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



359 



B 



1.000,000 2,000.000 



3,000.000 -[ 



2,000.000 



Stock size (no. of fish) 



1,000,000 



 Mathematical model • Simulation model 



Figure 6 



Stock-recruitment relationships from the mathematical models (Eqs. 3-5, aggre- 

 gated initial conditions! compared with simulation results: I Ai density-independent 

 mortality (m c/l I and preferential attachment (u'l evaluated at 4=1, r<=10". ii = l; (B) 

 density-dependent mortality proportional to fish im dR I and preferential attachment 

 (w ) evaluated at t=10~ 5 , a=3 x 10 5 , ,n = l; ( C ) density-dependent mortality propor- 

 tional to schools (rn dN ) and preferential attachment iw ) evaluated at t=5x 10~ 4 , 

 a=1.5x 10~ 6 , f(=l; and (D) density-dependent mortality proportional to school size 

 (m dk ) and preferential attachment (w ) evaluated at ^=10 -3 , a=2x 10 _li , ,11 = 1. 



erential interaction even when encounters are random: 

 schools are randomly encountered, but the encounter event 

 itself is weighted toward larger schools. Thus, the shape of 

 the detection space may be another mechanism by which 

 preferential attachment may be exhibited. 



In the models presented, it is blithely assumed that 

 mortality is caused by undefined mortality agents. How- 

 ever, most larval recruitment research has been directed 

 at starvation and predation as determinants of recruit- 

 ment variability (Lasker, 1975; Hunter, 1984; Bailey and 

 Houde, 1989; Chambers and Trippel, 1997, for example). 

 The mortality models used here clearly fit within the pre- 

 dation paradigm: mortality from predation results from 



encounters with mortality agents of specific density and 

 size. Whereas, mortality from starvation ensues from a 

 lack of encounters with prey agents of sufficient density 

 and size. In certain situations starvation processes might 

 be aptly described by the predation-encounter approach 

 used in this study. However, further research is needed 

 to evaluate their appropriateness and to develop alterna- 

 tive modifications to Equations 3-6. A mechanism to do 

 this may be the inclusion of fragmentation of schools into 

 the models. In the models as they are now characterized, 

 new schools are not created, the number of schools only 

 becomes smaller through either aggregation or through 

 mortality on schools of a single fish. Fragmentation might 



