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Fishery Bulletin 109(2) 
stocks. We excluded updated assessments, where data 
were simply refreshed and not extensively reviewed, 
because of strong constraints imposed on how much 
they could change from the last comprehensive assess- 
ment (PFMC 2 ). When the definition of biomass changed 
among the available assessments (e.g., mid-year bio- 
mass in one assessment and beginning-year biomass 
in another), we used ratio estimation (Cochran, 1977) 
over a common time period to standardize to a com- 
mon metric across all assessments that were conducted 
for that stock. We also limited the data points under 
consideration to no more than those that represent the 
last 20 years reported in the most recent assessment 
to focus attention on variation associated with the esti- 
mation of terminal year biomass. Finally, we trimmed 
the time series to include only the most recent 15, 10, 
and 5 years to evaluate the stability of the estimates 
of among-assessment uncertainty in relation to time 
interval selection criteria. 
Variation in biomass estimates among a set of stock 
assessments can be quantified in a number of ways. 
We evaluated three approaches to calculating variation 
around a point of central tendency: 
1 Consider all biomass estimates for a year as equally 
plausible representations of reality. Biomass varia- 
tion between two stock assessments was quantified 
by forming all possible ratios of estimated biomasses 
in common years. Specifically, if there was an esti- 
mate of biomass (B) for year t from assessments i 
and j, we calculated: Rj\ lt = B i t /B jr i.e., the propor- 
tional deviation of assessment i using assessment 
j as a standard. Based on a symmetry argument, 
we also calculated R^ it and all the ratios were log e - 
transformed. Note that because \n(R^j t )=-\n(R^ it ), 
the distributions were perfectly symmetrical. For 
each stock under consideration the standard devia- 
tion (<7*) of the ratios was calculated. This statistic 
is positively biased, however, because it is based on 
the ratio of two lognormal random variables (B l t and 
B /t ). The appropriate bias correction term (V 2) was 
derived (Mohr 3 ) and applied so that the corrected 
estimator is o=o*N2. Thus, in the first approach 
we used the bias-adjusted estimate of the standard 
deviation of the ln(i?-| t ) as a quantitative measure 
of among-assessment variation. 
2 Consider the mean of biomass estimates in a year 
as the best estimate of central tendency. In this 
2 PFMC. 2008. Terms of reference for the groundfish stock 
assessment and review process for 2009_2010, 35 p. Pacific 
Fishery Management Council, 7700 NE Ambassador Place, 
Suite 101, Portland, Oregon 97220-1384. [Available at: 
http://www.pcouncil.org/wp-content/uploads/GF_Stock_ 
Assessment_TOR_2009-102.pdf.] 
3 Mohr, Michael S. 2009. Groundfish ABC accounting 
for scientific uncertainty derivation of biomass scalar, 4 
p. Unpubl. document submitted to Pacific Fishery Manage- 
ment Council Scientific and Statistical Committee. Author’s 
address: NMFS, SWFSC, 110 Shaffer Rd., Santa Cruz, CA 
95060. 
approach, variation in biomass was measured as 
squared deviations from the annual mean in log- 
space. Specifically, we calculated the mean log-bio- 
mass in year t as: 
i 
where n t is the number of available assessments in year 
t(n t > 2). The standard deviation (<r) is then calculated as 
follows: 
3 Consider the most recent stock assessment as the 
best estimate of central tendency. This approach 
i s the same as the second, except that the mean 
(Ln[B,]) is replaced by the logarithms of the bio- 
mass estimates from the most recent stock assess- 
ment, and the most recent year is excluded from the 
summations and the calculation of the n t . With this 
approach, the most current information is assumed to 
represent the best estimate of the population mean. 
For lognormally distributed random variables, the CV 
on the arithmetic scale is equal to 
CV = 7exp(a 2 )-l, 
where a 2 is the variance on the logarithmic scale (John- 
son and Kotz, 1970). We used this relationship to convert 
variances on the logarithmic scale to the arithmetic 
scale for comparison. 
Meta-analytic inference for management 
The PFMC groundfish fishery management plan includes 
approximately 90 species and, with the exception of 
“ecosystem component” species and stock complexes, 
OFLs, ABCs, and ACLs need to be developed for them 
all. However, less than 30% of the stocks listed in the 
fishery management plan have been assessed. Even 
among stocks that have been assessed, several have been 
studied only once. Therefore, historical biomass variation 
among assessments cannot routinely be estimated on a 
stock-specific basis. Thus, there is some merit in pooling 
results from well-studied species to develop estimates 
of meta-analytic proxy variance for all groundfish and 
coastal pelagic species stocks, and potentially even for 
those that have been assessed multiple times. 
Based on management practices at the PFMC there 
are four natural groupings of species to consider, i.e., 
rockfish, roundfish, flatfish, and coastal pelagic spe- 
cies. The first three are groundfish categories that 
have group-specific proxy F MSY harvest rates (Dorn, 
2002; Ralston, 2002), whereas coastal pelagic species 
are managed in a separate fishery management plan. 
We considered two methods of pooling stock-specific 
variances: 1) take the square root of the average of 
the stock-specific variances; and 2) aggregate all the 
