a fish, school or mortality agent has no 

 global knowledge of the proportional size of a school that 

 is encountered. However, preferential attachment in these 

 models is a metaphor for aggregation strategies that are 

 weighted toward larger school sizes. Indeed, studies of 

 networks have shown that attachment may be proportional 

 to a power of school size and still produce scale-free prop- 

 erties (Albert and Barabasi, 2002). Also, network studies 

 have shown that scale-free distributions occur when a 

 wide number of attachment criteria are included, such 

 as the "fitness" of the object being encountered and the 

 attractiveness of local conditions (Bianconi and Barabasi, 



