FISHERY BULLETIN: VOL. 86, NO. I 



Knights ( 1982) show predatory mortality as 80 to 

 909c of M for age-0 cod, whiting, and haddock in 

 the North Sea (the fraction of M due to predatory 

 mortahty cannot be assessed accurately in the 

 older ages because predators appropriate to these 

 sizes were not included in the analysis). In an- 

 other example, estimating M from energy flow 

 models, Sissenwine (1984) demonstrated that 

 predation in the Georges Bank ecosystem can ac- 

 count for all production by prey fish; nonpreda- 

 tory mortality was negligible. 



Thus a multitude of factors, acting alone or in 

 concert, can be expected to produce variations in 

 M between individuals within single groups of 

 fish, as well as between groups. Differences can 

 be expected between species, between stocks 

 within species, and from place-to-place and time- 

 to-time within given stocks. In the following sec- 

 tion, I will review more completely existing evi- 

 dence for, and the extent of, this expected 

 variability in M . 



V. VARIABILITY WITHIN AND 

 BETWEEN GROUPS 



As discussed above (Section III), simulation 

 studies generally show that effects of choosing a 

 particular value or set of values for M can range 

 from insignificant to considerable, depending in 

 part on the model used, in part on the values 

 chosen for other parameters, and in part on the 

 form chosen for the estimate(s) of M. Authors 

 suggest that in the future, simulations should be 

 conducted with a range of values for M, to bracket 

 probable values (e.g., Beverton and Holt 1957; 

 Tyler et al. 1985). 



The problem with this advice is identifying the 

 appropriate range and distribution of M for any 

 given group offish. Obviously, wide ranges for M 

 will lead to great discrepancies between model 

 predictions based on one end of the range or the 

 other. It has been shown above, however, that 

 model output can be relatively insensitive to 

 small changes in M . This is particularly true if F 

 is much larger than M (i.e., if the stock is highly 

 exploited so that losses to fishing far exceed losses 

 to natural mortality). The problem is determining 

 whether, for a given stock in situ, changes in M 

 are in fact large or small. Compensatory changes 

 in M, in response to changes in F, will further 

 confound the problem, because variations in M 

 will then be a function of the value(s) of F, in 

 addition to the suite of other factors that may be 

 affecting estimates of M . 



M does appear to vary considerably between 

 groups offish. Estimates of M compiled by Pauly 

 (1980) (Fig. 1) for 175 stocks and species offish 

 worldwide differ greatly between groups, ranging 

 from a minimum of about 0.1 year"^ to several 

 unusual values as high as 7.0 year ^ Even 

 within a group as ostensibly homogeneous as the 

 tunas, the range of estimated mortality constants 

 spans the majority of the common values (0.2 to 

 2.0 year"i. Murphy and Sakagawa 1977). 



Estimates of variability in M within groups of 

 fish are much less common, but are actually more 

 important than the obvious differences between 

 groups with obviously different characteristics 

 such as differing lifespans. Most fishery analyses 

 are directed toward understanding or predicting 

 dynamics of single stocks (single groups offish). 

 The most important considerations for natural 

 mortality parameter values in these single- 

 species analyses are whether and if so over what 

 values M varies for the group of fish in question. 



But measuring trends or variability in natural 

 mortality rates withingiven groups (e.g., stocks) 

 is difficult and, with the exception of trends with 

 age, rarely attempted. This is primarily because 

 the only extant methods for estimating M depend 

 either directly or indirectly on analysis of catch 

 data (Section II), and catch data are prone to 

 many well known (but largely unsolved) prob- 

 lems. 



Problems with analysis of catch data fall into 

 two general categories: 1) problems with sam- 

 pling procedure, such that fish are caught or 

 counted out of proportion to their true abundance 

 and 2) problems with fish appearing or disappear- 

 ing from the "unit stock" due to causes other than 

 birth or natural mortality (i.e., migration, fishing 

 mortality, or tagging mortality), again resulting 

 in catch data that do not represent the true struc- 

 ture of the stock. If sampling biases can be over- 

 come, the problem reduces to partitioning total 

 disappearance offish into fractions owing to fish- 

 ing, tag mortality, and migration. The first parti- 

 tion can be eliminated by studying unfished popu- 

 lations, the second by quantifying tag mortality, 

 and the third by studying only closed or tagged 

 populations. 



Unfortunately, very few sampled populations 

 satisfy completely even one of these criteria. Re- 

 gardless, we still need at least some crude esti- 

 mates of M in order to determine whether M truly 

 varies enough to invalidate the standard assump- 

 tion in fisheries models that M is effectively con- 

 stant during exploited ages. The question here 



36 



