310 



Fishery Bulletin 102(2) 



tion of the cohort that died. Both the proportion of eggs 

 deposited and squid that died were expressed as negative 

 exponential functions. The cumulative eggs deposited up 

 to elapsed time t (days I for a mature female L. opalescens 

 is the difference of two terms: E SPl = E P - E YDt where E SP/ 

 is the total eggs deposited by one female up to time t, E P is 

 the potential fecundity, and E YDl is the standing stock of 

 oocytes in the ovary plus the standing stock of ova in the 

 oviduct remaining in the body at time t. If we assume that 

 E YDl declines at an exponential rate from E P : E YDl = E P 



e~ ut , where v is the daily rate of eggs deposited, then E SPt 

 = Ej, ( l-e _1 0. We constructed the cumulative egg deposition 

 curve as Qspt~ E SPl IE P = l-e~ vt . Assuming the mortality 

 (survival) curve for the squid is e~ zt , where z is adult daily 

 total mortality rate iz=m+f, where m is natural and f is 

 fishing mortality), we computed the mean fraction of the 

 potential fecundity deposited (Q SPt ): 



S 



80 

 70 



60 



50 



40 - 

 30 

 20 



10 



W= 0.000051 Z_ 28086 



,2=0.964 

 n = 42 



50 60 70 



n 1 1 1 1 1 1 



100 110 120 130 140 150 160 



80 90 



Dorsal mantle length (mm 



Figure 4 



Female squid whole body weight ( W) as a function of dorsal mantle 

 length (L) for the 158 females with fecundity analyses. The line 

 expresses the length-weight relation of females before weight 

 losses associated with spawning and was fitted to the combined 

 data for immature females (solid triangles), mature preovulatory 

 females (solid circles), and mature females judged by their mantle 

 condition to be new recruits to the spawning ground (solid circles). 

 Open circles indicate females that have spawned. 



| ze- zt a-e- vt )dt 



Qsp 





dt 



(!) 



= 1- 



zil-e' 



) 



(z + y)(\-e 



) z + v 



for large / n 



where t max is the total elapsed time (days). 



The mean fraction of the potential fecundity that 

 remains in the average female (standing stock of 

 oocytes and ova) over her lifetime is 1 - Qsp, and 

 mean Q SP is always less than one because of mor- 

 tality. The mean duration of the spawning period in 

 days is computed as the elapsed time correspond- 

 ing to the mean fraction of eggs deposited (Q SP : Eq. 

 1 and by setting Q SP =l-e-'''): 



^ sf =ln(l- Q P )/(-«). 



(2) 



We evaluated various rates of adult daily total 

 mortality (z) and egg deposition (r) using these 

 models to determine the combination of rates that 

 would provide estimates of fecundity nearest to our 

 observed field data. 



Modeling the effect of fishing effort on 

 egg escapement 



In theory we could manage the market squid fish- 

 ery by monitoring egg escapement, that is, the frac- 

 tion of the fecundity realized by the average female. 

 Under such a management scheme, egg escapement 

 would be maintained at a specified level by chang- 

 ing fishing effort whenever escapement of eggs 

 fell below it. In this section we develop a model to 

 explore the relative effects of fishing effort on egg 

 escapement. We use this model to discuss some of 

 the biological issues related to using egg escape- 

 ment as a management tool. 



In the modeling process, we follow one cohort of 

 spawners. The elapsed time is defined as the time 

 when squid start spawning. The total escapement 

 of eggs for a given elapsed time (t k in days) is the 

 sum of three sources of egg escapement: E c , the 

 total number of eggs deposited by mature females 

 in the catch; E M , the total number of eggs deposited 

 by mature females dying of natural causes; and 

 E A , the total number of eggs deposited by females 



