Matkm et al Abundance and residency patterns of two sympatric populations of Orcmus orca in the northern Gulf of Alaska 
145 
1 50°W 
1 40 C, W 
1 30°W 
B 
Prince William 
Sound 
' 
* * 
fjords 4 • "* 
*rf r 
Montague Strait 
WSg "Wm f 
r^r^i— 1 — | — I — r 
0 37.5 75 
150 Kilometers 
! 000m contour 
Figure 1 
(A) Location of the coastal study area of Prince William Sound and 
Kenai Fjords. (B) Locations of encounters with ATI (203, closed circles) 
and Gulf of Alaska (GOA) (91, open circles) transient killer whales 
(Orcinus orca) between 1984 and 2010, during which photo-identification 
data were collected. 
(Lebreton et al., 1992) does not account 
for animals that emigrate from the 
study area and return later. Instead, 
we followed Whitehead (1990) in de- 
veloping a mark-recapture model that 
parameterized emigration and re-im- 
migration probabilities in addition to 
survival. Our model was based on an 
individual-specific factorization (e.g., 
Schofield et al., 2009), allowing modu- 
larization into conditional distributions 
for capture probability, availability of 
whales for capture (temporary emigra- 
tion), and death. This formulation al- 
lowed imputation of partially observed 
data on availability in the study area 
(available in the study area when ac- 
tually identified) and survival status 
(alive when identified and between 
years of repeat identification), provid- 
ing identifiability of parameters and 
enabling time-varying formulations. 
Specifically, the model had the param- 
eters tp f , K t , A,, and 03, where <\> t l is the 
probability of survival from time t— 1 to 
time t; A,_ ; is the probability of tempo- 
rary emigration from the study area at 
time t- 1; K t is the annual probability of 
re-immigration back into the study ar- 
ea; and 03, is the probability of capture 
at time t for whales alive and avail- 
able to be captured in the study area. 
Note that owing to the geographic re- 
strictions of the surveys and the likely 
wider ranging patterns of the whales, 
survival in this case represented ap- 
parent survival that could comprise 
either death or permanent emigration 
(at least for the duration of the study). 
To fully quantify uncertainty about 
the unknown parameters, we adopted a 
Bayesian approach to model fitting and 
inference, where estimates were pre- 
sented as full probability distributions 
(Gelman et al., 1995). The Bayesian 
approach requires prior distributions to 
be specified for all model parameters, 
and we adopted similar hierarchical 
priors for each set of probability terms 
<p, A, k, and C3. To allow temporal variation across each 
parameter vector, each annual probability was initially 
specified as a function of a mean for each parameter 
vector and annual random effects terms: 
logit($,. A,, Kf, and 03,) = logit(p | k , *’ lc ’ ra ) + g AAtra e t 
0, A, K, 03 _ N ( 0 (J 0> ® ) 
g _ Bernoulli(0.5), 
where logit(a) = log(a/(l-a). 
The prior distribution for each parameter was thus 
determined by two hyper-parameters: p represented 
the mean value across each set of parameters and the 
standard deviation term o represented the year-to-year 
variability over the set, on the logit scale. Uniform(0,l) 
prior distributions were placed on each of the five mean 
probabilities pAA.h-.ra anc ] a un iform(0,10) prior distri- 
bution was adopted for ctAA kb a u ow annual differ- 
ences from the logit-transformed means to emerge. The 
probability (evidence) of temporal variability in each 
parameter vector was assessed through indicator vari- 
