1 
National Marine 
Fisheries Service 
NOAA 
Fishery Bulletin 
fy- established in 1881 
Spencer F. Baird 
First U.S. Commissioner 
of Fisheries and founder 
of Fishery Bulletin 
Abundance estimates and confidence intervals 
for the run composition of returning salmonids 
Email address for contact author: tim.copeland@idfg.idaho.gov 
Abstract — In 2-stage fishery sam- 
pling, abundance is often estimated 
by using a primary sampling gear 
and total abundance is then parti- 
tioned into groups of interest by ap- 
plying data on composition derived 
from a secondary sampling gear. 
However, the literature is sparse on 
statistical properties of estimates of 
run composition. We examined the 
accuracy and precision of estima- 
tors of composition of wild steelhead 
(Oncorhynchus mykiss) in the Snake 
River, in the Pacific Northwest. We 
simulated estimators, using pooled 
and time-stratified data. We com- 
pared confidence intervals (CIs) de- 
termined on the basis of asymptoti- 
cal normality or a 2-stage bootstrap 
method. Stratified estimators were 
unbiased, except in a few cases. 
Joint CIs (all groups considered si- 
multaneously) had coverages near 
nominal. Conversely, pooled estima- 
tors performed poorly; the propor- 
tion of biased estimates increased 
as the number of groups estimated 
increased. Using empirical data, we 
show that CIs met precision goals 
for most groups. Half-widths of CIs 
decreased and stabilized as the 
number sampled and group abun- 
dance increased. In complex scenar- 
ios, estimates of small groups will 
yield poor precision and some may 
be biased, but a stratified estimate 
with a conservative joint Cl can be 
of practical use. The 2-step bootstrap 
approach is flexible and can incorpo- 
rate other sources of variability or 
sampling constraints. 
Manuscripts submitted 22 December 2015. 
Manuscripts accepted 25 August 2016. 
Fish. Bull. 115:1-12 (2017). 
Online publication date: 18 October 2016. 
doi: 10.7755/FB.115.1.1 
The views and opinions expressed or 
implied in this article are those of the 
author (or authors) and do not necessarily 
reflect the position of the National 
Marine Fisheries Service, NOAA. 
Kirk Steinhorst' 
Timothy Copeland (contact author)^ 
Michael W. Ackerman^ 
William C. Schrader^ 
Eric C. Anderson^ 
' Department of Statistical Science 
University of Idaho 415A Brink Hall 
875 Perimeter Drive 
Moscow, Idaho 83844-1104 
2 Idaho Department of Fish and Game 
1414 East Locust Lane 
Nampa, Idaho 83686 
In 2-stage sampling for fisheries 
monitoring and research, abundance 
is estimated with a primary sam- 
pling gear and then partitioned into 
groups of management interest by 
applying compositional data (e.g., 
species, stock, sex, age, and size) 
derived from a secondary sampling 
gear. For example, biological samples 
obtained from gillnetting or electro- 
fishing can be used to allocate abun- 
dance estimates from hydroacoustic 
counts to species (e.g., Tarbox and 
Thorne, 1996; Pritt et al., 2013; Rud- 
stam et ah, 2013; Hughes and High- 
tower, 2015). Alternatively, a more 
highly controlled sampling regime 
can be instituted by counting fish as 
they move past barriers (e.g., weirs 
or dams) and by collecting biological 
samples or data from some portion of 
the fish in order to partition counts 
(e.g., Wagner, 2007; Campbell et ah, 
2012). However, the complexities of 
fishery sampling programs and the 
relevant groups into which the fish 
are parsed present difficulties for es- 
timating precision of the generated 
point estimates. 
Steelhead {Oncorhynchus mykiss) 
^ Eagle Fish Genetics Laboratory 
Idaho Department of Fish and Game 
Pacific States Marine Fisheries Commission 
1800 Trout Road 
Eagle, Idaho 83616 
'' Fisheries Ecology Division 
National Marine Fisheries Service 
Southwest Fisheries Science Center, NOAA 
1 10 Shaffer Road 
Santa Cruz, California 95060 
are an important cultural, economic, 
and recreational resource in the Pa- 
cific Northwest of the United States. 
After the construction of hydro- 
electric dams on the Columbia and 
Snake rivers during the late 1960s 
and early 1970s, the abundance and 
survival of steelhead in the Snake 
River decreased (Raymond, 1988). In 
response, steelhead within the Snake 
River basin were listed as threatened 
under the Endangered Species Act in 
1997. In recent years, abundances 
have increased slightly. However, the 
increase has been dominated by fish 
produced in hatcheries (intended to 
mitigate for reduced harvest opportu- 
nities and to supplement natural pop- 
ulations), while the returns of steel- 
head born in the natural environment 
remain critically low (Ford, 2011). 
Fishery biologists need to know how 
many wild versus hatchery-produced 
steelhead return in order to manage 
fisheries effectively, as well as to as- 
sess the conservation status of wild 
populations. Further, for wild fish, 
we need to know the numbers of fish 
returning by sex, age, and stock to 
inform viability analyses. 
