Oldemeyer et al.: A multiyear Bayesian model for incorporating sparse or missing salmonid data 
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0 
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Figure 1 
Abundance of juvenile Chinook salmon (Oncorhynchus tshawytscha) emigrating down¬ 
stream during 2014 by ordinal week, estimated by using 4 competing models with 
data collected at a rotary screw trap deployed in Marsh Creek, Idaho, in 2014. The 
4 models are the pooled-simple (M PS ), hierarchical within-year (M HW ), hierarchical 
penalized-spline (M S pline)> and hierarchical multiyear (M HB ) models. Gray regions 
denote estimates produced for temporal strata with missing data in 2014. 
dence intervals did not overlap for all (Table 2). The 
Mp S model estimated total population abundance at 
levels 8000-17,000 fish less than the 3 other models 
but had the smallest 95% credible interval width. The 
total population abundance estimate for M PS excluded 
potential fish migrating in ordinal weeks 11, 45, and 
46 (Fig. 1). In addition, the precision of M PS model 
estimates rely on the assumption that capture prob¬ 
abilities are constant across all weeks throughout the 
year and this condition is not likely satisfied because 
of fluctuating environmental and biological conditions. 
The M hw model had the largest credible interval width 
that was nearly as large as the total population abun¬ 
dance estimate. Most of the uncertainty around the to¬ 
tal population abundance estimate was acquired from 
strata with missing data at the beginning and end of 
the year. Posterior distributions for strata missing data 
using the M HW model relied on capture probabilities 
and abundance characteristics from strata across the 
entire sample season. Models M HB and M SPLINE had 
similar total population estimates but the M H b model 
produced 95% credible intervals wider by roughly 2500 
individuals. 
In contrast to estimates for Marsh Creek, total pop¬ 
ulation estimates for Big Creek for 2014 varied greatly 
among models (Table 2). The M PB model estimated to¬ 
tal population abundances using 28 out of the 37 strata 
owing to the removal of strata missing data (Fig. 2). 
As with results for Marsh Creek, the precision asso¬ 
ciated with the total population estimate for the M PS 
model is dependent on the assumption of homogeneous 
capture probabilities throughout the year and is likely 
overstated in this application. The population estimate 
produced by the MHW model was 216,291 fish with a 
credible interval width nearly double the median es¬ 
timate. The variability of abundance estimates and 
capture probabilities throughout the year at Big Creek 
increased the uncertainty associated with estimates for 
missing data from the M HW model. The M SPLINE model 
was not able to run because of the large number of 
consecutive strata missing data. The M HB model pro¬ 
duced a Uy ot of 148,110 individuals with a 95% credible 
interval width of 120,131 fish. 
To illustrate how the M HB model used past data to 
inform the 2014 estimates at the Big Creek RST dur¬ 
ing the missing strata, we show u, m, and n from the 
