ESTIMATION OF NATURAL MORTALITY IN FISH STOCKS: 



A REVIEW 



E. F VetterI 



ABSTRACT 



The instantaneous rate of natural mortality (M) is an important but poorly quantified parameter m 

 most mathematical models of fish stock dynamics. This report reviews methods used commonly to 

 estimate M for fish stocks, sensitivity of some common fishery models to values chosen for M, and 

 evidence refuting the common assumption that a constant value can be an adequate approximation 

 of A/ within single stocks. 



With the exception of simple surplus production 

 models (e.g., Schaefer 1954; Pella and Tomlinson 

 1969) all mathematical models offish stock dy- 

 namics include as a parameter the instantaneous 

 rate of natural mortality (M). The models do not 

 require explicitly any particular form for M; it 

 can be constant or can vary in any imaginable 

 form. But because natural mortality has proved 

 extremely difficult to measure directly, M is as- 

 sumed almost universally to be some constant 

 specific to whatever stock is being modeled. This 

 is particularly true for analyses of commercial 

 fish stocks, which often require estimates of M 

 only for the postrecruit ages. Decreases in natural 

 mortality with increasing age during egg and 

 postlarval stages are so dramatic compared to ap- 

 parent changes during postrecruitment ages (e.g., 

 Gushing 1975) or compared to differences be- 

 tween different sexes, collection sites, seasons, 

 years, cohorts, or stocks within species, that vari- 

 ations in M during these later (postrecruitment) 

 ages are often assumed negligible. 



Whether this assumption is in fact acceptable is 

 the subject of this report. The answer is no, it is 

 probably not acceptable in most cases. That an- 

 swer follows from the information presented in 

 Sections II through V, with the following conclu- 

 sions: 



Section II: Current methods for estimating nat- 

 ural mortality: a review of methods used cur- 

 rently to estimate M in fish populations. All of 

 these methods have strong limitations or disad- 

 vantages. 



^Southwest Fisheries Center La Jolla Laboratory, National 

 Marine Fisheries Service, NOAA, P.O. Box 271, La Jolla, CA 

 92038. 



Manuscript accepted October 1987. 

 FISHERY BULLETIN: VOL. 86, NO. 1. 1988. 



Section III: Sensitivity of fishery models to 

 choices for M: a review of the sensitivity of some 

 standard fishery models to different choices for 

 input value(s) of M. Existing studies show that 

 the models are sensitive and that sensitivity is 

 affected not only by the values chosen for M, but 

 also by interactions between M and the values 

 chosen for other parameters in the models. 



Section IV: Evidence for nonconstant M; factors 

 influencing death rate: a review of factors as- 

 sumed or shown to affect M in fish stocks. Avail- 

 able information implies that many such factors 

 exist, acting alone or in concert. 



Section V: Evidence for nonconstant M; vari- 

 ability within and between groups: a review of 

 existing quantitative evidence for the extent of 

 variability in M between but especially within 

 stocks. Because almost all fishery models focus on 

 single stocks, variability within stocks (as op- 

 posed to between stocks) is the most important 

 question. Some studies show strong differences 

 between mortality rates of various groups offish; 

 some do not. Those which do not have tended to 

 assume there would be none, and have often used 

 catch curve regression analysis to derive a single 

 estimate from data combined over many groups 

 (usually years) of data. The few studies from 

 which it is possible to determine ranges of esti- 

 mates show differences of at least 50 to 100% be- 

 tween minimum and maximum estimates for sin- 

 gle groups (e.g., stocks) offish. 



The report's major conlcusions are that natural 

 mortality is far from constant for many fish 

 stocks, and that this variability is extensive 

 enough that it should not be ignored. Analyses of 



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