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Fishery Bulletin 95(3), 1 997 
Table 1 
Age-based stock assessments of Atlantic menhaden. Y t in- 
dicates the terminal year the VPA. 
Y t 
Source 
1976 
AMMB, 1981; Powers, 1983 
1981 
Vaughan et al., 1986; Ahrenholz et al., 1987 
1984 
AMMB, 1986; Vaughan and Smith, 1988 
1988 
Vaughan, 1990; Vaughan and Merriner, 1991 
1990 
AMAC, 1992 (p. 40-50); Vaughan, 1993 
1992 
AMAC, 1992 (p. 17-30) 
1993 
Vaughan, 1994 7 
1994 
Vaughan, 1995 ; 
1995 
Vaughan, 1996 J 
1 Vaughan, D. S. Trigger variables for Atlantic menhaden. Natl. 
Mar. Fish. Serv., NOAA, Unpubl. AMAC reports. 
the VPA, provided that catch at age and natural mor- 
tality (M) are well estimated and fishing mortality 
(F) is at least moderate (Jones, 1961; Tomlinson, 
1970; Pope, 1972; Ulltang, 1977; Megrey, 1989). As 
stated in the Atlantic menhaden fishery management 
plan, “Trigger estimates for recent years from VPA 
are subject to large uncertainty, while estimates 2 to 
3 years old are more reliable” (AMAC, 1992). Con- 
sistency in successive stock assessments can be 
evaluated by using “historical analysis,” which com- 
pares estimates from the most recent assessment 
with contemporary estimates from prior stock assess- 
ments (Sinclair et al., 1985), 2 but historical assess- 
ments of the menhaden stock were not conducted 
with a common estimation rule. Consistency of the 
current estimation rule can be evaluated by using 
“retrospective analysis,” which recreates a historical 
series of VPA’s with a single estimation rule (Sinclair 
et al, 1990). 2 * * * 
The first objective of the current investigation was 
to report the general magnitude and potential bias 
of retrospective differences for guidance on interpret- 
ing current estimates and for providing fishery man- 
agement advice. The second objective was to attempt 
alternative estimation rules to improve consistency 
of estimates. 
2 Examples of historical and retrospective analyses, interpreta- 
tion, and discussion can also be found in the following two 
refererences: 
Int. Counc. Explor. Sea. 1991. Report of the working group 
on methods of fish stock assessments. ICES Council Meet- 
ing Assess., p. 25. 
Northeast Fisheries Science Center. 1994. Report of the 18th 
Northeast Regional Stock Assessment Workshop (18th 
SAW). NEFSC Ref. Doc. 94-22. 
Methods 
Historical comparisons 
Three Atlantic menhaden management variables 
derived from VPA (age-1 abundance [R], spawning 
stock biomass [SSB], and percent maximum spawn- 
ing potential [%MSP]) were compared among ten 
reported stock assessments (Table 1). The number 
of historical estimates of each variable differed be- 
cause some reports did not document all three popu- 
lation estimates. 
Consistency of successive stock assessments was 
measured by comparing historical estimates with 
revised estimates (from the 1995 VPA), which are 
more reliable. Inconsistency may result from histori- 
cal estimation error or inaccurate estimates for prior 
years in the current VPA (Sinclair et al., 1990). The 
population thresholds used to define overfishing are 
subject to some uncertainty because they are also 
VPA estimates; but they are converged estimates, which 
are much more certain than current estimates. In com- 
paring current VPA estimates with these overfishing 
thresholds for an annual assessment of stock status, 
converged and current estimates are assumed to be 
consistent. Estimates in the last year (Y ? ), and back- 
calculated years (Y t _ v Y t _ 2 , etc.) were compared with 
the time series of estimates derived in 1995. Differ- 
ences between historical estimates and revised esti- 
mates were calculated as follows: 
^t,t+k = ^t,t+k ~ ^, 1995 ’ 
where R ( 1995 = the most recent estimate of recruit- 
ment in year t; 
R t , +k = recruitment in year t as estimated 
when t+k was the last year in the 
assessment; and 
k = is the retrospective lag between year 
t and the last year of the historical 
VPA. 
For example, f? 1990 1993 is the 1993 estimate of 
1990 recruitment, which has a three-year retrospec- 
tive lag (i.e. k=3). When k = 0, R tt is an estimate 
of recruitment for the last year in an assessment and 
is referred to as a terminal estimate. Histor- 
ical differences in SSB and %MSP were similarly 
calculated: 
SSB t , t+ k = SSB tit+k -SSB t , 19 95 
A%MSP t ' t+ k = %MSP ty t+k - %MSP ty 1995 - 
Root mean square (RMS) difference was used as a 
measure of dispersion of historical estimates from 
