TILLMAN and STADELMAN: SIMULATION MODEL OF ANCHOVY FISHERY 



The fleet's catch in weight then is temporarily '^ 



computed as the sum 



CW(M) = ^CN(A)  WT(A,M) 



A 



where WT(A,M) is current weight at age. If 

 CW(M) exceeds the allowed harvesting capacity 

 of the fleet, CAPAC(M), the catch in weight is 

 adjusted downward: 



RC = CAPAC(M)/CW(M) 

 CW(M)' = 2RC  CN(A)  WT(A,M). 



Also, the fleet is rendered inactive for the re- 

 mainder of the week. 



Fish credited to the harvester in excess of ca- 

 pacity are subjected to natural mortality and then 

 returned to the population. Once the catch cycle 

 has been completed, the number of fish remain- 

 ing in an age-group is determined by subtracting 

 the numbers caught and the numbers taken by 

 natural mortality. 



Grov\i;h in length which occurred during the 

 month then is computed utilizing a von Berta- 

 lanffy equation (Beverton and Holt 1957). Figure 

 4 shows the growth in length curve for the follow- 

 ing parameter values: Loc = 15.91 cm, /^ = 0.32, 

 ^0 = -2.08. New individual weights at age are 

 then computed from a cubic weight-length 

 relation. 



Finally, future recruitment is calculated from 

 the number of eggs deposited on the stock's 

 spawning ground and an egg to recruit survival 

 rate: 



RECRT(M) ^EGGS(M)  SER  SMULT( RATIO) 



where SER is the equilibrium egg to recruit sur- 

 vival rate and SMULT( RATIO) is a multiplier 

 which adjusts SER in a density-dependent man- 

 ner Given Vrooman and Smith's (1971) estimate 

 of equilibrium spawning stock size (SEQ = 

 4.55 X 10« MT), Tillman (1972) estimated equi- 

 librium recruitment (REQ = 420 x 10^ fish) 

 and equilibrium numbers of eggs {EEQ = 2 x 

 1015 eggs) to obtain SER = 0.00021. The num- 

 ber of new recruits created during the current 

 month will subsequently enter the fishable stock 

 after a prerecruit period of 6 mo. 



The appropriate value of SMULT( RATIO) 

 is determined from 



14- 



12 



10- 





o Observed 

 * Calculated 



I 2 3 4 5 6 7 



Time (years) 



Figure 4. — Asymptotic growth in length of northern anchovy. 

 From Tillman ( 1972). 



SMULT(RATIO) 



A +B  RATIO 



where RATIO provides a measure of the current 

 spawning stock size, SP(M), relative to its 

 equilibrium level, SEQ: 



RATIO =SP(M)/SEQ. 



This formulation insures that the stock-recruit 

 process behaves in an asymptotic manner, as has 

 been assumed. 



Although data are lacking to estimate specific 

 values for stock-recruit parameters A andB, sets 

 of arbitrary values can be determined by defining 

 a family of curves which pass through the same 

 equilibrium point (SEQ, REQ). Following Till- 

 man (1972), a unique curve in this family is 

 distinguished by its asymptotic level of recruit- 

 ment, RMAX, which can be defined as some mul- 

 tiple of the equilibrium level of recruitment: 



RMAX = MULT  REQ. 



A particular set of stock-recruit parameters can 

 then be determined as 



B = IIMULT 



B. 



123 



