NOTE Gunderson et al : Natural mortality of Atheresthes stomias and Sebastes cramen 



181 



In the case of darkblotched rockfish, the estimate of 

 mortahty based on reproductive effort (M=0.11) was actu- 

 ally higher than the estimate based on longevity (M=0.05), 

 and neither undersampling nor underaging would explain 

 the differences. Overestimation of the gonadosomatic in- 

 dex (and the estimated M) by using macroscopic rather 

 than histological criteria to classify maturation stage may 

 explain the higher estimate but seems less likely than 

 underestimating it because several oocyte size classes 

 that might be included in the "vitellogenesis" stage are 

 not fully developed. Underestimation of the mean length 

 of a mature female could also lead to an estimate of GSI 

 (and M) that is too low, but estimates of GSI are relatively 

 insensitive to length. For darkblotched rockfish, the mean 

 length of a mature female would have to be 32.4 cm (below 

 the size at maturity) in order for M to equal 0.05. 



Indirect estimates of M offer access to a meta-analysis 

 that can be used to explore consistency of natural mortal- 

 ity estimates with prior knowledge on a variety of stocks 

 and put these estimates in the broader context of life 

 history theory. The use of several alternative indirect 

 techniques can minimize bias in stock assessment and ex- 

 pose any misconceptions or errors regarding reproductive 

 biology or age determination at an early stage in a stock 

 assessment program. 



Bias is clearly a more important problem than precision 

 when using indirect methods to estimate M. Each of the 

 methods used in our study has a firm basis in life history 

 theory (the M-K and M-GSI "invariants") or population 

 dynamics (Z=l/maximum age), and when derived from a 

 database for a large number of species, they can be rela- 

 tively precise (CV=5-17'7r for the estimates made in this 

 paper). Nevertheless, many of the original data points on 



which these relationships are based have become outdated 

 as improved methods of age determination and stock as- 

 sessment have come into wide usage and ignoring these 

 outdated data points can lead to significant bias when us- 

 ing them to estimate M. Indirect methods are widely used, 

 and it is important that the databases from which they 

 are derived be continually updated and expanded as new 

 information becomes available. 



Acknowledgments 



We thank Dan Kimura and Saang-Yoon Hyun for their 

 invaluable statistical advice and assistance, and Jean 

 Rogers, Tom Wilderbuer, and Eric Brown for providing 

 age and length data. This research was supported by 

 the Joint Institute for the Study of the Atmosphere and 

 Ocean (JISAO) under NOAA Cooperative Agreement No. 

 NA67RJ0155 (contribution 814). 



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Beverton. R. J. H. 



1992. Patterns of reproductive strategy parameters in some 

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Charnov, E. L. 



1993. Life history invariants: some explorations of sym- 

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2002. Reproductive effort, offspring size and benefit — cost 

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