382 



Fishery Bulletin 89(3), 1991 



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Figure 1 



Comparison of original catch-per-effort time series (solid line) 

 with unstandardized catch-per-effort (dashed line) for North 

 Pacific albacore. Both time series are pooled catch-per-effort 

 based on Equation 1. Effort values in the original time series 

 are standardized for size of fishing vessels. Effort values in 

 the other time series are not standardized. 



This variability is not taken into account in the existing 

 routine procedure. Our new time series, based on Equa- 

 tion 2 with unvisited strata ignored, gives a noticeably 

 different picture (Fig. 2). The pronounced rising trend 



since 1978 in the old time series is re- 

 placed by a continuing downward trend. 

 The new CPE time series in Figure 2 

 was calculated without regard to the time 

 sequence within a fishing season, that is, 

 all spatio-temporal strata in a particular 

 year were entered into the average for 

 that year. If the fishery has not been fully 

 covering the season in which albacore are 

 available in the eastern Pacific, and if 

 there has been a trend in the degree of 

 coverage, then the yearly averages in 

 Figure 2 could reflect that trend rather 

 than a trend in the albacore population. 

 We calculated a detailed time series with 

 a separate CPE strat for each 10-day peri- 

 od (Fig. 3) to look at the temporal pattern 

 of CPE within seasons. In some years 

 such as 1970, 1976, and 1989, it appears 

 that the fishery may have missed a por- 

 tion of the season of availability of alba- 

 core in the eastern Pacific. The CPE was 

 already high at the beginning of the fish- 

 ery, or the fishery quit before the CPE 

 had tapered off. In most years, however, 

 the fishery appears to have been active 

 from the arrival of the albacore at the 

 fishing ground to their departure. There 

 does not seem to be a trend in the degree 

 of coverage. In any case, it is not clear that variation 

 in the degree of coverage would affect the old and new 

 time series differently. 



Another factor that might cause a divergence be- 

 tween the old and new time series of CPE would be 

 an increasing ability of fishermen to locate areas of high 

 albacore abundance. We will demonstrate that this is 

 so with a simple model. Suppose there are two kinds 

 of strata in the fishing ground, ones with low abun- 

 dance and ones with high abundance, such that the 

 population density within each type is dj and dj, re- 

 spectively, and d]<d h . We assume that CPE is propor- 

 tional to fish density within the strata. Therefore we 

 can measure di and d h in catch-per-effort equivalents. 

 Suppose further that there are ni and n h of each type 

 of stratum in the fishing ground. If the fishery showed 

 no favoritism for either type, then the probability of 

 one unit of effort visiting any particular stratum would 

 be l/(n] + n^). We can model favoritism by defining 

 Pi and ph to be the probabilities that a unit of effort 

 would visit a particular low-abundance or high-abun- 

 dance stratum. We then let 



I'i = 



nj + ari), 



Ph = 



(4) 



ni + an h 



