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Fishery Bulletin 102(4) 



0.4 0.6 



DEPM weighting 



Figure 4 



The relationship between error variance between the two estimators for spawn- 



the optimally weighted estimate of B sp (i.e., B 



SPOPTIUAL 



). Error variance is 



shown for a range of error correlations from r = -0.9 to -0.2. 



= ( 1-w ) <J X + ap, 

 which requires iv = 1 + opl o~ v 



In the event of p = -a x la, B sp . 0pllmal will have w = 

 0, i.e., the optimal estimator will just be estimator 2 

 alone. 



The limited sample information available indicates 

 that c7j is approximately equal to ex, which we therefore 

 assume in order to simplify the next analysis. Because 

 B S p_pp S is based on estimates of PPS, which can be 

 estimated with more confidence than B sp DEPM , it must 

 be expected that often, if not always, Variance! B SPmPPS ) 

 < Variance(B sp . D£PW ). 



i.e., Var(e+e') < Var(<?) + f , for small £ >0; 

 i.e., a 2 + ct, 2 + 2p ct,ct< a- + e; 

 i.e., 2p < (-rjj- + e)la x a. 



This requires p < -0.5 when cr l = a, and e is small. This 

 relation has an important role in our decision of what 

 is the best estimator. 



In Figure 4 the error variance for the estimator B sp 

 optimal ' s shown for various DEPM weightings and a 

 theoretical range of error correlations (i.e., between e 

 and e) from r = -0.9 to -0.2. Our aim was to choose a 

 DEPM weighting that provides minimal error variance 

 along the most stable regions of the suite of error cor- 

 relation curves, i.e., where the error correlation curves 

 are flattest. The error correlation curves from -0.4 to 

 -0.7 were the most stable and across these the DEPM 

 weightings from 0.3 to 0.7 had the smallest error vari- 

 ance. Therefore we choose 0.5 as our preferred DEPM 

 weighting, which lies centrally within a stable part of 

 the range of theoretical error correlations. 



Results 



The decline in spawning area in each region (Fig. 2) 

 corresponded to declines in B sp DEm ( Table 1), which in 

 turn were reflected by the B sp .optimal estimates (Fig. 5). 

 We recognize that imbalance in the intensity of samples 

 between years poses a problem for the interpolation of 

 data between sampling stations but we contend that the 

 collapse in distribution observed is of sufficient contrast 

 to be a reliable reflection of the estimated 709f decrease 

 in Sardinops biomass that resulted from the 1998-99 

 epidemic (Gaughan et al., 2000; Ward et al., 2001). Note 

 that we have used Albany (Fig. 2A) as the primary sup- 

 port for this contention because of the larger data set. 

 The same pattern was observed at all regions, although 

 it was not so marked for the west coast Sardinops (Fig. 

 2D) because estimated B sp (this term hereafter is used 

 generically) had already declined substantially between 

 1996 and 1998. 



Despite sometimes large intervals between consecutive 

 surveys, there were two broad patterns in the trends for 

 Sardinops B sp during the 1990s (Fig. 5). Within each 

 region on the south coast (Albany, Bremer Bay, and 

 Esperance), B s 



P DEPM 



remained relatively high in the 

 early to mid 1990s before decreasing substantially by 

 1999. In contrast to the results from south coast DEPM 

 surveys, the west coast estimated B SP _ DEPM fluctuated 

 widely (Table 1). This fluctuation resulted in a rela- 

 tively poor fit of the optimal model and correspondingly 

 wide CIs. Since 1996, when substantially more samples 

 were routinely collected during each survey on the west 

 coast, there has also been a decrease in B sp consistent 

 with that observed on the south coast. 



Inconsistency in the determination of variability es- 

 timates around some B^ PI)EPM estimates precludes any 

 definitive statements about the relative precision of the 



