326 



Fishery Bulletin 102(2) 



Appendix I 



Terms 



E P potential fecundity (standing stock of oocytes 

 in the ovary of mature females prior to spawn- 

 ing) 

 E SPl the total eggs deposited on the bottom up to 

 time t. (t in days) 



E c total number of eggs deposited by mature 

 females in the catch or total number of eggs 

 escaped 



E M total number of eggs deposited by mature 

 females prior to death due to natural mortal- 

 ity 



E A total number of eggs deposited by females alive 

 and not caught by fishery 



E total number of eggs that would have been 

 spawned during a squid's lifetime if no fishery 

 existed 



E Y standing stock of oocytes in the ovary 



E D standing stock of ova in the oviduct 



E YD total fecundity, the sum of both the number of 

 oocytes in the ovary and ova in the oviduct 



E YD tlt stocking stock of oocytes in the ovary plus 

 those ova in the oviduct after spawning has 

 begun and up to the elapsed time t k , where t k 



ls £ 'max 



t max maximum elapsed time with the time being 

 the time when mature females are about 

 to ovulate or total elapsed time (in days) of 

 spawners on the spawning ground 



E R standing stock of oocytes remaining in ovary 

 at death 



m daily adult natural mortality rate 



f daily fishing mortality rate for adults 



v daily egg deposition rate 



Qsr i = EsPt IEp = 1- er vt fraction of potential fecundity 



deposited up to time t 



e~ zl mortality (survival) curve 



JV„ number of mature females at time 



N r total number of spawners in the catch 



R e tk egg escapement rate = ratio of eggs deposited 

 to total number of egg which would be spawned 

 if there was no fishery, at a given elapsed time 



R et egg escapement rate up to the maximum 



elapsed time U max ) 



Appendix II 



For any elapsed time t k , formulas for E c , E M , E A and E: 



E c = EpNJ 



E M = E P N m 



1-e 



-lm+f)t k ^_ e -(m+f+v)t), 



m + f m+f+v 



1-e 



-{m+f)t k -. _ -im+f+v)t k 



m + f m+f+v 



E A = (E P -E YD .)N k = AT e-"" +/ "* E P ( 1 - e" 1 "' ) 



V -mtJ , m 



e 1 e 



E = E P N 



The derivation for E A is straight forward and the deriva- 

 tions for £ r , E M , and E, similar among one another, are 

 as follows: 



where 



E c =\ E SP ,dC, = J Ep~a- <?"''' )dC, 



= Ep~N jn-e-")e-' m+n 'fdt, 



C.=N -^—a-e-"" +f ") 

 m + f 



is the number of removals of the cohort due to fishing up 

 to time t (Quinn and Deriso, 1999). 



E M =\E~T l dD nU =\Ep(\-e-«)dD nU 



EpNJ 



(m + f)(m + f + u) 



where 



D„, t =N -—;(l- 



!!!_h _<,-"»*/'") 



