Oldemeyer et al.: A multiyear Bayesian model for incorporating sparse or missing salmonid data 
263 
Week 
Figure 3 
Raw weekly abundance ( u> of Chinook salmon (Oncorhynchus tshawytscha) and raw weekly 
trap efficiencies, measured as the number of marked individuals in the population divided by 
the number of marked individuals counted or captured at a sampling event (min), at the rotary 
screw trap deployed in Big Creek, Idaho, during the spring from 2007 through 2013. In the top 
graph, catches within the same year are linked by a line. In the bottom panel, the middle line 
within the box represents the median, the upper and lower edges of the box represent the first 
and third quartiles (the 25th and 75th percentiles), the lines extending beyond the box corre¬ 
spond to the largest or smallest values or 1.5 times the interquartile range, and dots represent 
outliers (values outside of 1.5 times the interquartile range). 
ten results in completely pooled strata, and therefore 
loses the power to distinguish real changes in sampling 
efficiency. Additionally, neither approach addresses 
missing periods when the trap is not able to operate 
but fish are known to be migrating, as was the case 
with the M PS model in our study that was designed 
to represent these models. In the simulation, some 
of the M PS model bias was offset by removal of miss¬ 
ing strata. Because the M PS model can use data only 
from sampled strata within a single year, it will con¬ 
tain inherent bias. Therefore the M PS model precisions 
and biases reported in Tables 1 and 2 are misleading, 
because the model structure cannot incorporate the 
uncertainty associated with the missing strata. When 
data are not abundant and “well behaved,” more com¬ 
plex models are necessary. 
The hierarchical structures of the M SPLINE and M HB 
models incorporate information about the characteris¬ 
tics of salmonid migration to improve abundance esti¬ 
mates in situations with sparse or missing data. The 
Mjjw an d Mspune models share information among 
temporal strata within years. The M HB model shares 
recapture data from small populations, with application 
to estimating abundance of smolts from outmigrant trap 
data. NOAA, Natl. Mar. Fish. Serv., Southwest Fish. Sci. 
Cent. Admin. Rep. SC-00-02, 19 p. (Available from website.] 
information during the same temporal period between 
years, allowing data from previous years to inform pe¬ 
riods of sparse or missing data. Because the Mhb model 
shares information among years, it effectively uses the 
entire data set. 
Performance during the spring 2014 period in Big 
Creek shows best how the M HB model is useful. The 
basic Lincoln-Petersen approach as implemented in 
the Mpg model provided no estimates in missing stra¬ 
ta. Information from within 2014 was not very useful 
with the 2-month gap in operations, such that the M HW 
model had extremely wide credible intervals and spline 
components of the M SPL ine model could not bridge the 
missing period. The M HB model provided an estimate 
based on data from previous years and included the 
appropriate uncertainty around that estimate (e.g., 
higher variability between years leads to increased un¬ 
certainty for estimates with missing data during that 
time period). The spring peak in migration becomes 
more pronounced closer to the coast and at lower el¬ 
evations (Spence and Hall, 2010). hence the problems 
we address here may be greater elsewhere. Models that 
performed poorly with our data sets would fare even 
worse in more extreme environmental scenarios. 
For the applications made in this study, we relied 
only on mark-recapture data but one could incorporate 
other types of information to make further improve- 
