Cadrin and Vaughan: Virtual population analysis estimates for Atlantic menhaden stock assessment 
451 
rent VPA (Sinclair et al., 1990). For example, 
Lapointe et al. (1989) simulated Atlantic menhaden 
catch for VPA’s to show that 50% underestimates of 
M produced 12% overestimation of recruitment and 
6% overestimation of biomass and that overestima- 
tion of M produced similar underestimates of recruit- 
ment and biomass. Therefore, the assumption that 
M is constant when M varies among years and ages 
may cause VPA inconsistency. It appears that the 
inability to estimate fully recruited F accurately in 
terminal years accounts for a substantial portion of 
the retrospective differences in management vari- 
ables reported here. Inaccurate estimates of terminal 
F may result from abrupt changes in F or M. Catch- 
curve estimates of terminal F are not sensitive to 
changes in current mortality because they reflect the 
average mortality over the last three years more than 
mortality in the terminal year. 
Retrospective differences in management variables 
were positively skewed, and log transformation was 
necessary to test for bias. Skewed retrospective dif- 
ferences with no bias imply that positive and nega- 
tive differences occur with equal frequency, but 
positive differences are generally greater in magni- 
tude. Theoretically, normally distributed errors in 
F will produce lognormally distributed errors in R, 
