Ecological Applications, 23(7), 2013, pp. 1677–1690
Ó 2013 by the Ecological Society of America
Accounting for female reproductive cycles in a superpopulation
capture–recapture framework
E. L. CARROLL,1,9 S. J. CHILDERHOUSE,2 R. M. FEWSTER,3 N. J. PATENAUDE,4 D. STEEL,5 G. DUNSHEA,6,7
L. BOREN,8 AND C. S. BAKER1,5
1
School of Biological Sciences, University of Auckland, Private Bag 92019, Auckland, New Zealand
2
Blue Planet Marine, Kingston, Tasmania 7050 Australia
3
Department of Statistics, University of Auckland, Private Bag 92019, Auckland, New Zealand
4
Colle´gial International Sainte-Anne, 1300 Boulevard Saint-Joseph, Montre´al, Quebec H8S 2M8 Canada
5
Marine Mammal Institute and Department of Fisheries and Wildlife, Hatfield Marine Science Center, Oregon State University,
2030 SE Marine Science Drive, Newport, Oregon 97365 USA
6
Australian Marine Mammal Centre, Australian Antarctic Division, 203 Channel Highway, Kingston, Tasmania 7050 Australia
7
Marine and Antarctic Ecosystems, Institute of Marine and Antarctic Studies, University of Tasmania, Private Bag 129,
Hobart, Tasmania 7001 Australia
8
New Zealand Department of Conservation, Wellington 6143 New Zealand
Abstract. Superpopulation capture–recapture models are useful for estimating the
abundance of long-lived, migratory species because they are able to account for the fluid
nature of annual residency at migratory destinations. Here we extend the superpopulation
POPAN model to explicitly account for heterogeneity in capture probability linked to
reproductive cycles (POPAN-s). This extension has potential application to a range of species
that have temporally variable life stages (e.g., non-annual breeders such as albatrosses and
baleen whales) and results in a significant reduction in bias over the standard POPAN model.
We demonstrate the utility of this model in simultaneously estimating abundance and annual
population growth rate (k) in the New Zealand (NZ) southern right whale (Eubalaena
australis) from 1995 to 2009. DNA profiles were constructed for the individual identification
of more than 700 whales, sampled during two sets of winter expeditions in 1995–1998 and
2006–2009. Due to differences in recapture rates between sexes, only sex-specific models were
considered. The POPAN-s models, which explicitly account for a decrease in capture
probability in non-calving years, fit the female data set significantly better than do standard
superpopulation models (DAIC . 25). The best POPAN-s model (AIC) gave a superpopulation estimate of 1162 females for 1995–2009 (95% CL 921, 1467) and an estimated
annual increase of 5% (95% CL 2%, 13%). The best model (AIC) gave a superpopulation
estimate of 1007 males (95% CL 794, 1276) and an estimated annual increase of 7% (95% CL
5%, 9%) for 1995–2009. Combined, the total superpopulation estimate for 1995–2009 was
2169 whales (95% CL 1836, 2563). Simulations suggest that failure to account for the effect of
reproductive status on the capture probability would result in a substantial positive bias
(þ19%) in female abundance estimates.
Key words: abundance; Auckland Islands; calving interval; capture–recapture models; Eubalaena
australis; heterogeneity; New Zealand; POPAN model; southern right whale; superpopulation.
INTRODUCTION
Estimating abundance and trends in demographic
parameters is important for the management of populations, particularly in the context of endangered or
threatened species (Norris 2004). Estimation can be
problematic for highly mobile and migratory animals, as
individuals often occupy habitats asynchronously. Evidence suggests that capture–recapture methods that
account for the temporal variability of annual residency
are robust approaches for estimating abundance (WilManuscript received 26 September 2012; revised 4 February
2013; accepted 28 March 2013. Corresponding Editor: T. R.
Simons.
9 E-mail: ecar026@aucklanduni.ac.nz
liams et al. 2011). Hence, one of the most commonly
used models to estimate abundance at migratory
destinations is the superpopulation POPAN model
(Arnason and Schwarz 1996, 1999), a derivative of the
Jolly-Seber model (Jolly 1965, Seber 1965). The superpopulation parameter (NS), estimated by POPAN, is
defined as the total number of individuals that ever enter
the sampled population between the first and last survey
occasions, in addition to individuals present at the start
of the first survey. During each survey occasion, a
proportion of NS enters the survey area and is available
for capture. This proportion is estimated by a parameter
referred to as probability of entry. Superpopulation
models have been used to estimate abundance and
demographic trends in a range of species, including
whale sharks Rhincodon typus (Meekan et al. 2006) and
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E. L. CARROLL ET AL.
North Pacific right whales Eubalaena japonica (Wade et
al. 2011). Estimates of abundance are important for
species such as cetaceans, because it is primarily the level
of recovery compared with the pre-exploitation abundance that will determine future hunting pressure (Baker
and Clapham 2004).
A complexity not yet addressed by available superpopulation models is variation in capture probability
linked to breeding patterns. Factors such as environmental conditions, food availability, age, experience,
previous breeding events, and population density can
affect the breeding intervals of individuals (Lunn et al.
1994, Leaper et al. 2006). In many species with nonannual breeding cycles, females are more available for
capture on breeding or nursery grounds in breeding
years than in nonbreeding years. Heterogeneity in
capture probability is typically thought of as an intrinsic
characteristic of an individual that will create a bias in
abundance estimates if unaccounted for (Seber 1982). In
contrast, breeding status is not a permanent characteristic but one that can vary cyclically, and the bias
induced by this type of heterogeneity has not been
characterized previously in a superpopulation framework.
Here we present a novel version of the superpopulation POPAN model that explicitly accounts for the
variation in capture probability of females due to
reproductive status. We use the model to estimate
abundance for the New Zealand (NZ) southern right
whale Eubalaena australis (Baker et al. 2010; see Plate 1).
The population is considered nationally endangered due
to a combination of range restriction, low abundance,
and low estimated rate of increase (Baker et al. 2010).
Southern right whales migrate between high-latitude,
pelagic feeding grounds in the austral summer and
sheltered, coastal calving grounds in the austral winter
(IWC 1986). As most of the pelagic feeding areas are not
well characterized, the majority of our knowledge of the
species comes from data collected on the coastal calving
grounds where the whales predictably congregate each
winter. Long-term (20–40 year) photo-identification
studies have been conducted on coastal calving grounds
in Australia, Argentina, and South Africa (Cooke et al.
2003, Burnell 2008, Brandão et al. 2010). Reproductive
females in these studies demonstrate heterogeneity in
capture probability linked to their reproductive cycle
(Burnell 2001, Rowntree et al. 2001, Best et al. 2005).
Females calve at intervals of 2–5 years, with an average
of 3 years (Burnell 2001, Cooke et al. 2003, Brandão et
al. 2010). In non-calving years, females have a decreased
probability of capture, possibly due to a shorter
residency period or visiting alternative wintering
grounds (Payne 1986, Rowntree et al. 2001).
For these long-term, data-rich studies, the problem of
breeding-induced heterogeneity in capture probability
has been addressed using multi-state models that
characterize females as calving, resting, or receptive
(e.g., Brandão et al. 2010). Demographic parameters are
Ecological Applications
Vol. 23, No. 7
estimated by these models using detailed histories of
individual sightings and reproductive status (Cooke et
al. 2003). This method requires abundant, high-quality
data from long-term annual sightings records: for
example, Brandão et al. (2010) had 1968 sightings of
954 individual cows with calves collected during annual
aerial surveys from 1971 to 2006, from which they were
able to estimate age at first parturition, survival, and
population rate of increase.
The NZ population of southern right whales congregates during the austral winter in the subantarctic
Auckland Islands in the vicinity of Port Ross (Fig. 1;
see Patenaude et al. 1998, Patenaude 2002, Baker et al.
2010). Difficult conditions and the expense of working in
the subantarctic during the austral winter mean that
detailed long-term data sets are not available. Instead,
two sets of winter expeditions have been conducted in
the Auckland Islands: the first from 1995 to 1998 and
the second from 2006 to 2009 (Patenaude and Baker
2001, Patenaude 2002, Carroll 2011). Rather than
photo-ID, these surveys concentrated on the collection
of skin biopsy samples for individual identification
through DNA profile construction, including sex,
mitochondrial (mtDNA) control region haplotype, and
multilocus microsatellite genotype. These surveys, conducted a decade apart, provide an opportunity to
examine trends in demographic parameters in the NZ
population. However, in the absence of continuous
annual sightings records, new methods are needed to
deal with heterogeneity in female capture probability.
Analysis of mitochondrial DNA haplotype data
suggests that the NZ population is genetically distinct
from neighboring populations in Australia (Patenaude
et al. 2007, Carroll et al. 2011a). Matching of DNA
profile and photo-ID data suggests that the right whales
found around the main islands of NZ are an extension
of the primary concentration in the subantarctic,
although this might not have been the case historically
(Carroll et al. 2011a). Furthermore, evidence such as
consistent use and high density of whales suggests that
estimates of demographic parameters derived from data
collected in the Port Ross area are representative of the
overall NZ population (Patenaude et al. 1998, Childerhouse et al. 2010, Carroll et al. 2011a, b, Rayment et al.
2012). Previously, using the 1995–1998 field surveys,
capture–recapture analyses yielded superpopulation
estimates of ;900 whales for the NZ population over
this period, using photo-identification data (908 whales;
95% CL 755, 1123) and DNA profiles (910 whales; 95%
CL 641, 1354) (Carroll et al. 2011b). This estimate is less
than 5% of the estimated pre-whaling abundance
(Jackson et al. 2009).
Here, using individuals identified with DNA profiles,
we develop an extension of the POPAN model
(POPAN-s) to account for heterogeneity in female
capture probability, and apply it to the extended survey
period from 1995 to 2009. The parameters of interest are
abundance, apparent survival (U), and annual rate of
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HETEROGENEITY AND REPRODUCTIVE STATUS
1679
FIG. 1. Map of the southern right whale (Eubalaena australis) wintering ground at Port Ross in the subantarctic Auckland
Islands, New Zealand.
increase (k) for the NZ population of southern right
whales. We also conduct simulations to test the
robustness of the POPAN-s model to misclassification
of female reproductive status. Misclassification of
reproductive status can arise if fieldwork can only be
conducted for part of the breeding season, because some
females could calve after the observation period.
METHODS
Sample collection
Fieldwork was conducted from small vessels (4.6–5.2
m) in and near Port Ross, Auckland Islands (50832 0 S,
166815 0 E), during the austral winters of 1995–1998 and
2006–2009, following methods described by Patenaude
and Baker (2001). The length of the field seasons was
between 12 and 35 days (Table 1). Skin biopsy samples
were collected using small, stainless steel biopsy darts
deployed from a crossbow in 1995–1998 (Lambertsen
1987) or a modified veterinary capture rifle in 2006–2009
(Krützen et al. 2002). Skin samples were preserved in
70% ethanol on location and transferred to the
University of Auckland for storage at 208C.
In the field, sampled whales were classified into two
age groups based on their body length: adult or calf. The
latter was defined as a whale whose portion of body
visible at the surface was less than half of the length of
an accompanying adult (Carroll et al. 2011b). Adults in
close association with a calf were noted in the field as
cows and presumed to be their mothers.
Laboratory methods
Total genomic DNA was extracted from skin biopsy
samples using standard proteinase K digestion and
phenol/chloroform methods (Sambrook et al. 1989), as
modified for small samples by Baker et al. (1994). The
sex of the sampled whale was identified by amplification
of the male-specific SRY gene, multiplexed with an
amplification of the ZFY/ZRX region as positive
control (Aasen and Medrano 1990, Gilson et al. 1998).
Sequencing of the mitochondrial control region (500 bp)
was conducted as described by Carroll et al. (2011a).
Briefly, the primers dlp1.5 (Baker et al. 1998) and tphe
(Carroll et al. 2011a), both modified with a 5 0 -M13
primer extension to facilitate subsequent sequencing
reactions, were used to amplify ;950 bp of the mtDNA
control region. PCR products were purified for sequencing with ExoSAP-IT (USB, Cleveland, Ohio, USA) and
sequenced using BigDye Dye Terminator Chemistry
(Applied Biosystems, Foster City, California, USA) on
an ABI 3730 or ABI 3130 (Applied Biosystems).
Sequences were aligned and edited in Sequencher v4.2
(Gene Codes Corporation, Ann Arbor, Michigan, USA)
or Geneious (Drummond et al. 2006), and haplotypes
were identified from a 500 bp consensus region using
haplotype codes established by Carroll et al. (2011a).
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Vol. 23, No. 7
E. L. CARROLL ET AL.
TABLE 1. Number of samples collected and unique genotypes (assumed to represent individual whales) from southern right whales
at the New Zealand subantarctic Auckland Islands during winter field surveys 1995–1998 and 2006–2009.
Sample size
Year
Total
samples, n
Quality
control, nQC
Unique
genotypes, nY
Males
Females
Dependent
calves
Unknown
sex
Field
effort (d)
1995
1996
1997
1998
1995–1998 total
70
51
75
158
354
68
48
59
128
303
61
43
52
105
261
29
21
31
51
113
28
20
19
46
106
4
2
2
4
12
0
0
0
4
4
20
18
15
35
88
2006
2007
2008
2009
2006–2009 total
142
234
204
254
834
131
218
197
240
786
111
167
158
191
627
53
60
48
76
208
50
86
92
103
308
8
21
17
9
55
0
0
1
3
4
12
17
15
14
48
1188
1089
888
314
388
67
8
136
Overall total
Notes: The number of samples after quality control is nQC; nY is the number of unique genotypes by year; for ‘‘unknown’’
samples, sex could not be genetically determined. The number of males and females sampled is totalled by year, by survey period,
and overall. For male and female columns only, recaptures within survey periods (1995–1998 and 2006–2009) were reconciled, so
these numbers represent unique individuals. Dependent calves are included in the table but are not used in the model in the year of
birth. Field effort is given in days.
Thirteen microsatellite loci (EV1, EV37, and EV14
[Valsecchi and Amos 1996]; GATA28 and GATA98
[Palsbøll et al. 1997]; RW18, RW31, RW410, and RW48
[Waldick et al. 1999]; GT23 [Bérubé et al. 2000]; TR3G2
and TR3F4 [Frasier et al. 2006]) were amplified in
individual 10-lL PCR reactions as previously described
by Carroll et al. (2011a). Each 96-well tray included a set
of seven standard samples as an internal control to
ensure consistent allele sizing and a negative control to
detect contamination. Amplicons from 4–6 loci were coloaded for capillary electrophoresis with an ABI 3730 or
an ABI 3130. Alleles were sized with Genemapper v 4.0
(Applied Biosystems) and all automated calling was
confirmed by visual inspection (Bonin et al. 2004).
Identification of matching genotypes, i.e., recaptures,
was conducted as described in Carroll et al. (2011a).
Briefly, matching genotypes were identified using CERVUS v3.0 (Kalinowski et al. 2007). As a precaution
against false exclusion due to allelic dropout and other
genotyping errors (Waits and Leberg 2000, Waits et al.
2001), the initial comparison allowed for mismatches at
up to three loci. The genotype error rate was calculated
per allele using the number of mismatching loci found in
replicate samples (Pompanon et al. 2005).
A capture was defined as the identification of an
individual within one year, and an individual was
recaptured if it was sampled in a subsequent year.
Captures and recaptures were categorized into males
and females based on genetic sex identification results.
Using data collected in the field, dependent calves were
identified, and females were further categorized into
cows with calves (denoted breeders) and cows without
calves (denoted nonbreeders) in each year of capture.
We did not use dependent calves in the superpopulation
analyses because they are known to have a lower
survival rate than other age classes (Brandão et al.
2010).
Evaluating assumptions of capture–recapture models
To test for evidence of behavioral response to capture
and transiency, we used the program U-CARE (Choquet et al. 2009). The 2006–2009 and 1995–2009 time
periods for male, female, and combined data sets were
tested separately to examine overall and sex-specific
patterns. The 1995–1998 data were previously tested by
Carroll et al. (2011b). The strict Bonferroni correction
was used to account for multiple tests on the same data
due to the nested nature of the data (Rice 1989).
We tested for significant differences in recapture
frequencies due to sex (male vs. female), and female
reproductive status (observed breeder vs. nonbreeder).
Reproductive females are expected to be more available
for capture in the year of calving, and typically have a
calving interval of 2–5 years. We hypothesized that this
could create a difference in the pattern of recapture
between males and females. Specifically, we used a v2
test to see if there was a difference in the proportion of
males and females that were captured in consecutive
years, for the survey period 2006–2009.
Estimating POPAN superpopulation abundance (NS) and
population rate of increase (k)
We constructed a version of the standard superpopulation POPAN model in program R (R Development Core Team 2011) to estimate male superpopulation size (NS). The assumptions of the POPAN
Jolly-Seber model are general to most capture–recapture
models: for a review see Pollock et al. (1990). For t
capture occasions, the POPAN model provides up to t
estimates of capture probability ( p); t 1 estimates of
apparent survival (U); t 1 estimates of the proportion
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HETEROGENEITY AND REPRODUCTIVE STATUS
1681
of the superpopulation making their first entry into the
study site at each occasion ( pent); and superpopulation
size (NS). Superpopulation models constrain pent values
to sum to 1, by definition, so there are t values of pent in
total.
We investigated two parameterizations of the POPAN
model: the standard version, available through MARK
(White and Burnham 1999), and one we term kPOPAN. In the standard POPAN parameterization,
pent(2), . . . pent(t) are estimated as free parameters. In the
k-POPAN parameterization, the pent parameters are
constrained to follow a growth curve controlled by a
single parameter, k, where k is the annual growth rate,
taken as constant throughout the time period, such that
number of females alive in each survey year as derived
quantities from the fitted model. We construct annual
estimates using a parametric bootstrap from the fitted
model. Values of NS and k are drawn from a bivariate
normal distribution with mean and variance matrix
given by their fitted values under the selected model. For
each value of NS and k, we simulate a superpopulation
with size NS, and with pent probabilities specified by k,
and subject each animal to annual mortality governed
by U. We then find the number of animals alive in each
year of the superpopulation. We repeat this 1000 times
and use the mean and (2.5%, 97.5%) quantiles of the
1000 results as our estimate and 95% confidence interval
for the number alive in each year.
ENðtþ1Þ
¼k
ENðtÞ
Accounting for the female reproductive cycle
in a superpopulation framework
ð1Þ
where EN(t) is the expected number of animals in the
population at time t, including new entrants at time t
and survivors from previous years. If there are sampling
periods missing from the data set, such as 1999 to 2005
in the right whale data set, the pent calculation is
adjusted such that the value for 2006 accommodates the
survival and recruitment of the missing intervening years
(See the Appendix and R code in Supplement 2 for
additional information). The k-POPAN model has the
advantage of directly estimating the parameter k; the
standard POPAN model does not.
To estimate male and female abundance, we explored
models with constant (i.e., time-invariant) survival
denoted U(.); either time-variable entry proportions
pent(t) or a single constant annual growth rate k; and
time-variable probability of capture p(t). Given the
variation in field season lengths (Table 1), models that
held p constant in all years except for 1998 were
explored. Furthermore, due to a combination of a
shorter field season and a lower level of experience in the
crew, we explored models that held p constant in all
years except 2006. We also explored models that held
pent constant in all years after the first year 1995, with
the exception of 2006 to allow for the 8-year interval
between survey periods, and denoted these by pent(06).
In cases where not all model parameters were
estimable or boundary estimates were obtained, some
parameters were constrained. The first two p were
constrained to be equal in the p(t) models (i.e., p1 ¼ p2).
Survival could be fixed at 0.99, denoted U(0.99), a value
found for females in long-term studies of conspecific
populations (Brandão et al. 2010). The Akaike Information Criterion (AIC; Akaike 1973) was used to assess
support for each model (Burnham and Anderson 2002).
All models described were run in program R. Where
possible, the equivalent models were run in program
MARK (White and Burnham 1999) to validate our
custom model results.
Due to strong evidence of lifelong site fidelity among
females, it is likely that the survival parameter U reflects
true survival only. Therefore we can estimate the
As well as the standard POPAN and k-POPAN
models described previously, we developed an extended
model, which we term POPAN-s, to account for the
female reproductive cycle. This model includes additional parameters s1 and s2 to simulate the reduction in
capture probability in non-calving years. We refer to the
reduction in capture probability in the year prior to
calving as the ‘‘precalf’’ effect and model it by adding the
parameter s1 to the model. If the whale is sampled as a
breeder at time t, s1 is applied as a multiplier on the
capture probability of that whale in the single year prior
to calving, t 1. The capture probability for this whale
at time t 1 is therefore s1pt–1. This treatment is similar
to the Mb model for behavioral response to capture
(Chao et al. 2000); however, s1 only applies to the
capture probability in the year prior to capture as a
breeder, rather than to all years subsequent to capture as
in model Mb. Similarly, we describe the reduction in
capture probability in the year after calving as the
‘‘postcalf’’ effect, incorporating the parameter s2 into the
model. If the whale is sampled as a breeder at time t, s2
applies as a multiplier on the capture probability of that
whale in the single year after calving, t þ 1. If a female
was captured without a calf, it was classified as a
nonbreeder, and the capture probabilities were not
modified in the surrounding years. For estimating
female abundance, the standard POPAN and k-POPAN
models were run with and without parameters s1 and s2,
either estimated separately (s1, s2) or jointly (s1 ¼ s2 ¼ s).
Estimating combined male and female abundance
We estimated the combined male and female superpopulation size by adding the sex-specific estimates. The
standard lognormal confidence interval for total NS is
constructed by taking the variance of the combined
estimate to be the sum of the two component variances,
commensurate with independent estimates. It is reasonable to assume independence in the distributions of male
and female estimates about their true values, because
these distributions are governed by the randomness in
capture histories. We have no evidence that male and
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E. L. CARROLL ET AL.
female individuals form permanent social groups that
would lead to correlation in capture histories across the
two data sets.
Testing the robustness of POPAN-s to misclassification
of reproductive status
The reproductive status of all females sampled cannot
be known with certainty, as some may calve after the
survey period ends or could have lost calves prior to
being observed. Females not seen with calves were
assumed to be nonbreeders. Therefore this model was
based on the observed reproductive status of females
sampled as breeders during the field surveys, which is an
approximation of the true status. We ran simulations in
R to investigate how robust the estimates of k and NS
are to the misclassification of reproductive status. We
constructed a right whale population that comprised
50% adult females and 50% juvenile females in 1995
(Taylor et al. 2007). The juvenile females were randomly
assigned an age of 1 to 8 years with a probability of 1/8
each. The adult females were assumed to have last
calved 1, 2, or 3 years ago with a probability of 1/3 each.
The calving interval distribution for adult females was
approximated from studies on conspecific calving
grounds, such that females had a probability of 0.02 of
calving at an interval of 2 years, 0.83 of 3 years, 0.08 of 4
years, and 0.07 of 5 years (Cooke et al. 2001, Brandão et
al. 2010). We also applied these intervals to a whale from
6 years of age so that first parturition was most
commonly at age 9, as reported in the Australian and
Argentinean right whale populations (Cooke et al. 2003,
Burnell 2008). The NS, k, and U values were taken to be
those from the best (AIC) superpopulation model for
the female data set.
This simulated population was then subject to a
simulated capture–recapture study, where the capture
probabilities and s were those from the top-ranked
superpopulation model for the female data set. We
simulated imperfect classification of reproductive status
by specifying the probability that a breeding animal that
is seen in year t is correctly classified as a breeder in year
t. This probability was variously set at 40%, 60%, 80%,
and 100% for different simulation sets. We then fitted
the POPAN-s model to the sightings data with imperfect
classification. The whole process from generating the
population to fitting the model was repeated 500 times at
each level of classification accuracy, and the mean and
distribution of estimates of k and NS were examined and
compared to the values used to generate the simulations
(see Supplement 2 for R code).
RESULTS
Genotyping and individual identification
During the 1995–1998 field surveys, 354 skin biopsy
samples were collected, as described by Carroll et al.
(2011b). During the 2006–2009 field surveys, 834
samples were collected (Table 1). From a total of 1188
samples collected over both sets of surveys, 1089 (92%)
Ecological Applications
Vol. 23, No. 7
were successfully amplified at between 9 and 13 loci
(average 12.3 loci ) and were retained for further analysis
(Table 1).
Pairwise comparisons showed that replicate samples
matched at an average of 11 loci, and all pairs of
replicate samples were supported by mtDNA control
region haplotypes and genetically identified sex. The
least variable 11 loci provided a probability of identity,
or the chance that two individuals will have the same
genotype by chance, of 7.8 3 1014 (Paetkau and
Strobeck 1994) and a probability of identity for siblings,
or the probability that two closely related individuals
will have the same genotype by chance, of 1.7 3 105
(Evett and Weir 1998). Given these low probabilities, we
considered that the suite of microsatellite loci could be
used to confidently differentiate between even closely
related individuals in a population estimated to number
900 whales in 1998 (Carroll et al. 2011b). Based on
replicate samples, there were 103 single-allele errors in
16 770 successfully amplified alleles, giving a per allele
error rate of 0.61% (Pompanon et al. 2005).
During the 1995–1998 field survey period, 223 noncalf whales were captured: 113 males, 106 females, and 4
whales of unknown sex, as previously described in
Carroll et al. (2011b). During the 2006–2009 field survey
period, 520 non-calf whales were captured, including
208 males, 308 females, and 4 whales of unknown sex.
Overall, 710 non-calf whales were sampled, including
314 males, 388 females, and 8 whales of unknown sex
during the 8 years of survey. Of the 710 whales, 610
(85.9%) were captured in one year, 90 were captured in
two years (12.7%), 9 were captured in three years (1.2%),
and 1 was captured in four years (0.11%). The numbers
of unique genotypes sampled per year and survey period
are summarized in Table 1; between-year recaptures are
summarized in Table 2 by sex (see Supplement 1 for
capture history files).
Tests of model assumptions
The Stanley and Burnham (1999) Tests 3.SR and
2.CT implemented in U-CARE did not find significant
evidence of transiency or behavioral response to capture
(trap happy/shy), for any data set or time period
(Appendix: Table A1).
For the time period 2006–2009, there was no evidence
that the proportion of whales recaptured differed
between males (26/208) and females (23/308) (v2 ¼
3.10, df ¼ 1, P ¼ 0.08). In addition, there was no evidence
that the recapture rate differed due to female reproductive state, i.e., between females never seen with a calf
(nonbreeders, 14/158) and those seen in at least one year
with a calf (breeders, 9/150) (v2 ¼ 0.54, df ¼ 1, P ¼ 0.46).
Both of these results are consistent with the findings
from the 1995–1998 data set by Carroll et al. (2011b).
However, there was evidence for a difference in the
pattern of recaptures between males and females: males
(15/208) were more likely to be captured in consecutive
years compared with females (8/308; v2 ¼ 5.17, df ¼ 1, P
October 2013
HETEROGENEITY AND REPRODUCTIVE STATUS
1683
TABLE 2. Number of non-calf adult male and female southern right whales identified per year
(captured) using DNA profiles, and the number of between-year recaptures during austral winter
field surveys at the Auckland islands from 2006 to 2009 and between the 1995–1998 and 2006–
2009 field seasons.
Year of capture,
by sex
A) Males
1995
1996
1997
1998
2006
2007
2008
2009
B) Females
1995
1996
1997
1998
2006
2007
2008
2009
No. recaptured (by year)
No. captured
1996
1997
1998
2006
2007
2008
2009
29
21
31
51
53
60
48
76
4
3
2
2
3
6
0
0
0
0
0
0
1
3
5
1
1
2
2
2
4
0
0
0
0
2
10
9
28
20
19
46
50
86
92
103
0
2
1
2
2
0
0
1
0
2
3
1
0
1
4
2
2
1
9
4
1
2
1
3
3
3
8
3
Note: Several individuals were captured in more than two years, and count as multiple recapture
events in this table.
¼ 0.02). Furthermore, the number of females recaptured
between the two survey periods (n ¼ 26/388) was
significantly greater than the number of males recaptured (n ¼ 7/314) between the 1995–1998 and 2006–2009
periods (v2 ¼ 6.78, df ¼ 1, P ¼ 0.009). These results
indicate heterogeneity in recapture due to sex, both
within the 2006–2009 survey period and between the
1995–1998 and 2006–2009 survey periods. Due to the
need to estimate sex-specific parameters such as capture
probability and apparent survival, only separate superpopulation models for males and females are considered
in the rest of the study. This means that the capture
histories of whales of unknown sex (n ¼ 8), in addition to
dependent calves (n ¼ 67), were excluded from analysis.
Female NS and k estimates for 1995–2009
The best (AIC) model for the female data set was
U(0.99),p(t),k,s , providing an estimate of NS ¼ 1162
females (95% CL 921, 1467) for 1995–2009 (see Table 3
and Appendix Table A2 for results and Supplement 1
for capture history files). Modeling s1 and s2 separately
did not improve model fit compared with modeling the
parameters jointly; therefore, we only report models
with a single estimate of s (Table 3). The addition of the
parameter s significantly improved the fit of the models,
with the best-fitting standard or k-POPAN model
without s having DAIC . 25 compared with the bestfitting POPAN-s model (Table 3). There was a
correlation between AIC and NS, with poor-fitting
models (AIC) producing higher estimates of abundance
(Fig. 2).
The best estimate of k was 1.05, suggesting a
population increase of 5% per year; however, the 95%
confidence interval was wide (0.98–1.13) and contained
the value 1, so a positive rate of increase could not be
confirmed with 95% confidence. Worse-fitting models
(DAIC . 2) produced higher estimates of k, suggesting
annual increases of up to 12% (Appendix: Table A2),
but this is above the estimated maximum rate of increase
for the southern right whale (Best et al. 2001). Female
survival (U) was estimated to be high (0.97; Table 3)
and hit the boundary of 1.00 in many models. Fixing U
at 0.99 marginally improved model fit but did not have a
substantive effect on estimates of NS and k (Table 3), as
found previously (Carroll et al. 2011b, Wade et al. 2011).
The standard POPAN model implemented in program
MARK (White and Burnham 1999) and the R-based
version converged to the same solution for the same
model (see Appendix Tables A2 and A3 for model
results and Supplement 1 for MARK project files).
The estimated number of females alive in 2009 was
1074 (95% CL 812, 1339), which was close to the NS
estimate of 1162 females (95% CL 921, 1467) for 1995–
2009. The estimated numbers alive in 1995, 1998, 2006,
and 2009 were, respectively, 533 (95% CL 219, 1012),
610 (95% CL 305, 1022), 910 (95% CL 692, 1130), and
1074 (95% CL 812, 1339).
Male NS and k estimates for 1995–2009
The best estimate for male abundance was NS ¼ 1007
(95% CL 794, 1276) from the U(.),p(98),k model (Table
3). All models explored had comparable estimates of NS
(995–1066) and similar 95% CL. The models also
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Vol. 23, No. 7
E. L. CARROLL ET AL.
TABLE 3. Parameter settings and estimates (with 95% CL in parentheses) of non-calf female and male New Zealand southern right
whale superpopulation abundance (NS), apparent survival (U), and population growth rate (k) from a modified version of the
superpopulation model, POPAN-s, implemented in program R.
Model parameters
U
p
A) Females
0.99
0.99
.
.
0.99
0.99
t
t
t
t
06
t
B) Males
.
.
.
.
.
98
t
t
06
98
pent
Estimates (95% CL)
k
s
DAIC
np
.
.
.
.
.
.
0.00
0.25
0.93
1.39
1.56
25.21
10
11
11
12
11
9
1162
1120
1164
1113
1212
1520
(921, 1467)
(896, 1401)
(933, 1452)
(893, 1387)
(948, 1549)
(1185, 1951)
0.00
4.28
4.29
6.00
6.31
5
11
10
11
11
1007
1016
997
1066
1035
(794, 1276)
(800, 1289)
(784, 1267)
(835, 1359)
(09, 1324)
06
.
06
t
.
.
06
.
t
t
NS
k
1.05 (0.98, 1.13)
1.04 (0.97, 1.12)
1.06 (0.98, 1.13)
1.07 (1.05, 1.09)
1.07 (1.02, 1.12)
U
s
0.99
0.99
0.97
0.97
0.99
0.99
(fixed)
(fixed)
(0.92, 1.00)
(0.92, 1.00)
(fixed)
(fixed)
0.82
0.83
0.82
0.82
0.82
(0.75,
(0.75,
(0.75,
(0.75,
(0.75,
0.09
0.09
0.07
0.08
0.09
0.89)
0.90)
0.89)
0.88)
0.89)
Notes: Model parameters are shown on the left: U, survival; p, capture probability; pent, entry proportion; k, annual growth rate;
s, capture probability multiplier accounting for a calving event. Cells are blank where parameters are not estimated by the
particular model (e.g., standard parameterizations of POPAN do not estimate k but do estimate pent). For each model, the number
of parameters (np) and the increase in AIC from the best fitting model (DAIC) are reported. The estimate is based on individuals
identified from DNA profiles, using data from the 1995–1998 and 2006–2009 survey periods. The five best-fitting models are
reported, and also for the female data set the best-fitting standard or k-POPAN model without s. A ‘‘t’’ indicates that the parameter
varies with capture occasion; a dot (.) indicates that the parameter is constant over time; ‘‘06’’ indicates that the parameter was
allowed to vary in the 2006 capture occasion but was held constant over other capture occasions; similarly, ‘‘98’’ indicates that the
parameter was allowed to vary in the 1998 capture occasion but was held constant over other capture occasions; ‘‘fixed’’ indicates
that survival was fixed at 0.99 and as such has no CLs.
produced similar estimates of k, with the best model
producing k ¼ 1.07 (95% CL 1.05, 1.09). Male estimates
of U were lower than the female estimates at 0.82–0.83
(95% CL 0.75–0.90) (Table 3). The standard POPAN
model implemented in program MARK (White and
Burnham 1999) and the R-based version converged to
the same solution for the same model (see Appendix
Tables A2 and A4 for model results and Supplement 1
for MARK project files).
Combined NS for 1995–2009
The combined estimate of male and female total NS
was 2169 (95% CL 1836, 2563).
Robustness of POPAN-s to misclassification
of breeders
The simulations were based on the best-fitting
POPAN-s model for the female data set, U(0.99),p(t),k,s
(Table 3), and the probability of a sampled breeder
being correctly classified as a breeder ranged from 40%
to 100%. Results when breeding classification is 80%
correct are shown in Fig. 3A. The differences between
the true values of NS and k, namely the values used to set
up the simulations and their mean estimates derived
from the simulations, are minor, with ,5% bias for NS
and ,1% bias for k. The CI coverage percentage, or the
percentage of the time the CI contains the true value, is
equal to the nominal 95% (Fig. 3). Results for other
levels of breeding classification accuracy are shown in
the Appendix: Fig. A1. High CI coverage and accurate
estimates of NS and k indicate that the POPAN-s model
FIG. 2. Superpopulation estimate (NS) for the female
component of the New Zealand southern right whale population
plotted against DAIC for POPAN-s models and standard or kPOPAN models without s. POPAN-s models incorporate the
parameter s, which models the decrease in capture probability of
females at the wintering ground in non-calving years. The
estimate is based on southern right whales sampled at the
Auckland Islands during winter field surveys from 1995–1998
and 2006–2009 and identified using DNA profiles comprising
genetically identified sex, mitochondrial DNA haplotype, and
multi-locus microsatellite genotype (up to 13 loci).
October 2013
HETEROGENEITY AND REPRODUCTIVE STATUS
1685
FIG. 3. The performance of POPAN-s for estimating superpopulation abundance of female southern right whales, with column
(A) incorporating s and correctly classifying 80% of sampled breeders as breeders, and column (B) omitting s. Boxplots show
estimates of superpopulation size (NS) and the population growth rate (k) from 500 simulations. Bold black horizontal lines show
the mean estimates; thin black horizontal lines the width of each panel show the true mean values. Boxes are drawn between the
upper and lower quartiles, and whiskers extend to the last observation within 1.5 times the interquartile range from the quartiles.
Outliers are marked by short horizontal lines beyond the whiskers. By definition, k must be greater than survival (U ¼ 0.99; shown
in the lower panels as a dashed line). CI coverage percentage is stated below the boxplot for each month.
is able to estimate NS and k robustly, although with
increasing positive bias in NS as the probability of
correctly assigning the reproductive status of a breeder
decreases to 40%.
Results of the simulations conducted with the kPOPAN model without s are shown in Fig. 3B. The
difference between the mean estimate of NS and the true
NS is þ19%, implying that the model without s has a
þ19% bias under the simulation scenario. Even when
only 40% of sampled breeders are correctly classified, the
bias in NS (þ12%) is substantially less than that of the kPOPAN model without s (þ19%). In contrast, estimates
and CI coverage of k appear to be extremely robust in
models with and without s. However, confidence
intervals for k are wide for all models, as found in the
empirical data for females with these parameter values.
DISCUSSION
We have shown that our novel superpopulation
POPAN-s model, which explicitly accounts for the
variation in capture probability of females linked to
their reproductive cycle, performs substantially better
than the conventional POPAN model. It is an improvement both in terms of improved fit for our data (DAIC
. 25) and in terms of bias following our simulation
results. The POPAN-s model provided a 1995–2009
estimate of female abundance for the NZ southern right
whale population of 1162 (95% CL 921, 1467),
compared with 1520 (95% CL 1185, 1951) for the bestranked superpopulation model without s (Table 3). The
POPAN model’s 1995–2009 estimate of male abundance
was 1007 (95% CL 794, 1276). The addition of the
parameter s largely eliminated the difference in abundance estimates between males and females, suggesting
parity between the sexes in the NZ population. This is
consistent with the observed equal sex ratio of calves
(Carroll et al. 2011b).
In the case of the NZ southern right whale, females
appear to have a lower capture probability in noncalving years, possibly linked to shorter residency time
on the wintering ground when without a calf (Payne
1986, Rowntree et al. 2001, Best et al. 2003). If this is not
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Vol. 23, No. 7
E. L. CARROLL ET AL.
accounted for, the overall capture probability of all
females is decreased and the standard POPAN model
produces a positively biased estimate of the female
superpopulation size. In fact, the bias in the POPAN
model without s was larger than that of the POPAN-s
model even if a substantial amount of misclassification
of breeding females occurred (up to 60% misclassified).
Hence, we consider that the POPAN-s model represents
a significant improvement for modeling superpopulation
abundance in species that show variation in capture
probability linked to reproductive cycle.
Recovery of the NZ population
The annual rate of change was estimated most
precisely with the male data set, and showed a significant
positive trend of 7% (95% CL 5%, 9%) for the NZ
population. This estimate is captured within the wider
95% CL of (2%, 13%) gained from the female estimate
of k. The complexity of the female model (requiring 10
parameters compared with 5 parameters in the male
estimate) reduced the precision of the estimate of k; a
longer time series is required to obtain a precise estimate
of k based on data from females alone. The point
estimates of rates of increase for the NZ population are
slightly lower than those in southwest Australia (8.1%,
95% CL 4.5%, 10%; Bannister 2008); and very similar,
although less precise than those in South Africa (6.9%,
95% CL 6.4%, 7.4%; Brandão et al. 2010) and Peninsula
Valdes (6.8%, SE 0.5%; Cooke et al. 2001).
The female point estimate of apparent survival or U
often hit the boundary at 1.00, whereas the male
estimate of U was consistently estimated at 0.82–0.84.
Survival has previously been estimated to be 0.99 in
females based on multi-state models fitted to sightings
data (Cooke et al. 2003, Brandão et al. 2010), and there
are no published estimates of U for male southern right
whales. The POPAN-s estimate of U, or apparent
survival, is a composite of true survival and fidelity,
and the difference between males and females is
intriguing. There is no evidence that males have a
higher mortality rate than female right whales. For
example, deaths due to anthropogenic activities do not
show a sex bias and there is little evidence for male–male
aggression leading to injury or mortality in right whales
(Kraus and Hatch 2001, Kemper 2008).
If males show weaker migratory fidelity to calving
grounds compared with females, it would explain the
difference in apparent survival between the sexes.
Plasticity in philopatric behavior is known to occur in
a low level in southern right whales, but sex-biased
dispersal has not been detected (Best et al. 1993, Pirzl et
al. 2009, Carroll et al. 2011a). On the Peninsula Valdes
calving ground, males are regularly sighted, although
the resighting rate decreases with maturity (Rowntree et
al. 2001). However, as we do not have information on
individual ages, we can only conjecture that our results
for the NZ male population could be explained by a
similar age-related decline in site fidelity.
Available genetic and demographic evidence, based
on paternity analyses and comparisons of mtDNA
haplotype frequencies across wintering areas in NZ
and Australia, are consistent with the hypothesis that
the NZ population represents a relatively discrete,
reproductively autonomous unit. As such, the superpopulation size represents the number of whales that
used the wintering ground over the course of the survey
period, 1995–2009, and should represent this relatively
discrete population. The estimate of number of females
alive in 2009 (1074, 95% CL 812, 1339) is similar to the
estimate of NS, suggesting that for females NS is a useful
and meaningful parameter. Superpopulation size does
not take into account mortality: for females, this
appears to be minor, even over a 15-year period.
Utility of POPAN-s
The POPAN-s model could be applied in circumstances where species have irregular breeding intervals
for reasons such as variation in food resources linked to
environmental conditions (Forcada et al. 2008). This is
because it does not require direct information on the
breeding interval, but rather an observation of the
breeding event. Another advantage of the POPAN-s
model is its efficiency even when capture probabilities
are low. Standard multi-state and individual-based
models for estimating survival and abundance require
rich data sets to be effective (Lebreton et al. 1992). Here
we have demonstrated the success of the method using a
data set with a resighting rate of ;10%, low compared
with many capture–recapture studies, but typical for
cetacean species, e.g., 5.8% resighting rate in North
Atlantic humpback whales (Smith et al. 1999); 3.4%
resighting rate in humpback whales off Madagascar
(Cerchio et al. 2009); 21% resighting rate in Oceania
humpback whales (Constantine et al. 2012). We believe
that this method allows the effective use of data that
might otherwise be considered sparse. The POPAN-s
model uses observed breeding status as an approximation of true breeding status, so we recommend that its
performance is first verified by simulation if it is to be
applied in situations with very different parameters from
those presented here.
The POPAN-s model has the potential for use in
other species that have differences in behavior linked to
reproduction, including other baleen whales, seals, and
oceanic birds (Dawbin 1966, Tickell 1968, Gregor et al.
2000). For example, humpback whales migrate between
tropical and subtropical winter breeding grounds and
high-latitude summer feeding grounds (Dawbin 1966).
The timing of migration varies between demographic
classes, based on the analysis of whaling station catch
data from across the Southern Hemisphere (Dawbin
1966). Females with calves have a longer residency time
in the wintering grounds than receptive or newly
pregnant females, who spend approximately two months
longer in the feeding grounds (Dawbin 1966). This
means that on the wintering ground, newly pregnant
October 2013
HETEROGENEITY AND REPRODUCTIVE STATUS
1687
PLATE 1. Southern right whale (Eubalaena australis) mother (background) and calf (foreground) at Port Ross, Auckland Islands,
New Zealand. The calf is a white morph; such individuals make up approximately 5% of individuals in the Auckland Islands and grow
into gray-colored animals, compared with the typical black coloration seen in the mother. Photo credit: Carlos Olavarria.
females have a lower capture probability than females
with calves, and there is often a male sex bias (Smith et
al. 1999). Because humpback whales have a modal
reproductive cycle of two or three years (although it can
vary between one and five years), the migratory timing
of individual whales, and therefore availability for
capture on wintering grounds, appears to vary across
years depending on reproductive status (Baker et al.
1987, Craig et al. 2003). There is also evidence that sei
whale Balaenoptera borealis migration is structured by
age, sex, and reproductive status in a way similar to that
of humpback whales (Gregor et al. 2000, Best and
Lockyer 2002).
The apparent sex bias in capture records has posed a
problem when estimating abundance in humpback
whales. For example, Constantine et al. (2012) doubled
the male-specific value to estimate humpback whale
abundance on their breeding grounds in Oceania to
account for the difference in capture probability between
the sexes. Another study on humpback whales in the
North Pacific found that the known male sex bias in
breeding areas did not bias abundance estimates if both
sexes are proportionately sampled in the feeding areas
(Barlow et al. 2011). The POPAN-s model would be
suitable for estimating abundance of humpback whales
on their wintering grounds because it would be able to
account for the heterogeneity in female capture probability linked to the reproductive cycle. This situation can
produce a substantial positive bias in the standard
POPAN model (Fig. 2) and should be considered when
using the model to estimate abundance or rate of
recovery in endangered or vulnerable populations.
Overestimating recovery can have implications for the
protection measures afforded to populations, and in the
case of baleen whales, potential implications for
exploitation should the moratorium on commercial
whaling be lifted (IWC 1999).
Conclusion
POPAN-s represents a significant improvement in the
modeling of superpopulation abundance for a species
that shows variation in capture probability linked to the
reproductive cycle. Based on the results of this study, we
suggest that failing to account for variation in capture
probability linked to reproductive status can create bias
in abundance estimates, although we did not see bias in
estimates of k. Overestimating the abundance of
endangered or threatened species has important management implications, because abundance and evidence
of recovery are measures used to decide listings such as
IUCN red list status. POPAN-s is an example of the
tailoring of a superpopulation model to the reproductive
1688
E. L. CARROLL ET AL.
cycle of a specific species, but the model and general
concept are applicable in a wider context.
ACKNOWLEDGMENTS
We thank two anonymous reviewers and Rochelle Constantine for their constructive comments. Biopsy samples were
collected during the 1995–1998 field seasons under permit from
the Department of Conservation (DOC) to C. S. Baker and N.
Gales and University of Auckland Animal Ethics Committee
approved protocol to C. S. Baker. The 1995–1998 Auckland
Islands field trips were funded by the Whale and Dolphin
Conservation Society, the U.S. Department of State (Program
for Cooperative US/NZ Antarctic Research), the Auckland
University Research Council, and the New Zealand Marsden
Fund. Biopsy samples were collected during the 2006–2009 field
seasons under DOC Marine Mammal Research permit and
University of Auckland Animal Ethics Committee approved
protocol to C. S. Baker. The 2006–2009 field seasons were
funded by a Winifred Violet Scott Estate Research Grant Fund,
Australian Antarctic Division, Marine Conservation Action
Fund, Blue Planet Marine NZ Ltd, Holsworth Wildlife
Research endowment, New Zealand Ministry of Foreign
Affairs, DOC, South Pacific Whale Research Consortium,
National Geographic, and Brian Skerry Photography. Logistic
support was provided by the Southland DOC Conservancy, the
University of Auckland, and the Australian Antarctic Division.
We thank Captain Steve Kafka and the crew of the Evohe for
their help and support in the field. We thank M. Vant, K.
Munkres, S. Kraus, R. Rolland, L. Chilvers, C. Olavarrı́a, P.
McClelland, R. Cole, S. Cockburn, S. Smith, L. Douglas, W.
Rayment, and T. Webster for help in the field. We thank Vivian
Ward for help with Fig. 1. Lab work was funded by the NZ
Marsden Fund, DOC, the Heseltine Trust, and an OMV NZ
Ltd. Scholarship to E. Carroll. E. Carroll was supported by a
Tertiary Education Commission Top Achiever Scholarship and
the School of Biological Sciences, University of Auckland.
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SUPPLEMENTAL MATERIAL
Appendix
Equation for calculating pent parameters given k and U (Ecological Archives A023-086-A1).
Supplement 1
Capture history files and program MARK files (Ecological Archives A023-086-S1).
Supplement 2
R code for POPAN (k-POPAN and POPAN-s) models and simulations (Ecological Archives A023-086-S2).