176 



Fishery Bulletin 101(1) 



was obtained. Gonads were assigned a macroscopic ma- 

 turity stage based on external appearance, and were 

 removed and preserved in 10% formalin buffered with 

 sodium acetate. Gonads were subsequently removed from 

 formalin, weighed (+/-0.001 g) in the laboratory, and clas- 

 sified histologically to maturity stage. Only mature fe- 

 males (47 cm and greater) with ovaries in the "migratory 

 nucleus" stage (Zimmermann, 1997) were used in estimat- 

 ing the length-ovary-weight relation (n = 19), and fish in 

 the "late vitellogenesis" stage were added when estimat- 

 ing the length-somatic-weight relation (total «=59). 



A fresh-weight to formalin-weight conversion equation 

 for gonads was obtained by collecting 22 females during a 

 research cruise conducted during late October and early 

 November 1999 off Oregon and northern California. Go- 

 nads for these specimens were weighed fresh at sea (+/- 

 2 g) and again after being stored for 1-4 months in 10% 

 formalin buffered with sodium bicarbonate (+/-0.0G1 g). 

 Fresh ovary weights for these specimens ranged from 2 

 to 500 g. The equation for conversion of fresh weight to 

 formalin weight obtained by linear regression was 



Fresh weight = 1.04305 (formalin weight) 

 + 1.82277 



(P<0.001) 



and was used to correct all arrowtooth flounder ovary 

 weights to fresh weights. 



The length-somatic-weight (where somatic weight=total 

 weight minus gonad weight) and length-ovary-weight re- 

 lationships for both species followed allometric (y=aX^) re- 

 lationships and were fitted by using nonlinear regression 

 (EXCEL SOLVER, Microsoft Corp., 1998). The relation of 

 length to GSI (gonadosomatic index=ovarv weight/somatic 

 weight) was fitted to an allometric relationship because 

 the ratio of two allometric relationships will also be an 

 allometric relationship. The length-GSI relationship was 

 then used to predict the GSI for a mature female of aver- 

 age size in the population. 



The average size of a mature darkblotched rockfish was 

 estimated to be 42.7 cm, based on the size composition of 

 females greater than 36.5 cm (the size at 50% maturity, 

 Nichol and Pikitch, 1994) during the 1977 NMFS trien- 

 niel trawl survey (Rogers' ). There is no directed fishery for 

 arrrowtooth flounder, and they have been exploited only 

 lightly. As a result, the average size of a mature (47 cm 

 or greater; Zimmermann, 1997) arrowtooth flounder was 

 estimated to be 55.5 cm, based on the size composition in 

 the 1999 NMFS trawl survey, which covered their entire 

 size range with a single gear type (Brown-). 



The instantaneous rate of natural mortality was es- 

 timated from the equation M=1.79 GSI developed by 

 GundjTson ( 1997). The variance of this estimate was esti- 

 mated using the delta method to obtain 



' Rogers, J. B. 2001. Personal commun. Northwest Fisher- 

 ies Science Center, 2030 SE Marine Science Dr., Newport OR 

 97365. 



'^ Brown, E. S. 2002. Personal conimiin. Ala.ska Fisheries Sci- 

 ence Center, 7600 Sand Point Way NE, Si'altle, WA 981 1.5. 



Var(M) = VarikGSi) = {GSlf VaT{k) + k'^ Var(GS/), 



Var(GS/) = [ef^Ly-^f WariL J + (I^[War{e) 

 + [eZ:(, ln(Z:„, )f Var(/-) + (2Li,)feL;:, ln(L„,)Cov(e,/-)l; 



Var(/?) = -=i ^ (Draper and Smith, 



2_^{GSI,-GSI)~ 1981) = 0.03389) 



where L„, = mean length of a mature female in the unex- 

 ploited population; 

 e,f = coefficients in the length-GSI relationship 



{GSl=eLf)\ 

 s'^ = residual mean square from GSI-M regres- 

 sion equation (Gunderson, 1997); 

 GSI = mean value of GSI used to predict M in this 



study; 



GSI = mean value of GSI in regression sample 



(Gunderson, 1997); 

 GSI^ = GSI value for /"^ species in the regression 

 sample; and 

 k = constant from the GSI-M regression = 1.79. 



The Var (e), Var (f), and Gov (e,/l terms in Var (GSI) were 

 estimated from the variance-covariance matrix of a non- 

 linear regression algorithm for the length-GSI relation- 

 ship_by using S-PLUS (Venables and Ripley 1997). The 

 Var(L^^^) term was estjrnated from the length-frequency 

 data used to estimate L^^. 



Indirect estimates of M were also obtained using a modifi- 

 cation of Pauly's ( 1980) method. Jensen ( 1996) showed that 

 in terms of either the standard error or proportion of varia- 

 tion in predicted M, the simple linear regression of M on the 

 von Bertalanffy growth parameter K is as good as a multiple 

 linear regression model that includes asymptotic size and 

 temperature. The correlation between M and K' is a predict- 

 able result from life history theory when optimizing the 

 trade-off between survival and fecundity (Jensen, 1996), and 

 has been shown to occur in a wide variety of invertebrate 

 and vertebrate groups (Beverton, 1992; Charnov, 1993). 



Pauly's (1980) data for 175 stocks of fish were used to 

 estimate the coefficient (^ = 1.598; r'^=0.72) in the equation 

 M=gK. Estimates of A' were obtained by fitting age-length 

 data (sexes combined) for 3930 darkblotched rockfish and 

 706 arrowtooth flounder to the Von Bertalanffy growth 

 model (Ricker, 1975) by using a nonlinear regression al- 

 gorithm in AD Model Builder (Fornier, 2001;WilderbuerM. 

 The variance of the estimates was estimated with the 

 delta method to be 



Var(M) = g^Var(K) + K'^WaT(g). 



The Var(Ar) term was estimated by using AD Model 

 Builder, and Var(^) was estimated by using Pauly's data, 

 and the same method used above to estimate Var(^) (Draper 



and Smith. 1981). 



' Wilderbuer, T. K. 2002. Personal commun. Alaska Fisheries 

 Science Center, 7600 Sand Point Way NE, Seattle, WA 98115. 



