FISHERY BULLETIN; VOL 86, NO 1 



guish between losses (or gains) from migration or 

 recruitment versus losses due to fishing or natu- 

 ral causes, 2) imprecision in the estimates of M 

 obtained (e.g., Beverton and Holt 1957; Taylor 

 1958; Bishop 1959; Paloheimo and Dickie 1966 

 Ricker 1975, 1977; Doubleday 1976; Pauly 1980 

 Larkin and Gazey 1982; Paloheimo 1980, 1982 

 Myers and Doyle 1983; Roff 1984), 3) sensitivity 

 to size-specific mortality affecting the estimated 

 age-structure of the group (Ricker 1969), 4) errors 

 in estimates of age, such that abundances-at-age 

 derived from age-length conversions are unrepre- 

 sentative, 5) where analyses are conducted on 

 data combined over two or more cohorts, the un- 

 likely condition that mortality rates were in fact 

 similar for all cohorts, and 6) problems inherent 

 in the analyses themselves (e.g.. Barlow 1984). 

 Disadvantages 1, 4, and 5 may not apply to 

 marked fish. Disadvantage 5 does not apply to 

 single cohorts. But collections from marked 

 groups and single cohorts are still vulnerable to 

 the other problems. 



Further, although in principle it would be pos- 

 sible to estimate M for different ages, times, or 

 places, most commonly in practice a single, 

 fishery-wide constant M is estimated by pooling 

 data from throughout the fishery. By implication, 

 the analyst is assuming that the exploited stock 

 was more or less in steady-state over all times and 

 areas of catch so that M was relatively constant 

 while that data set was collected and while (his- 

 torically) the observed age-distributions were 

 being created. In fact, substantial evidence exists 

 that M is not constant, either within a single 

 stock over time (age) or between stocks of a given 



species in different areas (Sections IV and V). 



A final disadvantage is that catch-curve analy- 

 ses are fundamentally unmechanistic, generated 

 simply by charting changes in abundance. Catch- 

 curve analyses cannot predict the effect of 

 changes in factors that control M; thus there is 

 little hope of predicting M in the future should 

 conditions change. 



Life History Methods 



A second approach to estimating the instanta- 

 neous rate of natural mortality in fish stocks is 

 based on the observation that M often correlates 

 strongly with life history parameters, such as 

 growth rate, age at sexual maturity, costs of re- 

 production, and maximum age (Table 1). 



Typically in such studies, analytical formulas 

 are derived from theoretical relationships be- 

 tween the various parameters (e.g., Beverton 

 1964), or empirical formulas are derived from re- 

 gression of M against one or more of the parame- 

 ters (e.g., Hoenig 1983). These models have two 

 significant advantages: 1) they require minimal 

 amounts of data, and 2) they are useful in demon- 

 strating broad trends across species and in devel- 

 oping ecological theory. But because they produce 

 only a single and often very imprecise estimate of 

 M for any given group offish, they are not partic- 

 ularly effective for generating precise estimates 

 of natural mortality or for determining the exis- 

 tence or extent of trends and variability in M for 

 given stocks. They will also be no better than the 

 methods used to estimate the values of M used in 

 the regressions. 



Table 1. — Studies relating instantaneous rate of natural mortality to life history traits in fish. 



^Maximum age, 



2Von Bertalanffy growth parameter. 



3Maximum length. 



''Length at age of sexual maturity. 



^Maximum weight. 



6Age at occurrence of cohort's max biomass. 



''Age of sexual maturity. 



28 



