Kleiber and Pemn: Reappraisal of catch and stock status in U.S. North Pacific albacore fishery 



381 



visited strata were not a random sample of available 

 strata, the average CPE would be biased. To the ex- 

 tent that fishermen are able to locate strata with high- 

 er than normal population density, we expect them to 

 favor those strata. Therefore, we expect that our new 

 CPE values are only partially corrected for the effects 

 of heterogeneous population density. 



Either of the CPE series would still be useful, even 

 though biased, as long as the bias does not change over 

 time. But as noted above, the character of the fishery 

 has been changing. The declining effort over the past 

 approximately 20 years could lead to differential 

 dropout of the less able fishermen, and the increasing 

 availability and use of advisories in the past approx- 

 imately 10 years could be increasing the ability of the 

 remaining fishermen. The salient ability in this case is 

 that of locating concentrations of albacore. If that 

 ability has been changing, the bias in both old and new 

 CPE time series must also be changing. We will show 

 that the rate of change in bias is different in the two 

 time series. 



It would be useful to document the fact that the 

 fishery is increasingly favoring high-abundance strata. 

 Gulland (1956) suggested that the ratio of pooled to 

 stratified CPE could be used as an index of effort con- 

 centration. But in this case we do not have a proper 

 stratified CPE because of the problem of missing 

 strata. We have devised a different favoritism index 

 which is the proportion of the effort in any year that 

 is expended in strata with a CPE above some threshold 

 value, CPE*. The favoritism index in year y is given by 



favoritism index y = -^ JL - 



i = l 



T y = {[ | (Cj/es) > CPE y *} 



(3) 



where T y is the set of stratum indices for which CPE 

 is greater than CPEy, and CPE* is determined by 

 ranking the strata in year y according to CPE and 

 choosing the minimum CPE of the top 20th percentile 

 of the strata. 



Data 



Our data source is voluntarily contributed logbook in- 

 formation from the U.S albacore fishery. It is main- 

 tained on a database by the SWFSC and covers the 

 years 1961 to 1989. The portion of landings sampled 

 each year varies from 15% to 61%. 



For analysis of variance, we used the 1988 data, the 

 most recent year available at the time the analyses 

 were conducted. As with the routine standardization 

 procedure, we selected only jig boat records and or- 

 ganized the data by four large strata— early north, late 

 north, early south, and late south— where the division 

 between the early season and the late season is 1 

 September, and the division between north and south 

 is 38°N latitude. Again following the routine pro- 

 cedure, within the large strata we treated the data by 

 smaller time-area strata consisting of 3° latitude- 

 longitude squares and half-month time periods, and 

 classified vessels by 10-foot length classes. In contrast 

 to the routine procedure, we maintained records of in- 

 dividual vessels within strata and length classes to 

 allow analysis of variance with replicates. For calcu- 

 lating the CPE time series, we utilized 1° latitude- 

 longitude strata, which is the finest resolution available. 



Results and discussion 



We conducted several analyses of variance with various 

 subsets of the data, using CPE or ln(CPE) as the 

 dependent variable.* Vessel length appears to be a 

 significant factor in relatively few of these analyses 

 (Table 1) whereas time-area stratum is almost always 

 highly significant (low probability under H ). Because 

 the two-way analyses were unbalanced (unequal num- 

 ber of replicates), effects of the two factors could be 

 confounded to some extent, and rigorous interpreta- 

 tion of the results is difficult. The salient features of 

 the analyses are (1) that vessel size is of questionable 

 significance as a factor influencing CPE, and (2) that 

 time-area stratum tends to have a much higher statis- 

 tical significance than does vessel size. In other words, 

 it appears that vessel size does not matter nearly as 

 much as where the vessel is and when. 



Regardless of its statistical significance, the practical 

 significance of vessel size in the context of reporting 

 effort and CPE can be tested by seeing whether 

 substantially different results are obtained with and 

 without vessel size standardization. We recalculated 

 the 1961 to 1989 time series without such standardiza- 

 tion and found very little difference in CPE trends (Fig. 

 1). There appears to be little point in standardizing for 

 fishing power even though vessel size may be statis- 

 tically significant in some cases. 



The emphasis on accounting for the effect of vessel 

 size has obscured a more prominent feature of variabil- 

 ity in CPE, which is the effect of location and time. 



* In the routine standardization, In (CPE) is the dependent variable, 

 and instances of zero catch with positive effort are ignored. 



