Steinhorst et al.: Estimates of abundance for the run composition of salmonids 
5 
Stratum 
Figure 1 
Simulated abundance of wild steelhead trout {Oncorhynchus 
mykiss) by weekly time strata for (A) 5 age groups and (B) 10 
stocks, which are given generic designations, such as Stock A. 
( 11 ) 
The percentile bootstrap Cl for the true number of wild 
females, [Lp, l/p], is determined by finding the lOOa/2 
and 100(1 — -1) percentiles. Similarly, we calculated a 
bootstrap Cl for the number of wild males. Changing 
the binomial described previously to a multinomial, we 
generated B sets of ('ir;^i,...,'KAi),...,('KiB,...,'K^) to ob- 
tain bootstrap CIs for the true number of wild fish of 
ages 1, ..., A. We followed the same procedure for stocks 
1, ..., G and AxG ages by stock (ages within stocks). To 
ensure accuracy across all groups being evaluated at a 
particular time, joint CIs for numbers of wild fish by 
sex or age or stock were calculated by using the meth- 
ods of Mandel and Betensky (2008). 
Simulations 
Although our estimators and CIs are straightfor- 
ward, we did not know their statistical properties. 
We designed a simulation of the sampling process to 
examine the properties of sex, age, and stock estima- 
tors and CIs, using the methods defined previously to 
analyze each simulated sample. We set the total pas- 
sage of steelhead similar to the SY2011 observed count 
(200,000 fish). We set parameter values for all bino- 
mial and multinomial distributions similar to 
those of the stratified estimates obtained from 
the SY2011 data (Suppl. Tables 1 and 2). The 
percentage of wild steelhead ranged from 20% 
to 50%. The trapping rate varied from 3% to 
14%, and the subsampling rate varied from 
35% to 100%. Abundance and composition of 
the simulated population varied over 27 tem- 
poral strata loosely based on the character of 
the wild steelhead run in Snake River during 
SY2011 (Fig. 1). For simplicity, age and stock 
proportions in the population were generated 
by assuming age and stock are independent 
variables; therefore, we multiplied age and 
stock proportions to find age-by-stock propor- 
tions of the steelhead run. 
We generated 500 samples from the popula- 
tion in the following manner. First, we simu- 
lated number of trapped fish itg) by generating 
binomial samples for each time stratum with 
the number of binomial trials equal to the 
number of fish returning during that stratum 
and with probability equal to the proportion 
of fish trapped within that stratum. Second, 
we simulated the number of trapped fish that 
were wild for each stratum by generating bino- 
mial samples with the number of trials equal 
to tg and with probability equal to the true 
proportion of wild fish for that stratum. The 
remaining trapped fish were of hatchery origin. 
From these numbers, we generated a sample 
of trapped fish with 2 columns: time stratum 
and wild versus hatchery. The length of this 
data set was the sum of the numbers of wild 
fish trapped across the time strata Third, we 
calculated the number of wild fish whose sex, age, and 
stock had been determined in each stratum by multi- 
plying the simulated number of wild fish trapped by 
the proportion subsampled. These numbers by stratum 
were the number of binomial or multinomial trials for 
sex or age or genetic stock (rg). For example, we found 
the number of sampled fish that were wild females 
for a stratum by generating binomial trials of size Tg 
with probability equal to the true proportion of wild 
females during that stratum and with the remainder 
being males. 
Knowing the random number of wild females and 
males trapped in each stratum, we put together a 
simulated subsample of fish by sex by forming a data 
set with two columns (for stratum and sex). The size 
of this sample was equal to the sum across the time 
strata of the numbers of handled fish, J2s=i^s- Similar 
samples were simulated for age, stock, and stock by 
age (500 for each). The simulation generated 2 types 
of data from each sampling iteration: 1) a randomly 
generated trap sample with a random number of wild 
and hatchery fish, and 2) a randomly generated compo- 
sitional sample with random numbers of females and 
males or numbers of fish of various ages or numbers of 
fish of various stocks. 
