Steinhorst et a!.: Estimates of abundance for the run composition of salmonids 
9 
Figure 2 
Relationship of confidence interval (Cl) half-width for groups of wild steel- 
head (Oncorhynchus my kiss) spawning in 2011 in Snake River, Pacific 
Northwest, to (A) number of fish sampled (Cl half-width=47. 48 [number sam- 
pled]“°'®^^, coefficient of multiple determination [i?^]=0.872), and (B) abun- 
dance estimate (Cl half-width=144.74[abundance]‘‘’-^®2^ R^=0.870). Precision 
criteria levels of 10% (dotted line) and 25% (dashed line) Cl half-widths are 
shown for reference. 
research goal for precision if Pi„d 
was used, except for the BY2008 
group (Pi„d=10.1%). With the use of 
Pjoi, the 10% goal was met for all sex 
and age groups, except the BY2004 
and BY2008 groups. Stock groups 
did not meet the 10% goal, except 
the GRR and UPS stocks, if Pj„d was 
used. All sex, age, and stock groups 
met the 25% management goal for 
individual and joint CIs, except the 
LOS stock if Pjoi was used. Of the 
stock by age groups, 11% met the 
10% precision goal if Pi„d was used, 
but none met the goal if Pjo, was 
used. There was wider disparity in 
attainment of the 25% goal; 70% 
of the age-by-stock groups met the 
goal if Find was used, but only 35% 
of the age-by-stock groups met the 
goal if Pjoi was used. 
In general, half-widths of the CIs 
declined and stabilized as the num- 
ber of fish sampled and estimated 
abundance of the groups involved 
increased (Fig. 2). Precision scaled 
approximately with the cube root 
of sample size, indicating that re- 
ducing the Cl width by half would 
require approximately 8 times as 
many samples. Values of Pi„d with- 
in a percentage point of the 10% 
precision criterion were obtained 
when there were 26-233 fish from 
a given category in the subsample 
(mean=140) and when there were 
558-4374 steelhead in the category 
(mean=2794). Values of Pi^d closest 
to the 25% criterion were obtained 
when there were 5 and 6 fish in a 
subsample and when there were 
99-147 steelhead in a category. The 
power functions parameterized from 
the group estimates yielded values 
of 96 samples and 1982 steelhead 
at the 10% criterion and 7 samples 
and 147 steelhead at the 25% precision criterion. 
Discussion 
The stratified estimators had biases <5%, except for a 
few cases in the most complex analysis (age by stock). 
Individual CIs for most constituent groups had cov- 
erages very near the nominal 90%. For conservation 
assessments, the greatest need is data on abundance 
of each stock. Coverage of CIs was good even for the 
smallest stock. Age structure is important for compu- 
tation of productivity for each stock (i.e., for summa- 
rizing the adult progeny from a brood year returning 
across years and for computing progeny per parent). 
Accuracy of productivity estimates typically are large- 
ly controlled by the most abundant age groups, which 
had unbiased estimates in our study. When the strati- 
fied estimators were used, only a few of the smallest 
stock-by-age groups had bias >5.0% or Cl coverage 
<85%. 
Conversely, pooled estimators performed poorly ex- 
cept for the simplest variables of interest: sex and age. 
As variable complexity increased from age (5 cases) to 
stock (10 cases) to age-by-stock (50 cases), the propor- 
tion of estimates biased >5% increased from 0% to 30% 
to nearly half, respectively. Initially, we expected pooled 
estimators to be acceptable because of the highly con- 
