Multi-state open robust design applied to opportunistic data
reveals dynamics of wide-ranging taxa: the sperm whale case
REBECCA M. BOYS ,
RUI PRIETO ,
ONICA A. SILVA
Okeanos R&D Centre - University of the Azores and IMAR –Institute of Marine Research, 9901-862 Horta Portugal
MARE –Marine and Environmental Sciences Centre, 9901-862 Horta Portugal
Whale Watch Azores (WWA), Estrada da Caldeira, 2, Horta 9900-089 Faial
Biology Department, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts 02543 USA
Citation: Boys, R. M., C. Oliveira, S. P
erez-Jorge, R. Prieto, L. Steiner, and M. A. Silva. 2019. Multi-state open robust
design applied to opportunistic data reveals dynamics of wide-ranging taxa: the sperm whale case. Ecosphere 10(3):
Abstract. Capture–mark–recapture methods have been extensively used to estimate abundance,
demography, and life history parameters of populations of several taxa. However, the high mobility of
many species means that dedicated surveys are logistically complicated and expensive. Use of opportunis-
tic data may be an alternative, if modeling takes into account the inevitable heterogeneity in capture proba-
bility from imperfect detection and incomplete sampling, which can produce signiﬁcant bias in parameter
estimates. Here, we compare covariate-based open Jolly-Seber models (POPAN) and multi-state open
robust design (MSORD) models to estimate demographic parameters of the sperm whale population sum-
mering in the Azores, from photo-identiﬁcation data collected opportunistically by whale-watching opera-
tors and researchers. The structure of the MSORD also allows for extra information to be obtained,
estimating temporary emigration and improving precision of estimated parameters. Estimates of survival
from both POPAN and MSORD were high, constant, and very similar. The POPAN model, which partially
accounted for heterogeneity in capture probabilities, estimated an unbiased super-population of ~1470
whales, with annual abundance showing a positive trend from 351 individuals (95% CI: 234–526) in 2010
to 718 (95% CI: 477–1082) in 2015. In contrast, estimates of abundance from MSORD models that explicitly
incorporated imperfect detection due to temporary emigration were less biased, more precise, and showed
no trend over years, from 275 individuals (95% CI: 188–404) in 2014 to 367 (95% CI: 248–542) in 2012. The
MSORD estimated short residence time and an even-ﬂow temporary emigration, meaning that the proba-
bility of whales emigrating from and immigrating to the area was equal. Our results illustrate how failure
to account for transience and temporary emigration can lead to biased estimates and trends in abundance,
compromising our ability to detect true population changes. MSORD models should improve inferences of
population dynamics, especially when capture probability is low and highly variable, due to wide-ranging
behavior of individuals or to non-standardized sampling. Therefore, these models should provide less
biased estimates and more accurate assessments of uncertainty that can inform management and conserva-
Key words: abundance; capture–mark–recapture; mobile taxa; multi-state open robust design model; opportunistic
data; photo-identiﬁcation; POPAN model; population dynamics; sperm whales (Physeter macrocephalus); survival;
temporary emigration; transients.
Received 18 April 2018; revised 22 November 2018; accepted 9 January 2019. Corresponding Editor: Tanya Berger-Wolf.
Copyright: ©2019 The Authors. This is an open access article under the terms of the Creative Commons Attribution
License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
❖www.esajournals.org 1March 2019 ❖Volume 10(3) ❖Article e02610
Application of capture–mark–recapture (CMR)
methods to estimate life history parameters from
photo-identiﬁcation data of naturally marked indi-
viduals has been extensively used on several taxa,
such as cetaceans (Hammond et al. 1990), mana-
tees (Langtimm et al. 2004), sharks (Arzoumanian
et al. 2005), and a variety of felids (Broekhuis and
Gopalaswamy 2016). Ideally, CMR studies would
involve extensive sampling effort across the geo-
graphic range of the target population (Kendall
and Nichols 2004). In addition, in the case of long-
lived species, sampling over multiple years is
usually required to efﬁciently estimate survival or
recruitment. However, such effort is expensive
and logistically demanding. A cost-effective app-
roach could be the use of individual-identiﬁcation
data that are opportunistically collected (Tezanos-
Pinto et al. 2013, Strandbr
aten Rødland and
Bjorge 2015, Bertulli et al. 2017).
The application of CMR methods to highly
mobile species can be challenging though. Differ-
ences in movement patterns and site ﬁdelity
among individual animals over time can lead to
heterogeneous capture probabilities, violating
the standard assumptions of conventional mod-
els (Kendall et al. 1997). Heterogeneity may also
arise from the uneven distribution of survey
effort, if individuals are more likely to be
detected at some locations and times than others
which may be exacerbated in opportunistic sam-
pling. Ignoring individual heterogeneity in cap-
ture probability can affect accuracy and precision
of CMR estimates and may result in false trends
being observed (Pfaller et al. 2013, Sanders and
The most commonly used modeling approa-
ches to deal with individual heterogeneity and
imperfect detection are random-effects, ﬁnite-
mixture, and models with individual covariates.
Random-effects (Gimenez and Choquet 2010)
and ﬁnite-mixture (Pledger et al. 2010) models
are especially appropriate when heterogeneity
cannot be measured or when individual covari-
ates are not applicable (Gimenez et al. 2017).
When heterogeneity is adequately explained by
individual covariates, capture and survival prob-
abilities can be modeled as a function of these
covariates (Pollock 2002). Continuous time-vary-
ing individual covariates can be observable
attributes of individuals (e.g., age class or body
mass) or variables that allow inference about
hidden states (e.g., capture frequency data from
previous sampling periods; Pollock 2002). Con-
tinuous time-varying covariates are challenging
to model, but discrete time-varying individual
covariates, known as states (Gimenez et al.
2017), can be analyzed with multi-state models.
In essence, multi-state CMR models assume that
animals may be in a discrete set of states (deﬁned
by geographic location, reproductive status, age,
etc.), some of which may be observable and
others unobservable, and individuals may transi-
tion between states over time (Schwarz et al.
1993, Lebreton and Pradel 2002).
Therefore, multi-state models provide a conve-
nient way of modeling heterogeneity caused by
temporary emigration, by implicitly assuming
that animals present in the study area are observ-
able, whereas unobservable individuals are those
temporary emigrants, absent from the study area
during a given period. These models can pro-
duce unbiased estimates of state-speciﬁc parame-
ters (abundance, apparent survival, capture
probability) and of the probability of animals
changing between states. A special case of these
models is the multi-state open robust design
(MSORD) that combines features of multi-state
models with Pollock’s robust design sampling
strategy and implicitly accounts for imperfect
detection probability (Kendall et al. 1997, 2018,
Schwarz and Stobo 1997, Kendall and Bjorkland
2001, Ruiz-Gutierrez et al. 2016). Pollock’s robust
design (Pollock 1982) consists of two or more sec-
ondary samples over relatively short intervals
(days to weeks) within each primary period (usu-
ally seasons or years). Multi-state open robust
design models beneﬁt from the extra information
in the secondary occasions to estimate abun-
dance for each state within each primary period
and to improve precision of survival and transi-
tion probabilities (Kendall and Bjorkland 2001).
An important assumption of MSORD models is
that animals may enter and exit the study area
once during each primary period (Kendall and
Bjorkland 2001), allowing the population to be
geographically open. Therefore, MSORD models
permit animals to arrive and depart the study
area at different times within a primary period,
accounting for transience and temporary emigra-
tion, and only assume equal capturability among
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BOYS ET AL.
those individuals present in the area during a
Multi-state open robust design models can be
more complex and data-hungry than open mod-
els incorporating individual covariates but offer
greater ﬂexibility in modeling heterogeneity in
capture probabilities. Here, we apply both meth-
ods to a large sperm whale (Physeter macro-
cephalus) photo-identiﬁcation dataset collected
opportunistically by whale-watching operators
and researchers around Faial and Pico islands, in
the Azores. Our aim was to examine the ability
of these methods to handle strong individual
heterogeneity and estimate the abundance and
demographic parameters of highly mobile taxa
from data collected opportunistically.
Sperm whales are widely distributed from the
tropics to near the ice edges in both hemispheres,
but males and females occupy distinct parts of
this range (Whitehead 2003). Females stay in
tropical and subtropical waters year-round where
they live in long-term social groups with their
immature offspring (Lyrholm and Gyllesten 1998,
Whitehead 2003). Males disperse from their natal
group as they approach puberty and gradually
move to higher latitudes reaching as far as polar
waters (Whitehead 2003). In their late twenties,
males start migrating periodically to the warm
waters inhabited by females to mate (Rice 1989).
The Azores is an important feeding, calving and
possibly mating ground for sperm whales in the
North Atlantic (Clarke 1981). Whales of both
sexes and all age classes use the area year-round,
but the majority of the observations consist of
social groups in late spring and summer (Silva
et al. 2014). Sperm whale social groups are noma-
dic (Whitehead et al. 2008), and the Azores
encompasses only a part of their range. Although
a few groups appear to regularly use the area,
none permanently remain there (Silva et al. 2006,
2014; Appendix S1: Fig. S3).
Photo-identiﬁcation of sperm whales in the
Azores began in 1987, and since then, photo-
identiﬁcation data are regularly collected by
whale-watching operators and researchers. So
far, there has been a single study applying CMR
methods to these data (Matthews et al. 2001),
using a two-sample closed model to estimate
annual abundance during summer (May–
September), and an open model to estimate sur-
vival and birth rates. Unfortunately, these
estimates are likely biased because such classical
closed and open population models cannot ade-
quately account for the inevitable heterogeneity
in capture probabilities resulting from differ-
ences in sperm whale movements and uneven
sampling effort in space and time (Otis et al.
1978, Kendall et al. 1997).
In the present study, we investigate alternative
CMR methods that incorporate individual
heterogeneity and imperfect detection. We
applied the Schwarz and Arnason (1996) param-
eterization of the open Jolly-Seber model with an
individual covariate (hereafter called POPAN)
and MSORD models to the sperm whale photo-
identiﬁcation catalogue collected opportunisti-
cally. We explored the potential of POPAN
models to account for transience and temporary
emigration by modeling survival and capture
probabilities as a function of previous capture
histories (PriorCapL; Cooch and White 2017). We
also applied the MSORD approach that explicitly
accounts for heterogeneity in capture probabili-
ties due to movement, using a model with one
observable state (P,present in the study area) and
one unobservable state (E,temporary emigrant), to
estimate population size, survival, average resi-
dence time, and temporary emigration.
Study area and data collection
We analyzed 28 yr (1987–2015) of photo-iden-
tiﬁcation data collected in the Azores (37°–41°N,
25°–31°W) by three main contributors: a whale-
watching operator, a research institution, and a
non-governmental organization (Appendix S1:
Table S1). Survey platforms, photographic equip-
ment, and data collection procedures differed
among data contributors and throughout the
study period (Appendix S1: Table S1; see Mat-
thews et al. 2001, Steiner et al. 2012, Silva et al.
2014 for further details), though most data were
obtained during 6- to 8-h daily trips. We
restricted the study area to the waters around the
islands of Faial and Pico (Fig. 1) where most
sampling effort was undertaken and discarded
photographs taken outside this area. Still,
because photo-identiﬁcation data were not
obtained during random or systematic surveys,
sampling effort was unevenly distributed across
the study area.
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BOYS ET AL.
Photographic processing and matching
Sperm whales were individually identiﬁed
from photographs of the ventral side of the ﬂuke,
based on natural markings on the trailing edge.
Photographs were graded for quality based on
Arnbom (1987; ranges from Q1 =bad quality to
Q5 =excellent quality), irrespective of distinc-
tiveness of ﬂuke markings. Each whale was
assigned a distinctiveness value that ranged from
D0 =no markings to D5 =missing portion of
ﬂuke, based on certainty of future re-identiﬁca-
tion using the shape and marks on the trailing
edge of the ﬂuke (Dufault and Whitehead 1995,
Childerhouse et al. 1996). To minimize hetero-
geneity in captures due to misidentiﬁcation of
non-distinctive ﬂukes, only high-quality pho-
tographs (Q ≥3) of large sub-adult and adult
whales with distinct ﬂukes (D ≥3) were used in
this study, as calves usually bear few distinct
marks. Potential matches were found using
Match and Phlex 1.3 software (Beekmans et al.
2005), and these probable matches were checked
visually by two independent observers. Adult
males, females, and sub-adults have not been
analyzed separately as they are indistinguishable
from ﬂuke photographs.
The full dataset consisted of 4815 high-quality
photographs of 2342 distinctive individuals col-
lected on 1188 survey days between 1987 and
2015 (Appendix S1: Fig. S1). In our study, a cap-
ture event represents the photographic record of
an individually identiﬁed sperm whale. Analysis
of the encounter histories built from this dataset
showed that 76% of the whales identiﬁed were
only captured once (i.e., transients according to
Pradel et al. 1997), and the average number of
captures of the remaining whales was low (3.97).
As a result, capture probability (p) over the study
period was low (p=0.108, SD =0.02) and all
models tested provided a poor ﬁt to the data and
Fig. 1. Location of Azores and of sperm whales identiﬁed in the study area from 2009 to 2015.
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BOYS ET AL.
few identiﬁable parameters (not shown here).
Therefore, we discarded data from years and
months with lower sampling effort and models
were ﬁt to a subset of data collected for approxi-
mately 2 months (July–early September) from
2009 to 2015.
As expected, results from the program CloseT-
est (Stanley and Burnham 1999) indicated that
the sperm whale population was not closed
(P≤0.001) within each 2-month sampling period
(Appendix S1: Table S2), likely, and at least par-
tially, due to the high proportion of transients.
Therefore, we used two different classes of open
models: the POPAN model (i.e., the Schwarz and
Arnason (1996) parameterization of the Jolly-
Seber model) with an individual covariate and a
MSORD model (Schwarz and Stobo 1997). All
models were ﬁtted in program MARK version
8.0 (Cooch and White 2017).
Transient animals were deﬁned as those that
permanently emigrated from the study area after
initial capture, such that they were not avail-
able to be encountered in the future (Pradel et al.
1997). However, models including only live
captures cannot distinguish between death and
permanent emigration, meaning that a transient
individual will appear to have died after ﬁrst
capture. If this is not accounted for, then survival
estimates will be negatively biased for those
animals that remain in the study area
(Pradel et al. 1997). Nevertheless, since transients
are not captured again after the ﬁrst capture, the
negative bias on survival will only affect the
ﬁrst occasion. Therefore, a common way to
account for transience is to use a model that
allows for the estimate of survival from the ﬁrst
occasion to be different from the following occa-
sions. This can be done using time since marking
(TSM) models which generally provide satisfac-
tory results (Pradel et al. 1997, Cooch and White
2017). Since TSM models are not applicable in
POPAN due to the model structure, we used the
PriorCapL covariate function instead.
Similarly to TSM, this function distinguishes
individuals based on whether they have been
captured before or not, and estimates survival
separately for the interval after ﬁrst capture
and for subsequent intervals (Cooch and White
POPAN models were used to estimate the fol-
lowing parameters: (1) abundance of the super-
), which is the total number of
sperm whales using the study area in the sum-
mers of 2009–2015; (2) annual abundance (N
the abundance of sperm whales summering in
the study area in sampling year t; (3) apparent
survival probability (/
), hereafter survival,
which is the probability of whales surviving and
returning to the study area between sampling
years tand t+1; and (4) the probability that a
sperm whale from the super-population entered
the study area between years tand t+1(pent
Captures of individual sperm whales made
during the same year were pooled, and each year
was treated as a sampling occasion. Models were
built with the capture (p) and survival (/) proba-
bilities set as constant (.), time-dependent (t), or
varying as a function of prior capture. The indi-
vidual covariate function PriorCapL was applied
to indicate whether a whale was observed or not
on speciﬁed sampling occasions (Cooch and
White 2017). Here, PriorCapL was incorporated
in the models to enable survival (/) to be esti-
mated separately for transients and those whales
seen twice or more, thus avoiding the negative
bias on survival from transient individuals.
PriorCapL (t,j) applied to /took the value 1 if
the whale was captured on any previous occa-
sion t,t+1,...,jand 0 otherwise. PriorCapL was
also applied to the capture probability (p)to
account for some heterogeneity from temporary
emigration. In this case, PriorCapL(t) was 1 for
whales seen on the preceding occasion t1 and 0
for whales not seen on that occasion. Finally, pent
was modeled as constant or varying over
Multi-state open robust design models are
based on observations from multiple secondary
(typically within-season) sampling occasions
over multiple primary occasions (typically
years). The extra information on capture proba-
bilities from secondary periods allows estimation
of movement in and out of the study area, as well
as achieving unbiased and more precise parame-
ter estimates (Kendall and Bjorkland 2001).
However, MSORD models require large amounts
of data to obtain estimates for additional
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BOYS ET AL.
within-primary period parameters. Consequently,
MSORD models could only be ﬁt to a subset of
data of the same 2 months from 2011 to 2015. We
modeled these data as ﬁve primary periods, cor-
responding to the years 2011–2015, where each
primary period was composed of three sec-
ondary occasions of 3 weeks (Appendix S1:
Table S4). The 3-week secondary occasions were
chosen to ensure sufﬁcient captures and because
3 weeks is a compromise between the average
residence time estimated from a preliminary
analysis of the 2011–2015 dataset (33.1 d) and
residency estimated using the emigration and
re-immigration model with lagged identiﬁcation
rates (Whitehead 2007) on the 1997–2004 dataset
(14.9 d; Silva et al. 2006). Similarly to the
POPAN models, the MSORD method also
assumes a super-population of individuals, part
of which may be present (P) in the study area and
available for detection (observable state) on a
given sampling occasion, while others may be
outside the area (temporary emigrants, E) and
therefore be unobservable. Using a two-state
model structure, we estimated the following
parameters describing the annual dynamics of
the sperm whale population: (1) the apparent
) hereafter survival, the probability of
whales surviving between sampling years tand
t+1 for those occupying state P; (2) the transi-
tion probabilities (wPE
t) and (wEP
t), which indi-
cate the probability of whales transitioning from
being present (P) in the study area to being tem-
porary emigrants (E), and vice-versa, between
years tand t+1, conditional on survival.
Because of the multinomial nature of transition
probabilities, the probability that a whale
remains in the original state is simply derived by
subtraction; that is, wPP
t. In addi-
tion, we modeled the movement dynamics and
detectability of sperm whales present in the area
in each year: (3) the entry or arrival probability
), the probability that a whale arrives to the
study area in secondary period j; (4) the persis-
tence probability (uj), the probability of being
present in the study area at occasion j, given it
was present at occasion j1 (departure probabil-
ity =1u); (5) the capture probability (p
probability of being detected at occasion j, given
it was present.
MSORD models assume that survival is the
same for animals occupying the observable and
unobservable state, so Sfor temporary emigrant
whales was set to equal that of whales present in
the area. To avoid bias in survival probability
from transient whales, Swas modeled as a func-
tion of time since marking (TSM) to allow a sepa-
rate survival estimate for newly and previously
captured whales (Pradel et al. 1997). The Prior-
CapL function was also applied to Sto under-
stand whether there were differences in estimates
based on the function applied. To investigate the
pattern of movement of sperm whales, we com-
pared four different emigration models: Marko-
t) where the probability of
being a temporary emigrant depends on whether
or not the individual was present in the previous
year, random (wPE
t) where the probabil-
ity of being a temporary emigrant is independent
of the individuals’previous availability, even-
t) where emigration out of and
immigration into the area occur with the same
probability, and no movement (wPE
where there are no transitions into or out of the
area. We also modeled was constant (.) and vary-
ing across years (t). Arrival (pent), persistence (u),
and capture (p) probabilities for temporary emi-
grants (E) were ﬁxed to 0, since these whales
were not available for capture. For whales present
in the study area pent,uand pwere allowed to
vary between years and secondary occasions or
were set to constant. In addition, uwas also mod-
eled as a function of TSM to test whether the
probability of whales leaving the study area
within a year varied as a function of their time
Estimates of the total number of sperm whales
from the super-population visiting the study area
each summer (N
) and of their residence time (R
calculated as the average number of secondary
occasions whales remained in the study area)
were obtained as derived parameters of the
The model with no emigration (wPE
0) was deemed biologically unreasonable but
was used as a basis to assess the effects of time
and TSM dependence on other parameters
(S,pent,u,p). Following the selection of the most
parsimonious model based on only these param-
eters, models were then built to incorporate other
emigration types. In some models where param-
eters were time-dependent, the ﬁrst and second
or, ultimate and penultimate occasions were
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BOYS ET AL.
constrained equal to avoid confounding parame-
ters (Kendall et al. 1997).
Model assumptions and selection
Currently, there are no methods to assess
goodness of ﬁt (GOF) and estimate overdisper-
sion of models with individual covariates or
MSORD models. In the case of POPAN models, a
Cormack-Jolly-Seber (CJS) model was built with
the same dataset and GOF tests performed on
the most general data structure without covari-
) using program RELEASE (Burn-
ham et al. 1987) in MARK. Model overdispersion
was examined by calculating the median ^
the same CJS global model.
Two different GOF tests were used to assess
the MSORD data. The ﬁrst was constructed as an
annual CJS model where secondary occasions
were pooled. This allowed for a time-dependent
model to be tested in RELEASE to examine cap-
ture heterogeneity (Test 2) and heterogeneity in
survival, for example, transience (Test 3; Cooch
and White 2017). Following this, transience was
accounted for in the CJS model and the median ^
approach used to estimate overdispersion. The
second GOF test was through the Pearson chi-
square test available in program ORDSURV
(Hines 2001). This tested whether the data were
appropriately structured to be modeled with
MSORD. This program also provides an indica-
tion of the type of temporary emigration in the
data by setting the emigration parameter to dif-
ferent values and comparing model ﬁt. Results
from ORDSURV GOF were then used to calcu-
late model overdispersion.
Model selection was based on the Akaike
information criterion corrected for the effective
sample size (AIC
; Burnham and Anderson 2002)
or on the quasi-likelihood AIC (QAIC
son et al. 1994) where overdispersion and ^
applied. Models with DAIC
were considered to have some support from the
data and were used to estimate parameters and
respective standard errors (SEs; Burnham and
Estimating total population size
Abundance estimates from POPAN and
MSORD models only pertain to individuals with
sufﬁcient distinct natural markings to allow their
identiﬁcation and must therefore be corrected to
include unmarked individuals as well. Total pop-
ulation size (N
) of sperm whales in the area
during the sampling years was calculated by
dividing model-based abundance estimates (N)
by the proportion of marked animals (h). This
was calculated using only photographs of Q ≥3,
as the number of whales with recognizable
marks divided by the total number of whales.
The SEs of the corrected abundance estimates
were then calculated as:
Log-normal conﬁdence intervals were calcu-
lated following Burnham et al. (1987), where Cis
and the lower conﬁdence limit is N
Cand the upper conﬁdence limit is N
The majority of photographs were obtained
during encounters with social units and likely
include both adult females and immatures of
both sexes. Although a few adult males may
have been mixed with social units, the popula-
tion estimates presented here should pertain to
the female and immature component of the
sperm whale population.
POPAN: model assumptions and selection
A total of 539 individual sperm whales were
photo-identiﬁed during the summer months
between 2009 and 2015. The number of whales
identiﬁed per year ranged between 48 in 2013
and 91 in 2015 (mean =68.5, SD =16.32). Only
122 of the 539 individuals had been captured in
previous years, meaning that most captures
(77%) were of animals seen once.
Not surprisingly, the full time-dependent CJS
model ﬁtted the data poorly (^
df =16, P =0.001). Lack of ﬁt was due to signiﬁ-
cant heterogeneity in survival probabilities (Test
3: P =0.000) in agreement with the high propor-
tion of transients found in the data, but not in
capture probabilities (Test 2: P =0.181). Account-
ing for the transient effect by stratifying the
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BOYS ET AL.
survival parameter with a TSM model reduced
the overdispersion and resulted in a good ﬁtting
=133.87, df =118, P ≤0.10).
We assumed ^
c=1.13 to be a liberal estimate of
the overdispersion value of our POPAN models,
since the application of PriorCapL function on
survival and capture probabilities is expected to
account for part of the excess of variation in the
data from transients, as well as temporary emi-
grants (G. White, Colorado State University, per-
sonal communication). The most parsimonious
model had 86% of the support in the data and
was used for parameter inference. This model
had apparent survival and capture probabilities
varying as a function of whether or not the indi-
vidual was previously captured (PriorCapL) and
constant probability of entry into the study area
POPAN: estimates of abundance and apparent
Estimates of the model-based annual abun-
dance of sperm whales summering in the study
area varied between 250 and 545 (Appendix S1:
Table S5). Abundance for the ﬁrst year (2009)
could not be reliably estimated due to confound-
ing survival and capture parameters. The esti-
mated proportion of identiﬁable individuals
varied between 0.64 and 0.78 (SD =0.05) per
year. The corrected abundance estimates account-
ing for the unidentiﬁable sperm whales ranged
from 351 (95% CI: 234–526) in 2010 to 718 (95%
CI: 477–1082) in 2015 (Fig. 2). These estimates
showed an increasing trend until 2013, after
which it leveled off.
The POPAN model estimated the total size of
the super-population of sperm whales at 1062
individuals (95% CI: 877–1286), which was 1468
(95% CI: 1203–1791) when corrected for the
unidentiﬁable individuals. This abundance esti-
mate represented all sperm whales summering
in the study area from 2009 to 2015, including
transient individuals and those that may have
died. Although calves were not included in the
analysis, those that became juveniles during the
study period and possessed distinctive marks
could also be included in this estimate. The prob-
ability that a sperm whale from the super-popu-
lation entered the study area between years was
0.078 (SE =0.012).
The mean apparent annual survival probability
of sperm whales was 0.95 (SE =0.07), while the
apparent survival for newly captured whales was
0.33 (SE =0.05). Applying the Pradel et al. (1997)
formula to these estimates yields a proportion of
transients in the sperm whale population of 66%.
MSORD: model assumptions and selection
A total of 426 individual sperm whales were
identiﬁed in the summers of 2011–2015. The
number of whales captured per secondary occa-
sion ranged between 20 (in the third occasion of
2014) and 46 (in the ﬁrst occasion of 2014;
mean =34.3, SD =8.77). The number of recap-
tured individuals per secondary occasion varied
from 1 to 20, and 81% of individuals were only
The full time-dependent CJS model showed
poor ﬁt to the data (^
=31.62, df =8,
P=0.00). As with the POPAN results, Test 2 was
Table 1. Summary of best ﬁtting POPAN models ﬁt to sperm whale data ranked by the lowest Akaike
information criterion corrected for the effective sample size (AIC
No Structure AIC
1/(PriorCapL) p(PriorCapL) pent (.) 631.51 0.00 0.86 1.00 6 1345.63
2/(PriorCapL) p(.) pent (t3 =t4) 636.65 5.14 0.07 0.08 9 1346.69
3/(PriorCapL) p(PriorCapL) pent (t1 =t2, t5 =t6) 637.01 5.50 0.06 0.06 9 1346.33
4/(PriorCapL) p(.) pent (.) 640.27 8.76 0.01 0.01 5 1334.81
5/(PriorCapL) p(.) pent (t4 =t5) 640.80 9.29 0.01 0.01 9 1342.54
6/(t)p(.) pent (.) 652.50 20.99 0.00 0.00 11 1335.03
7/(.) p(2a) pent (t) 652.82 21.31 0.00 0.00 10 1332.61
8/(t)p(t)pent (t) 653.02 21.51 0.00 0.00 20 1353.78
9/(.) p(.) pent (t) 653.57 22.06 0.00 0.00 9 1329.78
Notes: Model parameters are /, apparent survival probability; p, capture probability; pent, probability of entry; where
PriorCapL, previous capture function; t, time-dependent; and ., constant.
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BOYS ET AL.
not signiﬁcant (P =0.20), while Test 3 was signif-
icant (P =0.001). Incorporating TSM on survival
improved overall model ﬁt and reduced overdis-
=115.5, df =118, P ≤0.20).
Models with TSM and PriorCapL gave similar
results, but as models with covariates cannot be
adjusted for overdispersion, we decided to
model transience with TSM. Also, results from
ORDSURV indicated that Markovian emigration
poorly ﬁt the data (^
df =42, P ≤0.00), while both constant and ran-
dom temporary emigration ﬁt reasonably with
low overdispersion (constant: ^
36.814, df =24, P ≥0.05; random: ^
=36.748, df =21, P =0.05). Models were
adjusted for overdispersion using the constant ^
The best ﬁtting MSORD model had 42% of the
support of the data and was only three times bet-
ter supported than the second and third candi-
date models (Table 2). The top model included a
different survival probability for newly and pre-
viously captured whales (TSM effect), even-ﬂow
temporary emigration that varied over time,
time-dependent probability of whales entering
the study area within-primary periods and con-
stant between primary periods. The probability
of whales remaining (u) in the study area and
probability of capture (p) were constant within
and between primary periods. The top model
was used for parameter inference (Table 2).
MSORD: estimates of abundance, survival, and
The survival estimate for the whales captured
more than once was 0.93 (SE =0.11). Annual
abundance varied from 183 (95% CI: 117–249) in
2013 to 270 (95% CI: 173–368) in 2011 (Appen-
dix S1: Table S6). Model-based abundance esti-
mates were adjusted by the proportion of
marked whales from the corresponding years to
give total abundances ranging between 275 (95%
CI: 188–404) in 2014 and 367 (95% CI: 248–543) in
2012 (Fig. 2).
The top model in the candidate set included
time-dependent even-ﬂow temporary emigration.
Fig. 2. Estimated total abundance and 95% log-normal conﬁdence intervals based on best ﬁtting POPAN
model and multi-state open robust design (MSORD) model.
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BOYS ET AL.
Models with no emigration also had some sup-
port from the data, but we found little support for
models with random or Markovian emigration.
The probability of emigrating from and immigrat-
ing into the study area varied between 0.22
(SE =0.20) in 2014–2015 and 0.66 (SE =0.17) in
2013–2014. After applying the Pradel et al. (1997)
method, we estimated that 56% of the sperm
whale population consisted of transient animals.
MSORD: estimates of within-year dynamics
Within a year, the probability of sperm whales
entering the study area between secondary sam-
pling occasions varied from 0.32 (SE =0.027) to
0.40 (SE =0.028) and the probability of remaining
in the study area was constant at 0.053
(SE =0.025). The average residence time within a
primary period was 1.06 (SE =0.02), where one
unit represented a 3-week period, and the proba-
bility of persistence was a function of time since
arrival. The capture probability was constant
between secondary occasions at 0.44 (SE =0.10).
By combining MSORD models and individual
covariates in standard open models, we estimated
key parameters of the population dynamics of
sperm whales summering in the Azores, which
would not be possible with conventional analyti-
cal approaches. POPAN estimated a super-popu-
lation abundance of about 1500 sperm whales
using the Azores as part of their summer habitat.
However, not all whales visit the area every sum-
mer; the MSORD estimates suggest that the
annual population comprises about 20% of the
super-population. Apparent survival rates from
both models were high and constant over time, as
expected for a long-lived mammal. The sperm
whale population in the study area is character-
ized by short residence times, with an even-ﬂow
of animals entering and leaving the area in con-
Our results highlight the ability of MSORD
models to estimate demographic parameters
with reliability and precision, when there is sev-
ere heterogeneity in capture probabilities due to
non-standardized sampling and wide-ranging
behavior of animals. This method could be appli-
cable to CMR studies of wide-ranging taxa and
may be especially suited for the analysis of data
Comparing modeling approaches: POPAN vs.
Even if some model assumptions were not
fully met, diagnostic tests indicated that both
POPAN and MSORD models ﬁtted the data well
Table 2. Summary of best ﬁtting multi-state open robust design models ﬁt to sperm whale data ranked by the
No Model structure QAIC
1S(tsm) Ψ(EVENt) pent (t.) φ(..) p(..) 1178.41 0.00 0.42 1.00 10 1157.98
2S(tsm) Ψ(0) pent (t.) φ(t.) p(.t1 =t2 t) 1180.61 2.20 0.14 0.33 10 1160.18
3S(tsm) Ψ(0) pent (t.) φ(..) p(..) 1181.06 2.65 0.11 0.27 6 1168.90
4S(tsm) Ψ(0) pent (..) φ(..) p(..) 1181.83 3.42 0.08 0.18 5 1171.71
5S(tsm) Ψ(0) pent (t.) φ(.t)p(.t1 =t2) 1182.46 4.05 0.06 0.13 13 1155.75
6S(tsm) Ψ(EVEN.) pent (t.) φ(..) p(..) 1182.84 4.43 0.05 0.11 7 1168.63
7S(tsm) Ψ(0) pent (.t)φ(..) p(..) 1183.46 5.06 0.03 0.08 9 1165.11
8S(tsm) Ψ(EVEN.) pent (t.) φ(t.) p(.t) 1184.54 6.13 0.02 0.05 12 1159.93
9S(tsm) Ψ(RANDOM.) pent (t.) φ(..) p(..) 1184.71 6.30 0.02 0.04 7 1170.49
10 S(tsm) Ψ(MARKOVIAN.) pent (t.) φ(..) p(..) 1184.75 6.34 0.02 0.04 8 1168.47
11 S(tsm) Ψ(0) pent (..) φ(.t)p(.t) 1184.86 6.45 0.02 0.04 13 1158.15
12 S(tsm) Ψ(0) pent (.t)φ(t.) p(.t) 1184.95 6.54 0.02 0.04 14 1156.12
13 S(tsm) Ψ(EVENt) pent (t.) φ(..) p(.t) 1185.50 7.09 0.01 0.03 14 1156.67
14 S(tsm) Ψ(EVENt) pent (t.) φ(t.) p(.t) 1185.68 7.27 0.01 0.03 15 1154.73
15 S(tsm) Ψ(EVENt) pent (t.) φ(.tp(.t) 1186.32 7.92 0.01 0.02 16 1153.25
Notes: Model parameters are S, survival probability; Ψ, transition probability; pent, probability of entry; φ, probability of
remaining; p, capture probability; tsm, time since marking; Ψ(0), no movement; Ψ(EVEN), even-ﬂow emigration; Ψ(RANDOM),
random emigration; Ψ(MARKOVIAN), Markovian emigration; t, time-dependent; and ., constant. For pent,φ,and pparameters,
the ﬁrst annotation in brackets refers to within the primary period and the second annotation to between primary periods.
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BOYS ET AL.
and variance was within acceptable limits.
Nonetheless, there were important differences in
the estimates between the two types of models,
resulting from their different abilities to handle
Estimates of annual abundance from the
MSORD were lower and had smaller conﬁdence
intervals than those based on POPAN. Moreover,
POPAN estimates showed an increasing trend
over time, whereas those of MSORD varied only
slightly between years. The best ﬁtting MSORD
model indicated high rates of temporary emigra-
tion in the sperm whale population, with an
even-ﬂow of animals into and out of the area.
MSORD models account for the temporary
unavailability of individuals and estimate only
the number of animals observable in the study
area in a given sampling period. POPAN models
ignore temporary emigration and estimate the
total abundance of individuals from the super-
population found in the study area during at
least one sampling period and the probability
that an animal from the super-population
entered the study area at each sampling occasion
(Pollock et al. 1990, Arnason and Schwarz 1995,
1999, Schwarz and Arnason 1996). Thus, in cases
of even-ﬂow temporary emigration, we expect
capture probabilities from POPAN to be nega-
tively biased and estimates of annual abundance
to be positively biased with respect to the num-
ber of animals in the sampled area in a given
sampling period (Pollock et al. 1990, Arnason
and Schwarz 1995, 1999, Schwarz and Arnason
1996). Our attempts to eliminate this bias by
modeling capture probabilities as a function of
previous capture histories with the PriorCapL
function were unsuccessful, and capture proba-
bilities estimated in POPAN models were sub-
stantially lower than those of MSORD.
Furthermore, capture probabilities decrease with
increasing rates of temporary emigration (Ken-
dall et al. 1997), which may explain the increas-
ing trend in abundance in the ﬁrst years of the
study when emigration rates were higher. These
results illustrate how failure to explicitly account
for imperfect and incomplete detectability can
strongly inﬂuence population size estimates and
eventually lead to detection of false population
An advantage of the POPAN model compared
to the MSORD is its ability to provide unbiased
estimates of the total number of individuals
using the study area throughout the survey per-
iod (Arnason and Schwarz 1995, 1999, Schwarz
and Arnason 1996). The super-population esti-
mates may be especially useful in studies of
migratory animals where the main interest is
determining the number of individuals going
through a speciﬁc area. Apparent survival rates
from POPAN and MSORD models were very
similar and the difference could simply be due to
the different study periods analyzed. Except in
the case of Markovian emigration, survival rates
from POPAN models are robust to heterogeneity
in detection probability (Kendall et al. 1997) and
estimates of survival from our models should be
unbiased although their precision may be lower.
In the case of MSORD, survival would only be
affected by temporary emigration if there is more
than one entry and exit per primary period
(Kendall et al. 2013) which, if occurring, would
not be detectable with only three sampling occa-
sions. The presence of transient individuals nega-
tively biases survival estimates (Pradel et al.
1997). Our results indicate that using the Prior-
CapL function to model survival as a function of
previous captures should give reliable estimates
of survival probability, providing a suitable alter-
native to TSM models that can handle transients
in POPAN models.
Population size and survival probability
Although true values for this sperm whale
population are unknown, the fact that the
MSORD model accounts for individual move-
ments, whereas the POPAN model does not,
leads us to suggest that the MSORD is more
robust (Pfaller et al. 2013, Ruiz-Gutierrez et al.
2016). The MSORD model estimated that 275–
367 sperm whales used the area around Faial
and Pico islands each summer. This estimate
includes all whales that visited the area in a
given summer regardless of their residence time,
including transiting individuals. Abundance esti-
mates from the MSORD varied slightly between
years but showed no annual trend, suggesting a
fairly constant number of individuals using the
area each summer. The super-population size
estimated from POPAN was ~1470 whales,
which summered in the area over the 7-year
study period. It should be stressed that our study
area encompasses a small fraction of the Azorean
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BOYS ET AL.
waters, so the number of sperm whales visiting
the archipelago is expected to be greater than the
estimates presented here. The assumption of
individual capture probabilities being indepen-
dent is violated in social species, such as the
sperm whale (Hammond 1986, Wells et al. 1987).
We did not account for this violation, and
although the effect on abundance estimates
should be negligible, the variance of parameter
estimates may be negatively biased, resulting in
higher precision than reality (Gupta et al. 2017).
Using a standard POPAN formulation, Mat-
thews et al. (2001) estimated that about 450–900
female and immature whales visited the central
islands of the Azores each summer from 1988 to
1990, increasing to 1800–2500 animals in 1991–
1994. The two-sample closed estimator used by
these authors indicated that 340–900 whales were
present at any given time. Compared to our
study, Matthews et al. (2001) covered a wider
geographic area and slightly longer season (May
to mid-September), but >85% of their whale iden-
tiﬁcations were from the same area and months
as ours. Although care should be taken when
comparing these results, the POPAN estimates
reported by Matthews et al. (2001) point to a
much larger population than our MSORD esti-
mates, which could indicate that the number of
whales summering in the area declined between
study periods. Instead, we believe the difference
in the estimates between the two studies reﬂects
the inability of POPAN models to deal with high
temporary emigration (Kendall et al. 1997), over-
estimating population size. Additionally, esti-
mates from the closed models were probably
biased by violation of the closure assumption, as
acknowledged by the authors (Matthews et al.
The boundaries of the sperm whale population
sighted in the Azores and connectivity to other
populations in the North Atlantic are not well
known. The information currently available sug-
gests that this population may have its core
habitat within Macaronesian waters (Azores,
Madeira and Canary Islands; Steiner et al. 2015).
The only abundance estimates within this region
are from the Canary Islands. An acoustic line-
transect survey conducted in autumn and winter
in the territorial waters of this archipelago gave
an absolute abundance of 224 sperm whales
(95% log-normal CIs: 120–418; Fais et al. 2016).
These authors suggest that the Canary Islands
may be acting as a population sink due to high
rates of mortality from ship strikes in the area.
Thus, information on the size, structure, and pro-
ductivity of the population inhabiting Macarone-
sia is urgently needed. Application of MSORD
models to sperm whale photo-identiﬁcation data
from multiple sites could provide information on
movement rates of the population and enable
estimation of global and site-speciﬁc demo-
graphic parameters (Nichols et al. 2007, Cha-
banne et al. 2017).
In our study, models incorporating PriorCapL
or TSM effects on survival provided the best ﬁt
to data. These models enabled separating
transients from temporary emigrants, producing
estimates of apparent survival that should
approximate well to true survival of whales
(Lebreton et al. 1992). All the best ﬁtting
POPAN and MSORD models indicated that sur-
vival of sperm whales was constant over time,
with estimates of 0.95 (95% log-normal CIs:
0.56–0.99) and 0.93 (95% log-normal CIs: 0.74–
1), respectively, for POPAN and MSORD. These
estimates were higher than previous estimates
reported in the study area (Matthews et al.
2001), which we expect were negatively biased
by the large percentage of transient whales in
the dataset that were not accounted for in the
Our estimates are consistent with known adult
survival rates of sperm whales in Southern Aus-
tralia (Evans and Hindell 2004) and in the East-
ern Caribbean (Gero and Whitehead 2016), and
are considerably higher than those found in
Japan, where the population is subject to signiﬁ-
cant mortality in ﬁshing gear (Evans and Hindell
Survival rates of mammals tend to be high and
constant for most of their adulthood, whereas
juvenile survival is usually lower and tends to
increase as the animals approach maturity (Gail-
lard et al. 1998). We could not ﬁt separate models
for females and immatures because they were
indistinguishable from ﬂuke photographs and
the criteria used to identify them in the ﬁeld were
not consistent among data providers. Thus, the
survival probabilities reported here may be
slightly overestimating the true survival of
immature sperm whales and underestimating
survival of adult females.
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BOYS ET AL.
Inter- and intra-annual movement dynamics
POPAN models cannot inform about move-
ments of animals. Conversely, MSORD models
enable investigating movement dynamics through
the estimation of transition probabilities between
states representing the presence or absence of ani-
mals in an area. The models that best described
the temporary emigration of sperm whales
included time-dependent even-ﬂow. This means
that the probability of whales temporarily leaving
the area between consecutive primary periods
was the same as the probability of whales immi-
grating into the area, but movement rates varied
between years. About 41% of the whales encoun-
tered in the study area in 2012 were not observed
in 2013, the same proportion of individuals not
encountered in 2012 but observed the following
year. The symmetric ﬂow rate of whales increased
to 66% between 2013 and 2014 and decreased to
22% in 2014–2015. However, inter-annual varia-
tions in movement rates should be interpreted
cautiously because the conﬁdence intervals on the
transition parameters were wide.
Temporary emigration meant some individu-
als were not observable during the two-month
sampling period in a given year, either because
they were outside the sampled area or because
they were present but were not detected. Our
study site is relatively small compared to the
overall range of the population, which makes it
unsurprising that a large proportion of the pop-
ulation is away during a primary period. This is
supported by the analysis of the full CMR data-
set (Appendix S1: Figs. S2, S3) spanning
28 years and covering most of the spring and
summer. Of the 2342 individuals identiﬁed, only
34% were captured more than once and most
recaptures occurred within the same year and
month of the initial capture; only 17% of the
whales were captured in four or more years. A
few social units, however, seem to return to the
area in consecutive years over an extended per-
iod (average 8 years), usually in the same
month. Interestingly, three of the 15 matches to
the Canary Islands were of whales captured in
the study site every year between 2009 and
2015, which shows that even whales that exhib-
ited inter-annual ﬁdelity to the study site also
used distant habitats. Several individuals
(n=92) were photographically matched
between the Azorean islands (Steiner et al.
2015), sometimes within the same year, indicat-
ing that some temporary emigrant whales could
also have been elsewhere in the archipelago.
Nonetheless, some whales could have been pre-
sent in the study area at the time of sampling
but were not captured, overestimating tempo-
rary emigration. Foraging sperm whales spend
a large proportion of their time submerged and
tend to spread out over a large area (Whitehead
2003), which makes it difﬁcult to detect and sys-
tematically photograph all members of a group.
Models with no movement that disregard tem-
porary emigration (Cooch and White 2017) also
received some support in the data. Lack of tem-
porary emigration in this CMR dataset is highly
unlikely, and we suspect this result to be the con-
sequence of low capture probabilities in some
sampling periods leading to the confounding of
survival and transition parameters (Schaub et al.
The MSORD is a useful tool to infer intra-
annual movement patterns in the absence of
direct measurements. The estimated average resi-
dence time, of adult females and immatures
within the study area, was just over 3 weeks,
slightly higher than the 15 d estimated from
lagged identiﬁcation rates (Whitehead 2007) for
the 1997–2004 period (Silva et al. 2006). We note
that our estimate of residence time is coarse, con-
ditioned by the necessity to aggregate data from
multiple sampling occasions to increase capture
probability (see Challenges of modeling opportunis-
tic photoidentiﬁcation data).
The distribution of sperm whales in the Azores
is strongly correlated with primary productivity,
suggesting that prey availability is an important
driver of local movements and habitat use
na et al. 2016). The displacement of sperm
whales from the study area may be a direct
response to changes in food resources, feeding
success, or be mediated by increased density and
intraspeciﬁc competition (Whitehead and Ren-
dell 2004, Whitehead et al. 2008, Cantor et al.
2017). Other factors may inﬂuence the movement
dynamics of sperm whales over periods of days
to weeks, including occasional presence and
harassment by adult males attempting to mate
(Sundaresan et al. 2007, Craig et al. 2014) or
repeated disturbance from whale-watching boats
(Gordon and Steiner 1992, Magalh~
aes et al. 2002,
Christiansen et al. 2013). All these factors may
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BOYS ET AL.
affect the estimates of residence time, probability
of remaining and temporary emigration patterns.
As intrinsic and extrinsic drivers of movement
patterns are expected to vary both within and
between years, so should the probability of indi-
viduals persisting and entering the area, but this
was not observed in our models. In fact, the
probability of whales remaining in the study area
was low and constant, while the entry probabil-
ity varied slightly between secondary periods
(0.32–0.40) but was constant over years. While
these results are consistent with the even-ﬂow of
whales into and out of the area, lack of temporal
variability in these parameters may be the conse-
quence of an insufﬁcient sample size for model-
ing parameters describing both the inter- and
intra-annual population dynamics (Kendall and
Bjorkland 2001, White et al. 2006). Improved esti-
mation of intra-seasonal movements can be
achieved in the future by focusing only on those
parameters that model dynamics within primary
periods (Ruiz-Gutierrez et al. 2016).
Whale-watching has become an increasingly
important economic activity in the Azores. Dur-
ing the summer, 23 boats operate in our study
area, each making two daily trips of approxi-
mately 3 h (Oliveira et al. 2007). The Azores is
an important foraging, calving, and nursing area
for sperm whales (Clarke 1981), raising concerns
about the detrimental effects of whale-watching
on foraging and reproductive success of the pop-
ulation. Females accompanied by calves incre-
ased aerial behavior and mean blow interval
when approached by whale-watching boats
aes et al. 2002). Such short-term changes
in behavior could translate into increased ener-
getic costs and reduced foraging and nursing
times (Williams et al. 2006). Negative effects will
likely be higher for individuals frequently
exposed to whale-watching interactions because
repeated behavioral disruption can result in a
constant imbalance of bioenergetic budget
(Bejder et al. 2006, Christiansen et al. 2013).
Our results indicate that approximately 300
sperm whales summer in the study area every
year. Despite a relatively small population, the
short residency time and low inter-annual ﬁde-
lity mean that exposure to whale-watching activ-
ities in the area is likely limited within and
across years for most individuals. However,
cumulative effects due to whale-watching distur-
bance may occur in some social units that visit
the area nearly every year and remain there for a
few months. Furthermore, sperm whales may
also be exposed to whale-watching activities out-
side the study area, scaling up potential negative
impacts. Finally, even though exposure levels
may be low, disturbance from whale-watching
may result in behavioral and physiological
changes that might affect individuals’health and
vital rates, and have implications to the dynam-
ics of this population. As it is yet unknown how
this may reﬂect on the super-population demo-
graphics, local dedicated studies are needed to
assess potential effects of whale-watching to this
Challenges of modeling opportunistic photo-
Data from opportunistic platforms, such as that
collected by whale-watching vessels, are often
ﬂagged as a panacea for lack of long-term dedi-
cated monitoring programs of animal popula-
tions, with the advantage of being low cost.
However, application of CMR models to oppor-
tunistic data is challenging and our study pro-
vides a good example of some of those difﬁculties.
One problem with opportunistic data is that
sampling is often insufﬁcient and detection prob-
abilities are low. When numbers of captures and
recaptures are low and vary across sampling
occasions, precision and accuracy of CMR esti-
mators are generally poor (Burnham et al. 1987,
Pollock et al. 1990, Lebreton et al. 1992). In our
case, this led us to discard 21 years of data col-
lected year-round, to restrict the analyses to
times with more whale encounters and ensure a
sufﬁcient number of captures and recaptures for
reliable estimation. Another way to overcome
this problem, such as described here for MSORD
models, is to aggregate data across sampling
occasions to increase the number of captures and
recaptures to generate estimates. This solution
comes with several costs. First, some information
will be lost. In our case, by pooling data into 3-
week secondary periods, we were only able to
get a coarse estimate of the residency and within-
seasonal movements of whales. Second, it may
force the combination of data that are more
heterogeneous with respect to detection
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BOYS ET AL.
processes, requiring complex models for detec-
tion probability and, consequently, more data
(Litt and Steidl 2010). The aggregation process
should be driven by biological information and
weigh the beneﬁt of increased data for modeling
against model complexity (Litt and Steidl 2010).
Opportunistic platforms typically do not sam-
ple the entire study area at every sampling occa-
sion. If animals remain outside the sampled area
during the study, they are simply excluded from
all the estimates. Issues arise when animals
occupy well-deﬁned home ranges, but these
change between primary periods. When this
occurs, incomplete surveying can bias estimates
of temporary emigration because some individu-
als may remain unobservable for the duration of
a primary period but not in others (Sanders and
Trost 2013). In the case of sperm whales, there is
no evidence that individuals or groups exhibit
ﬁdelity to speciﬁc regions within the study area
and we expected whales to move randomly in
and out of surveyable areas, and, therefore, be
exposed to sampling every primary period.
Despite these challenges, our study demon-
strates the feasibility and value of opportunistic
data to improve demographic estimates when
combined with robust statistical models, such as
MSORD. The substantial advantage of this
method is in its ability to estimate the size and
various parameters describing the inter- and
intra-annual dynamics of populations with imper-
fect detectability. We believe MSORD models
could provide relevant information on the demog-
raphy of many wide-ranging species where data
are regularly collected by the public through eco-
tourism activities (Davies et al. 2012, Dennhardt
et al. 2015, Bertulli et al. 2017). We do not advo-
cate that opportunistic data could or should
replace data collection under well-designed CMR
studies. Rather, CMR analyses of opportunistic
data may be carried out alongside and comple-
ment those based on dedicated monitoring
schemes and may be used to investigate speciﬁc
aspects of the ecology of the target population.
Future work should focus on exploring other
methods, such as spatially explicit CMR models,
and integrating photo-identiﬁcation data from
other geographic areas and ancillary information
(e.g., from telemetry or focal follows) to obtain
robust demographic estimates and understand the
dynamics of the population. Finally, a possibility
could be the use of a custom-built model (e.g.,
Conn et al. 2011) for this dataset, to speciﬁcally
model any biases caused by heterogeneity and
incorporate in the model likelihood, the unmarked
animals and misidentiﬁcation parameters, which
could improve estimates of uncertainty.
We acknowledge IFAW for providing photo-identi-
ﬁcation data from the early period of the study (1987–
1993), Biosphere Expeditions and clients of Whale
Watch Azores for making data collection possible. We
thank Sara Magalh~
aes, Tiago S
ao Medeiros, Yves
Cuenot, Pablo Chevallard Navarro, and numerous vol-
unteers that over the years helped with data collection
and organization of the photo-identiﬁcation catalogue.
We are deeply grateful to Gary White, Bill Kendall, Jim
Hines, James Nichols, Paul Conn, and Olivier Gimenez
for offering guidance and advice on CMR modeling.
We thank Jonathan Gordon for his comments on an
earlier version of the manuscript. We are thankful to
the three anonymous reviewers for providing very
This work was supported by Fundac
e Tecnologia (FCT), Azores 2020 Operational Pro-
gramme, and Fundo Regional da Ci^
encia e Tecnologia
(FRCT) through research projects FCT-Exploratory pro-
ject (IF/00943/2013/CP1199/CT0001), WATCH IT
(Acores-01-0145-FEDER-000057), and MISTIC SEAS II
(GA11.0661/2017/750679/SUB/ENV.C2) co-funded by
FEDER, COMPETE, QREN, POPH, ESF, Portuguese
Ministry for Science and Education, and EU-DG/ENV.
The Azores 2020 Operational Programme is funded by
the community structural funds ERDF and ESF. We also
acknowledge funds provided by FCT to MARE, through
the strategic project UID/MAR/04292/2013. Rebecca M
Boys is supported by an Estagiar L scholarship, Cl
Oliveira by a research assistant contract from WATCH
IT and M
onica A Silva by an FCT-Investigator contract
(IF/00943/2013), and Rui Prieto by an FCT postdoctoral
onica A Silva conceptualized the project, acquired
funding, administered, and supervised the project. Lisa
audia Oliveira, Rebecca M Boys, and M
A Silva involved in data curation. Rebecca M Boys,
onica A Silva, Sergi P
erez-Jorge, and Cl
involved in formal analysis, investigation, and method-
ology. Rebecca M Boys preparation and visualization of
the data. Rebecca M Boys, M
onica A Silva, Sergi P
Jorge, Rui Prieto wrote the original draft of the manu-
script. Rebecca M Boys, M
onica A Silva, Rui Prieto,
audia Oliveira, and Lisa Steiner
wrote, reviewed, and edited the manuscript.
❖www.esajournals.org 15 March 2019 ❖Volume 10(3) ❖Article e02610
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