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Fishery Bulletin 90(4). 1992 



the assumption that the selectivity pattern remained 

 stable during that period. For that analysis the terminal 

 fishing mortality was set to 0.2/yr and selectivity for 

 the oldest age group was 3.0. (2) The ADAPT ap- 

 proach to sequential population analysis was then 

 used for calibration, with each abundance index used 

 separately. A weighting factor for each index was ob- 

 tained by setting the weight for the ith index equal to 

 the reciprocal of the mean squared error after 

 calibrating with the index. In performing the calibra- 

 tions, ages 5 and above were assumed to be fully 

 recruited (8^=1.0 for a = 5,6,. . .,9 -i-) and the partial 

 recruitment for the other ages was as determined from 

 the SVPA (i.e., from step 1). (3) The set of weights 

 computed for the abundance indices were then rescaled 

 so that they summed to unity. (4) The weights were 

 then used in recalibrating the ADAPT SPA using all 

 of the abundance indices at once. In doing so, the 

 following constraints were used: Si was taken from 

 the separable virtual population analysis, S2 through 

 S5 were directly estimated through calibration, and Se 

 through 89+ were set equal to the estimated 85. The 

 objective function used in the calibration was to mini- 

 mize the weighted sum of the squared deviations from 

 the predicted abundance indices as in equation (4). 



After the fishing mortalities and population sizes 

 were computed by the sequential population analysis, 

 the values of F„^s.\ ^•nd Fqi were calculated from yield- 

 per-recruit computations. Data from the terminal year 

 (i.e., the most recent year available) were used to pro- 

 ject the catch in the current year and then project the 

 catch for the next year. For this, recruitment in the 

 current year and the following year were assumed by 

 ICCAT to be equal to the long-term mean recruitment 

 obtained in the sequential population analysis. The pro- 

 jections were made for a variety of fishing mortalities, 

 specifically Fqi, F^^ax- and Fstatusquo- 



Specification of uncertainty in the inputs 



One thousand simulated data sets were analyzed using 

 a version of ADAPT written in FORTRAN 77 (avail- 

 able from the authors). The formulation of the problem 

 was made to mimic the 1989 ICCAT assessment for 

 North Atlantic swordfish. However, we emphasize that 

 the uncertainties in the inputs specified below are our 

 ad hoc choices and, although realistic, are intended 

 mainly for illustrative purposes. 



Natural mortality Uncertainty in the natural mor- 

 tality rate (M) was specified as a uniformly-distributed 

 random variable in the interval 0.1-0.3/yr. The value 

 of 0.2 used by ICCAT (1990) is at the center of this 

 range, and the choice of a uniform distribution places 

 equal confidence in all values in the interval. 



^ 

 ■o 



"^e ^ , 



L^ 





Figure 4 



Coefficients of variation of outputs from the sequential popula- 

 tion analyses of simulated swordfish Xiphias gladius data 

 sets, (a) Age- and year-specific estimates of population num- 

 bers; (b) age- and year-specific estimates of instantaneous 

 fishing mortality. 



Catch-at-age Total annual catches were represented 

 by lognormally-distributed random variables with coef- 

 ficients of variation of 10% and expected values equal 

 to those in the assessment. A coefficient of variation 

 of 10% indicates that the catches are known with high 

 precision. The proportions of the total catch in any year 

 that make up each age component were assumed to 

 follow a multinomial distribution with expected values 



