10 
Fishery Bulletin 1 15(1) 
trolled sampling regime at LGD, which was very con- 
sistent for SY2011. The realized sampling rate in the 
simulation (the product of trap rate and subsample 
rate) averaged 4.7% (standard deviation 1.3%). How- 
ever, stock and age composition changed through the 
run, as did the number of steelhead crossing the dam. 
As the variable of interest became more complex, accu- 
racy and precision of pooled estimators decreased. 
Steinhorst, et al. (2010) estimated the run compo- 
sition of fall-run Chinook salmon (O. tshawytscha) at 
LGD on the basis of counts from observation windows 
from 18 August through 15 December (their meth- 
od 1). They used a stochastic model based on a fast 
Fourier transform to model the distribution of daily 
window counts, which were summed to obtain total 
abundance. Steinhorst, et al. (2010) used 2 bootstrap 
steps — a nonparametric bootstrap associated with the 
Fourier model and a parametric bootstrap applied to 
an estimate of composition pooled over the season. 
They did not report composition by stratum because 
composition was calculated with a complex accounting 
algorithm that could not be applied to individual stra- 
ta. In essence, they assumed that either the propor- 
tions of their sex-by-age-by-origin groups were fairly 
uniform over the season or that a constant proportion 
of the run was sampled for each stratum. However, if 
the groups of interest returned at different times, a 
pooled estimate of composition applied to total escape- 
ment would not be accurate, especially over longer 
temporal spans (e.g., the steelhead run). In our study, 
the simulation results from the pooled estimators in- 
dicated precisely that outcome. 
Precision may be computed for each group of inter- 
est, one at a time (i.e., Find); or more conservatively 
across all groups within a variable of interest (Pjoi), 
minimizing study-wide error. However, the conservative 
approach resulted in wider CIs; for example, joint CIs 
were 14-17% wider than the individual CIs for sex in 
the SY2011 run. For stocks, Pjoj values were about 47- 
76% wider than Pjnd CIs. Given the number of stocks, 
we were not paying a large penalty for computing 
joint CIs. For age-by-stock groups, the joint CIs were 
on average 85% wider than the individual CIs (range: 
71-158%). This difference likely was due to the uneven 
distribution of numbers by age and the large number of 
age-by-stock groups. Because we were trying to achieve 
joint coverage across so many groups simultaneously, a 
much greater expansion of the CIs was necessary. The 
results of our study show the cost to statistical power 
caused by the inclusion of many groups in an analysis. 
Investigators must consider whether the more conser- 
vative approach affects the usefulness of the resulting 
estimates and which groups are truly of management 
interest. For the latter consideration, investigators may 
combine some groups or decide that loss of precision is 
acceptable for their application. In our case, we com- 
bined strata to achieve greater sample sizes and used 
total age rather than the combinations of years spent 
in freshwater and years spent in saltwater that salmon 
biologists often use (Quinn, 2005). 
Precision is related to the amount of information 
available, and the quality of this information declines 
as group size becomes smaller or as the realized sam- 
ple rate is reduced. The problem in our case was that 
the steelhead run in Snake River is protracted over 
time, compounded by the complexity of the life history 
and stock structure of steelhead. Therefore, multinomi- 
al proportions must be estimated for many groups over 
many time strata unless the groups of interest can be 
simplified. Even so, we generally met the research goal 
of half the 90% Cl width within 10% of the estimate 
for sex and age groups present in SY2011. For stock 
groups, we met the management goal of half the 90% 
Cl width within 25% of the estimate for sex and age 
groups but our 10% precision goal was not attained, ex- 
cept with the 2 largest stocks when the less stringent 
Find measure was used. 
To develop guidance for interpretation of the esti- 
mates we obtained from the data, we relied on Pjnd 
because it was not affected by the number of other 
groups in the analysis. Precision of the estimates for 
individual groups declined rapidly when group abun- 
dance was <2500 individuals or when <100 individu- 
als from that group were collected in the subsample. 
However, if there were few fish in a group, analysts 
and managers probably would be content with a more 
lenient precision criterion. For example, if our esti- 
mate was 50 and the Cl was 20-80, the percent half- 
width would be 60% of the estimate but the fact that 
the true number is between 20 and 80 should be suf- 
ficiently precise for management purposes, especially 
if the numbers of fish in other groups are decidedly 
larger. With Pinj as a measure of precision, the 10% 
research precision goal could be reached if group 
abundance were to exceed 2000 individuals or if >100 
samples from that group were collected. The 25% 
management precision goal was much more attainable 
and was achieved at group abundances >150 individu- 
als and when very few samples were collected (<10). 
These values can be used as thresholds for the lenient 
precision criterion in our application. 
Our results have implications for monitoring fish 
populations. If the interest is on the largest groups in 
a mixed population, most sampling programs will yield 
sufficient results. However, weak stocks are frequently 
a problem for conservation and fisheries management, 
and precision of abundance estimates of smaller groups 
becomes important. Obviously, there is a tradeoff be- 
tween sample size and number of subdivisions that 
can be maintained. Previous work by Gerritsen and 
McGrath (2007) has supported this notion, but their 
criteria for success focused on overall (average) preci- 
sion. Thompson (1987) found that a sample size of 510 
fish should suffice under a worst case scenario for a = 
0.05 (equal proportions among groups, but number of 
groups does not matter) as long as desired precision is 
expressed in absolute terms. If desired precision is ex- 
pressed in relative terms (as was done in our study), no 
sample size will be sufficient if group size approaches 
zero. However, our results provide useful guidance for 
