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Fishery Bulletin 102(2) 



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Icsooz size 



1,000 -| 



Figure 5 



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

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

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

 ot=1.5x 10~ 6 . The top panel shows school-size distributions (in log-log scalei 

 at selected times it). The lower panel gives the mean school size ikbar) and 

 school abundance (N ) versus time. 



2001; Calderelli et al„ 2002; Vazquez, 2003). Biological 

 concepts of fitness, feeding behavior, predator-avoidance 

 behavior, and habitat suitability appear to fall within 

 the attachment criteria examined in physics literature. 

 Oceanographic stability (Myers and Pepin, 1994), assorta- 

 tive schooling by color patterns (Crook, 1999), chemosen- 

 sory stimuli (Quinn and Busack, 1985), and larval fitness 

 indices from RNA/DNA ratios (Pepin, 1991; Suneetha et 

 al., 1999) may be mechanisms that directly or indirectly 

 influence aggregation size and, thus, distribution. 



The geometry of the school size itself may be sufficient to 

 produce preferential attachment behavior, as well. In the 



models of this study, the detection spaces (G, +G f in Equa- 

 tion 1) were set to unity and assumed to be independent of 

 school size. However, the detection space may be related 

 to school size. For example, if a school of one fish has a 

 spheroid detection space around itself with radius equal 

 to 1, then using the geometry of an aggregation of /<■ fish, 

 the detection space of the aggregate would be proportional 

 to k v: \ Alternatively, if the detection space were a two-di- 

 mensional circle with a radius of 1, then the aggregate's 

 detection space would be proportional to &"'-'. Substituting 

 size-dependent detection spaces into the random mortality 

 and aggregation models would be sufficient to induce pref- 



