264 
Fishery Bulletin 116(3-4) 
ments. For example, spawner abundance, flow charac¬ 
teristics, and data from co-migrating species could help 
explain variability in U and p in the respective exam¬ 
ples. In particular, data on the number of previous-year 
spawners could explain annual differences in juvenile 
abundances, thus accounting for significant changes 
in abundances and timing of migration from year to 
year. Inclusion of data from co-migrating species could 
bolster estimates for species with extremely low abun¬ 
dances. With appropriate assumptions, a multi-species 
model could be a powerful approach to obtain informa¬ 
tion for threatened and endangered species. 
The framework of the Mhb model is flexible and can 
easily be elaborated upon in other ways. For another 
example, one could combine the M SPLINE model and 
M hb model to create a multiyear spline model to apply 
within- and between-year information. Strata with con¬ 
sistent capture probabilities between years that would 
potentially benefit the most from the multiyear spline 
model may not improve much because capture and re¬ 
capture rates are typically high and data are abundant 
in these strata. In addition, the use of the multiyear 
spline model would still be limited by large periods of 
missing data and running such a model would take 
substantial computing power and time. We surmise 
that it would be more beneficial to include environmen¬ 
tal and biological covariates into the M HB model than 
creating a multiyear spline model. We chose not to in¬ 
vestigate the hybrid spline model or to include covari¬ 
ates because we wanted to illustrate the basic concept 
and functionality of the competing models and because 
additional data are not always available. However, if 
conditions are extreme, then these more complex op¬ 
tions may be desirable. 
Throughout this study we focused on 2 long-term 
monitoring projects with data sets ranging from 8 to 
21 years; the M HB model could produce estimates for 
missing data with fewer years of data. The accuracy 
and precision of abundance estimates produced for pe¬ 
riods with sparse or missing data from short data sets 
will depend on the amount of data collected during 
years that the trap was able to operate and the consis¬ 
tency of recurring life-history characteristics between 
years. The effects of relevant factors on the quality of 
information in the data record can be tested but that 
is beyond the scope of this article. However, so long 
as the assumption that the species exhibits a recur¬ 
ring life-history characteristic that is expressed during 
the same temporal period between years, the estimates 
from sparse and missing data would be accurate but 
the uncertainty with these estimates will be expressed 
in wide, credible interval widths. 
The hierarchical multiyear Bayesian model has 
broad application to fish and wildlife studies that em¬ 
ploy mark-recapture approaches to obtain population 
abundance estimates, particularly when addressing is¬ 
sues of sparse or missing data. Other studies have used 
similar Bayesian approaches to calculate adult salmo- 
nid abundance estimates in Alaska (Sethi and Tanner, 
2013), survival estimates of harbor seals (Phoca vitu- 
lina) in Scotland (Mackey et al., 2008), and wolverine 
(Gulo gulo) densities in Alaska (Royle et al., 2011) in 
order to address issues associated with sparse data. In 
this study, we were able to produce abundance esti¬ 
mates for populations of anadromous salmonids with 
sparse data by structuring a hierarchical model that 
incorporated prior biological information about the 
species behavior. The M HB model has applicability to 
a wide range of fish and wildlife research that uses 
mark-recapture data to estimate species abundance. 
This model will be particularly useful in assessments 
of species for which long-term monitoring has occurred 
but for which low abundances and variable environ¬ 
mental conditions affect sampling efforts. 
Acknowledgement 
We thank the Idaho Department of Fish and Game 
(IDFG), University of Idaho, and Bonneville Power Ad¬ 
ministration (projects 1989-098-00, 1990-055-00 and 
1991-073-00) for the opportunity and financial support 
to conduct this research. We greatly appreciate the dis¬ 
cussion, reviews, and feedback provided by M. Quist, 
R. Kinzer, members of B. Kennedy’s laboratory, and nu¬ 
merous other fisheries biologists from the IDFG and 
Nez Perce tribe. We are particularly grateful to K. Ap- 
person, L. Jansen, D. Venditti, and B. Barnett for pro¬ 
viding the RST data that made the analysis possible. 
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