254 
National Marine 
Fisheries Service 
NOAA 
Fishery Bulletin 
established in 1881 
Spencer F. Baird 
First U S Commissioner 
of Fisheries and founder 
of Fishery Bulletin 
A multiyear hierarchical Bayesian mark-recapture 
model incorporating data on recurring salmonid 
behavior to account for sparse or missing data 
Email address for contact author: bryce@henrysfork.org 
Abstract —Mark-recapture studies 
using data collected at rotary screw 
traps (RSTs) are used to estimate 
abundances of migrating juvenile 
salmonids exiting natal rearing hab¬ 
itats. Frequently, environmental con¬ 
ditions and mechanical failures de¬ 
crease RST efficiencies, or complete¬ 
ly halt operations, leading to sparse 
and missing data. In this study, we 
show how a time-stratified hierar¬ 
chical Bayesian model framework 
can incorporate prior information to 
increase the accuracy and precision 
of estimates made with sparse and 
missing data. To do this, we incor¬ 
porated annually recurring salmonid 
emigration characteristics into the 
model using multiple years of data. 
We compared abundance estimates 
of the hierarchical multiyear model 
with 3 single-year Bayesian models, 
using simulated and real RST data. 
The hierarchical multiyear model 
was as accurate and precise as the 
best model when data were complete 
and abundant, but outperformed 
other models when data were sparse 
and missing for multiweek blocks. 
For species with low abundances or 
low detection efficiencies, the hier¬ 
archical multiyear model used data 
from all years and recurring emigra¬ 
tion characteristics to increase the 
accuracy and precision of estimates. 
This model is a valuable tool for fish 
and wildlife biologists who repeat 
mark-recapture studies annually 
and encounter sparse and missing 
data. 
Manuscript submitted 5 January 2018. 
Manuscript accepted: 10 May 2018. 
Fish. Bull. 116:254-265 (2018) 
Online publication date: 7 June 2018. 
doi: 10.7755/FB. 116.3-4.4 
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. 
Bryce N. Oldemeyer (contact author) 1 
Timothy Copeland 2 
Brian P. Kennedy 3 
' Henry's Fork Foundation 
801 Main Street 
Ashton, Idaho 83420 
2 Idaho Department of Fish and Game 
600 South Walnut Street 
Boise, Idaho 83686 
3 Department of Fish and Wildlife Resources 
University of Idaho 
875 Perimeter Drive 
Moscow, Idaho 83844 
To effectively manage free-ranging 
animals, information on survival 
rate, population growth rate, and 
recruitment are needed to under¬ 
stand factors influencing popula¬ 
tions (Fryxell et al., 2014). It is of¬ 
ten necessary to know abundances 
during various life stages to calcu¬ 
late this information but obtaining 
censuses of natural populations is 
difficult (Seber, 2002). Studies struc¬ 
tured around sighting, capturing, or 
counting individuals and expanding 
these counts based on detection or 
sampling efficiencies are regularly 
implemented to estimate abundances 
when a census is not feasible (Nich¬ 
ols, 1992; Mill, 2007). These types of 
mark-recapture studies have broad 
application and have been used to 
estimate abundances of blue whales 
(Balaenoptera musculus) and hump¬ 
back whales (Megaptera novaeangli- 
ae) (Calambokidis and Barlow, 2004), 
grizzly bears (Ursus arctos) (Mowat 
and Strobeck, 2000), herbivorous in¬ 
sects (Kareiva, 1983), and numerous 
other species so that marked indi¬ 
viduals in the population can be de¬ 
tected during later sampling periods. 
The Lincoln-Petersen model is 
foundational for estimating abun¬ 
dances using mark-recapture data 
where unmarked abundance, U, 
is estimated using the number of 
marked individuals in the popula¬ 
tion, n, the number of unmarked 
individuals counted or captured at 
a sampling event, u, and the num¬ 
ber of marked individuals counted or 
captured at a sampling event, m: 
U = num~ l ■ (1) 
Lincoln-Petersen model assumptions 
can be difficult to satisfy, primar¬ 
ily the assumption of equal capture 
probability throughout a sampling 
period, necessitating modifications 
to the model. Commonly, mark-re- 
capture studies occur continuously 
over time where individuals are 
marked, captured, and recaptured 
for several weeks or months. The 
accuracy of an abundance estimate 
obtained from pooling data relies on 
the assumption that capture prob- 
