Cadrin and Vaughan: Virtual population analysis estimates for Atlantic menhaden stock assessment 
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1 1 I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I II I I I I ! 
1955 1960 1965 1970 1975 1980 1985 1990 1995 
Year 
Figure 2 
Retrospective catch-curve estimates of Atlantic menhaden fishing mortal- 
ity and back-calculated estimates from the 1995 VPA (above) and retro- 
spective differences (below). The broken line in the upper chart indicates 
provisional estimates. 
ample, in 1992, recruitment was esti- 
mated to be 3.4 billion greater than the 
1995 estimate of 1992 recruitment. Es- 
timates converged to within 160 million 
recruits of 1995 VPA estimates, when 
the retrospective lag ( k ) was greater 
than one year. 
Only five terminal estimates of SSB 
and %MSP were available, including 
1995 estimates. Two historical esti- 
mates of SSB were greater than revised 
estimates and two were less than 
revised estimates. Historical estimates 
of SSB converged to within 1,500 t of 
1995 VPA estimates when k>l year. 
Historical estimates of %MSP were 
greater than revised estimates for three 
assessments and less than revised esti- 
mates for two assessments. The 1992 es- 
timate of 1991 %MSP (i.e. backcalculated 
one year) was 3.6, but subsequent esti- 
mates of 1991 %MSP were below the over- 
fishing threshold of 3 %MSP. Therefore, 
an overfishing trigger fired, but it was not 
detected until two years later. Estimates 
of %MSP converged to within 0.6 of 1995 
VPA estimates when k>l year. 
Retrospective comparisons 
Conventional catch curves produced the 
most consistent estimates of fully re- 
cruited F among the three ad hoc meth- 
ods used. Retrospective differences from 
catch-curve estimates in terminal years 
ranged from —1.12 to 0.92 (Fig. 2). The 
RMS difference was 0.51 and the RMS 
relative difference was 33% (n= 36). The 
mean retrospective difference in fully 
recruited F was not significantly differ- 
ent from zero. Therefore, although ter- 
minal estimates were imprecise, they 
were not biased. Retrospective differences in catch- 
curve estimates were negatively correlated with 
back-calculated F from the 1995 VPA (r=-0.62)(i.e. 
when F was low, catch-curve estimates were gener- 
ally greater than revised estimates; when F was high, 
catch-curve F was generally less than the revised 
estimate). Retrospective differences in fully recruited 
F produced opposite inconsistencies in SSB and 
%MSP For example, in 1993, catch-curve F was 
greater than the revised F (Fig. 2), and initial VPA 
estimates of SSB and %MSP were less than revised 
estimates (Fig. 1). Alternative methods of estimat- 
ing fully recruited F produced even greater incon- 
sistency. The RMS retrospective difference from 
modified catch curves was 0.60 (49% relative differ- 
ence), and log catch ratios produced a RMS differ- 
ence of 0.61 (52% relative difference) (n = 36 for both 
methods). 
Retrospective differences in estimates of age-1 F 
from SVPA ranged from -0.59 to 0.45 for all retro- 
spective SVPA’s and were not significantly different 
from zero (n=31 for each series). RMS difference was 
minimized when seven years of catch-at-age data 
were used and increased regularly as the number of 
years deviated from seven (Fig. 3). The RMS 
retrospective difference for estimates of age-1 F was 
