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Fishery Bulletin 1 10(2) 
ables g (e.g., Kuo and Mallick, 1998). Each of these 
indicators was assigned a Bernoulli prior distribution, 
such that the prior probability of including any annual 
effect was 0.5. 
We used the freely available WinBlJGS software 
(Lunn et ah, 2000) to implement Markov Chain Monte 
Carlo (MCMC) sampling to make repeated draws from 
the “posterior distribution” of each parameter — the pri- 
or distribution was updated conditionally on the data 
and structural relationships of the model. We sampled 
10,000 values from the posterior distribution of each 
parameter, after discarding an initial burn-in deter- 
mined by the method of Brooks and Gelman (1998). 
The sampled values were then used to estimate sum- 
mary statistics for the posterior distributions. MCMC 
approaches can similarly be used to sample from the 
posterior distribution of quantities that can be derived 
as functions of parameters. Notably, we used the same 
MCMC simulation approach to generate predictive ob- 
servations from the model parameters and compared 
the fit of our re-immigration model to a standard Cor- 
mack Jolly Seber model based on the mean squared pre- 
dicted error (MSPE; Gelfand and Ghosh, 1998; Durban 
et al., 2010). As with other model selection methods, 
this predictive approach achieves a compromise between 
the goodness-of-fit and a penalty for model complexity 
(Gelfand and Ghosh, 1998). As such, the model with the 
smallest MSPE was estimated to provide the best fit. 
Assessing trends 
We used estimates of the capture probabilities (03,) to 
derive estimates of the abundance of animals {N t ) using 
the study area in any given annual survey period (t). 
These parameters were linked to the observed data by 
specifying the number of individuals actually observed 
in the study area (n t ) as a binomial sample from the 
study area abundance (N t ) with the binomial proportion 
given by the estimated G3 r To assess trends across years, 
we modeled each N t as Poisson distributed and adopted a 
model for the unknown Poisson means (m ( ) that governed 
the form of the variation between years. Specifically, 
we therefore adopted a flexible change-point model to 
describe temporal transitions (e.g., Carlin et ah, 1992): 
log (m t ) = /3 0 + gPfifiit - c) + e, N 
e t N ~ N(0, c A) (2) 
gP ~ Bernoulli(0.5). 
The parameter )3 0 described the general intercept of the 
model (or level of abundance on the log scale before the 
change-point), and the function 50 represented a step 
function, defined as 1 if its argument was zero or posi- 
tive and zero otherwise. The parameter j\ described the 
magnitude of a step change (on a log scale), at time c 
(known as a change-point). We assumed the timing of 
the change-point was unknown and used the data to 
assess the evidence for a change-point in each of the 27 
years. This problem therefore involved estimating the 
posterior distribution of the unknown temporal change- 
point (c) to identify when a change-point may have 
occurred, and with what probability. The model offers a 
flexible approach for modelling changes in abundance, 
because uncertainty about the year of the change-point 
results in uncertainty over how the trend is apportioned 
over the time series of between-year transitions. Because 
the step function 50 was specified on a discrete time 
period (t - c), we placed a discrete uniform prior for c 
over T-21 years) (e.g., Carlin et ah, 1992): 
c ~ U(1,T) (3) 
with discrete prior probability of 1/T being placed on 
each of the 27 years. We assumed that the direction and 
magnitude of the change was unknown, and we there- 
fore assigned diffuse prior distributions for the hyper- 
parameters [i 0 and /3,, each with mean 0 and standard 
deviation of 10. We assessed the probability of a trend 
in abundance by estimating the indicator probability^ 
of including the trend parameter /3j in the model for the 
abundance estimates. 
Rather than perform this trend analysis independent- 
ly of the mark-recapture model, we combined these two 
components into a single Bayesian hierarchical model to 
propagate uncertainty in estimation of capture probabil- 
ities ( 03 ,) into estimates of abundance (N t ) and trend pa- 
rameters. We did not assume that the N t fell exactly on 
the trend line, or had a common variance, but instead 
we included annual random-effects terms (e t N ) that al- 
lowed over-dispersion in contrast to a fixed-effects Pois- 
son trend model. A normal random effects distribution 
was adopted for the e t N ~ N(0, o N ), with overdispersion 
controlled by the standard deviation ( o N ), which was 
assigned a uniform (0,10) prior distribution. As with 
the mark-recapture parameters, we used WinBUGS to 
sample 10,000 values from the marginal posterior dis- 
tributions for the annual estimates of abundance, N r 
Additionally, interest was focused on making inference 
about the posterior distributions of the parameters of 
the trend model, specifically the change-point (c), the 
rate of change (/3j), and the probability of a trend (gP). 
Tracking whale movements 
To examine movements of whales relative to our mark- 
recapture modeling estimates (extent of temporary emigra- 
tion away from the study area), we compared photographs 
used in our analysis with those taken during parallel 
research efforts in southeastern Alaska, British Columbia, 
and Washington State (e.g., Ford and Ellis, 1999) to iden- 
tify annual overlap of individuals. Previous analyses had 
shown no overlap of ATI or GOA transients with those in 
the Aleutian Islands (Durban et al., 2010). In addition, we 
attached satellite transmitter tags to individual GOA and 
ATI transient whales to provide fine-scale tracks of daily 
movements. The tag design was a low impact minimally 
percutaneous external-electronics transmitter (LIMPET) 
satellite tag (Andrews et al., 2008). In this tag, the main 
electronics package, an Argos-linked, location-only SPOT 
