175 



Indirect estimates of natural mortality rate 

 for arrowtooth flounder (Atheresthes stomias) 

 and darkblotched rockfish iSebostes cramerD 



Donald R. Gunderson 



School of Aquatic and Fishery Sciences 



Box 355020 



University of Washington 



Seattle, Washington 98195 



E mail address (for D R Gundersoni dgunm^uvvashington edu 



delta method (Seber, 1982) to derive 

 estimates of the variance of predicted 

 values of M using Gunderson's tech- 

 nique and Jensen's ( 1996) modification 

 of Pauly's technique. In the case of the 

 method developed by Hoenig, where 

 natural mortality is estimated from 

 longevity, no comparable variance es- 

 timator could be obtained because the 

 results depend on the sample size used 

 to estimate longevity (Hoenig, 1983). 



Mark Zimmermann 



Daniel G. Nichol 



Alaska Fishenes Science Center, 

 National Marine Fishenes Service 

 7600 Sand Point Way N E 

 Seattle, Washington 98115-0070 



Katherine Pearson 



School of Aquatic and Fishery Sciences 



Box 355020 



University of Washington 



Seattle, Washington 98195 



Indirect estimates of instantaneous 

 natural mortality rate (M) are widely 

 used in stock assessment and fisheries 

 management. They are essentially a 

 form of meta-analysis, in which prior 

 information on M and key life history 

 parameters from a variety of stocks 

 is used to estimate M for the stock in 

 question. 



In this study we report indirect 

 estimates of M for arrowtooth floun- 

 der (Atheresthes stomias) and dark- 

 blotched rockfish (Sebastes crameri) 

 obtained by the methods described in 

 Gunderson (1997), and a modification 

 of Pauly's method (1980), and com- 

 pare them with estimates previously 

 derived by Hoenig's (1983) method. 

 Pauly's original method was based on 

 the correlation of M with von Berta- 

 lanffy growth parameters (A' and L ) 

 and temperature. The modification 

 we used was indicated by a number 

 of reviews of Pauly's data (Charnov, 

 1993; Pascual and Iribarne. 1993; 

 Jensen, 1996) and relies only on the 

 correlation between M and K. The high 

 correlation between these variables 

 has been observed in a number of taxa 

 and is the basis for the M-K "invari- 



ant" used widely in life history theory 

 (Beverton, 1992; Charnov, 1993). 



Gunderson's method is based on the 

 high correlation between reproductive 

 effort and natural mortality rate and 

 has a well-established basis in experi- 

 mental ecology and life history theory 

 (Reznick, 1996). Increases in reproduc- 

 tive effort often come at a cost, and 

 trade-offs between reproductive effort 

 and adult growth or survival have 

 been reported in a wide range of field 

 studies and manipulation experiments 

 (Roff 1992; Stearns, 1992). Gunderson 

 (1997) found a linear relationship 

 (/•-=0.75) between M and reproduc- 

 tive effort as measured by the gonad- 

 osomatic index (GSI=ovary weight/ 

 somatic body weight) for 28 stocks of 

 fish, and theoretical analysis (Charnov 

 et al.. 2001; Charnov, 2002) has shown 

 that this equation can be a predictable 

 result when maximizing the lifetime 

 production of young. 



Pascual and Iribarne (1993) noted 

 that one shortcoming of indirect 

 methods of estimating natural mor- 

 tality is that no variance estimate is 

 usually associated with the predicted 

 value of M. In this study, we used the 



Materials and methods 



Data on darkblotched rockfish were col- 

 lected in 1986 and 1987 during re- 

 search surveys conducted off the Ore- 

 gon coast (43°10'-45°50') aboard com- 

 mercial groundfish and shrimp trawl- 

 ers. Fish were weighed to the nearest 

 gram, and fork length was measured 

 to the nearest millimeter. Gonads were 

 removed and weighed to the nearest 

 0.01 g. Gonad color, size, and struc- 

 ture were recorded for each specimen, 

 and macroscopic obsei^vations were 

 made at sea for the presence of fertil- 

 ized eggs, eyed lai-vae, and residual 

 larvae in the ovaries. Gonads were 

 preserved in 10'7f phosphate-buffered 

 formalin and histological analysis was 

 conducted later in the laboratory for 

 selected specimens. It was assumed 

 that the ovaries collected during No- 

 vember-January were fully mature 

 because oocyte fertilization occurs 

 during December-February (Nichol, 

 1990). Only mature females (36.7 cm 

 or greater) classified as being in the 

 "vitellogenesis" stage (Nichol and 

 Pikitch, 1994) during November-,Jan- 

 uary (n=28) were used to estimate 

 the parameters for the length-ovary- 

 weight relationship, and fish collected 

 during August-November were added 

 when estimating the length-somatic- 

 weight relationship (total /!=86). 



Data on arrowtooth flounder were 

 collected from research trawls made 

 during September 1993 on Portlock 

 Bank near the eastern end of Kodiak 

 Island, Alaska (Zimmermann, 1997). 

 Fish (less stomach contents) were 

 weighed (-I-/-2 g) and fork length (cm) 



Manuscript accepted 10 July 2002. 

 Fish. Bull. 101:175^182 12003). 



