445 
Retrospective analysis of 
virtual population estimates for 
Atlantic menhaden stock assessment 
Steven X. Cadrin 
Massachusetts Division of Marine Fisheries 
50 A Portside Drive 
Pocasset, Massachusetts 02559 
Present address: Northeast Fisheries Science Center, 
National Marine Fisheries Service, NOAA 
Woods Hole, Massachusetts 02543-1097 
Douglas S. Vaughan 
Beaufort Laboratory, National Marine Fisheries Service 
Beaufort, North Carolina 285 1 6 
Abstract - Historical and retrospec- 
tive comparisons of Atlantic menhaden 
virtual population analyses ( VPA) from 
1955 to 1995 revealed substantial in- 
consistency in estimates of man- 
agement variables in the last year of 
stock assessments. Estimates of man- 
agement variables from several histori- 
cal stock assessments were generally 
consistent throughout most of the time 
series. In the last two years, however, 
historical estimates have deviated from 
revised estimates. Relative performance 
of alternative ad hoc methods for esti- 
mating fully recruited fishing mortal- 
ity (F) in terminal years showed that 
all methods were imprecise, but con- 
ventional catch-curve estimates were 
unbiased and had the least retrospec- 
tive inconsistency. Retrospective differ- 
ences in terminal estimates of age-1 F 
by separable VPA ranged widely for 
eight alternative settings but were 
clearly minimized by using seven years 
of catch data. The general magnitude 
of retrospective difference was ±1.2 bil- 
lion recruits (46% relative difference), 
±9,000 metric tons of spawning stock 
biomass (33% relative difference), and 
±4.7 percent maximum spawning po- 
tential (106% relative difference). Ret- 
rospective differences in recruitment, 
spawning stock biomass, and spawn- 
ing potential were positively skewed 
but not biased, indicating that the fre- 
quency of positive and negative incon- 
sistencies are equal but that the posi- 
tive differences are much greater in 
magnitude. The skewed distribution of 
retrospective inconsistency should be 
considered for managing the Atlantic 
menhaden fishery. 
Manuscript accepted 26 February 1997 
Fishery Bulletin 95:445-455 (1997). 
The Atlantic menhaden, Brevoortia 
tyrannus, is a planktivorous clupeid 
that schools in coastal waters off the 
east coast of the United States. At- 
lantic menhaden dominated total 
U.S. fishery landings from 1946 to 
1962 ( Ahrenholz etal., 1987), yield- 
ing approximately 600,000 metric 
tons (t) per year 1953-62 (Henry, 
1971), after which landings steadily 
declined to 162,000 t in 1969 owing 
to recruitment failure and subse- 
quent overfishing. Since then, catch 
has increased to an average of 
330,000 t per year 1970-95 ( AMAC, 
1992 L 1 The Atlantic menhaden fish- 
ery is currently managed according 
to six fishery and population thresh- 
olds that indicate overfishing in re- 
lation to historic production (AMAC, 
1992). Three of the minimum popu- 
lation thresholds (2 billion recruits, 
17,000-t spawning stock biomass, 
and 3% maximum spawning poten- 
tial) are derived from virtual popula- 
tion analysis (VPA) (Megrey, 1989). 
Atlantic menhaden landings have 
been reported from processing 
plants since 1940 and have been 
sampled for length, weight, and age 
since 1955 according to a two-stage 
cluster sampling design in which 
fish were sampled weekly from each 
port where menhaden were pro- 
cessed (Nicholson, 1975; Chester, 
1984; Smith et al., 1987). The fre- 
quency of fishery samples and 
the consolidated nature of the fish- 
ery provide an extremely reliable 
41-year series of catch at age, ages 
0-6 + , for estimation of abundance 
and mortality through VPA (Table 
1). Unfortunately, no independent 
indices of relative abundance are 
available to calibrate abundance 
estimates for the last year of catch: 
commercial catch per unit of effort is 
a biased index because commer- 
cial catchability is inversely related 
to abundance (Schaaf, 1975; Ahren- 
holz et ah, 1987; Vaughan and Smith, 
1988; Atran and Loesch, 1995) and 
fishery-independent survey indices 
are not correlated with abundance 
(Ahrenholz et ah, 1989). In the ab- 
sence of reliable abundance indices, 
and therefore of a formal statistical 
estimator for year-class abundance 
in the last year of the VPA, ad hoc 
estimation rules have been used to 
approximate abundance. 
The error in estimates of abun- 
dance is progressively less in previ- 
ous years than in the last year of 
1 1992-95 landings from Joseph Smith, 
Beaufort Laboratory, National Marine 
Fisheries Service, Beaufort, NC. Per- 
sonal commun. 
