FISHERY BULLETIN: VOL 86, NO 1 



early from 0.3 at age 1 to 0.1 at age 10, average 

 about 0.2) and F equal to 0.2, then analyzing the 

 catch with F equal to 0.2 or 0.6, and M equal 

 either to 0.1 or 0.2. Choice of M made little differ- 

 ence in estimates of stock size for the case of high 

 F (0.6), because most of the deaths were due to 

 (observed) fishing. When F was low (0.2), stock- 

 size estimates were much more sensitive to incor- 

 rect choices for M , because most of the deaths 

 were due in this case to M, which was unmea- 

 sured and therefore unobserved. 



Ulltang (1977) simulated seasonal changes in 

 M by concentrating all deaths in either the first or 

 last quarter of a year. Estimated stock sizes (N, ) 

 changed relatively little; with F = 1.2 and 

 M - 0.4, A'^, was a maximum of 10% higher if all 

 deaths occurred first quarter, 10% lower if all oc- 

 curred in the last quarter. 



A serious problem with the conclusions reached 

 by Ulltang (1977) is also common to all the other 

 studies discussed above; they are based on rela- 

 tively few combinations of values for the various 

 parameters, and relatively few simulations. For 

 example, the conclusion that random errors in M 

 will tend to even out is intuitively attractive, pro- 

 vided the time scale of variation is short relative 

 to the generation time of the fish. In fact random 

 variation in M did even out in the two sets of 

 simulations he conducted. But the examples he 

 chose included only one set of ages (2 to 10 years), 

 with relatively high values of F (0.5 to 0.8 year"^) 

 compared to the values tested for M (0.1, 0.3 

 year"M. The gravity of consequences from choos- 

 ing an incorrect M depends very heavily on the 

 size of M relative to the size of F, i.e., on E. Had 

 he chosen different values for his simulations, he 

 might have reached very different conclusions. 

 This is probably the basis for the discrepancy be- 

 tween Ulltang's conclusion that seasonal effects 

 are minor, versus Sims' (1984) conclusion that 

 seasonal effects can be quite large, if M is high. 



Sims (1984) attempted to overcome this prob- 

 lem (trying to draw general conclusions from the 

 results of simulations based on particular, or rel- 

 atively few, sets of parameters) by analytically 

 deriving formulas for relative error in stock-size 

 estimates, and then testing the formulas with 

 data from actual fisheries. He used this approach 

 twice: once to assess the effects of seasonality 

 (Sims 1982a) and once to consider in general the 

 effects of different choices (errors) for constant M 

 (Sims 1984). But his results (and equations for 

 error) show clearly that error in estimated stock 

 sizes depends on several parameters and that the 



effects of one can be strongly dependent on the 

 values chosen for the others. Choosing a high M 

 (0.6 year~M and concentrating catch during the 

 first quarter of the year overestimated R by 20%; 

 concentrating catch during the last quarter 

 underestimated R by 23% (compared with the 

 10% error found by Ulltang). 



Within the same analysis, reducing M by half 

 (to 0.3 year^ ^) reduced the error in R by half, but 

 the same reduction of error inR was also achieved 

 by leaving M high and reducing F . In assessing 

 specifically the effects of error in M on error in R , 

 Sims (1984) showed very different effects on esti- 

 mates of/? in heavily fished versus lightly fished 

 cohorts of Atlantic bluefin tuna. Changing M by 

 50% led to changes in estimated R of 60 to 260% 

 in the lightly fished cohort, but only to relatively 

 smaller changes of 35 to 70% in the heavily fished 

 cohort. Again, the magnitude of the error in 

 model predictions depended not just on the mag- 

 nitude of M, but on its relationship to the other 

 parameters in the catch equation, particularly F. 



Errors (expressed as percentage change in out- 

 put for a given change in input) in model output 

 in the simulations described above, all of which 

 tried to use apparently realistic values for model 

 parameters, rarely exceeded 50%, and were often 

 less than the error introduced into values chosen 

 for M . By implication, the effects of incorrectly 

 guessing M may be relatively unimportant if M is 

 relatively small (e.g., in this situation not more 

 than about 0.5 year"M and relatively invariant, 

 although the actual magnitude of effect due to 

 any given percentage change in M depends on the 

 values chosen for other parameters. 



So, inaccurate estimates of M might be impor- 

 tant or they might not. It all depends on the mag- 

 nitude and variability of M within a given stock 

 (or group). Although untested, it seems likely 

 that estimates of M for groups in which M varies 

 little and is relatively low, are more likely to be 

 reasonably accurate than estimates of M from 

 groups in which M is large and variable. The fol- 

 lowing section reviews evidence that M does in 

 fact vary both within and between groups of fish, 

 and the succeeding section reviews evidence for 

 the magnitude of that variability in ostensibly 

 similar groups. 



IV. FACTORS INFLUENCING DEATH 

 RATE 



Despite the fact that in most fishery models, M 

 is assumed to be constant for all exploited ages in 



34 



