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65
Journal of Mammalogy, 84(1):65–80, 2003
ESTIMATING SURVIVAL AND CAPTURE PROBABILITY OF FURSEAL PUPS
USING MULTISTATE MARK–RECAPTURE MODELS
COREY J. A. BRADSHAW,* RICHARD J. BARKER, ROBERT G. HARCOURT,
AND LLOYD S. DAVIS
Department of Zoology, University of Otago, P.O. Box 56,Dunedin,
New Zealand (CJAB, LSD)
Department of Mathematics and Statistics, University of Otago,
P.O. Box 56,Dunedin, New Zealand (RJB)
Marine Mammal Research Group, Graduate School of the
Environment, Macquarie University,Sydney, New South Wales 2109,
Australia (RGH)
Present address of CJAB: Antarctic Wildlife Research Unit,
School of Zoology, University ofTasmania, GPO Box 252-05, Hobart,
Tasmania 7001, Australia
We use a multistate mark–recapture model incorporating
information on body mass, sex,time of capture, and natal colony to
estimate the probabilities of survival, capture, andmass-state
transition of New Zealand fur seal (Arctocephalus forsteri) pups
from 3 sites(colonies) on Otago Peninsula, South Island, New
Zealand. Apparent survival for a meansampling interval of 47 days
was high ($0.850) after correcting for tag loss, and there
wasevidence that there were differences between sexes and among
sites even after controllingfor mass at capture. Survival did not
differ among body-mass classes. Heavier pups hadlower capture
probabilities; however, differences in mass adequately explained
any potentialdifferences in capture probability due to sex.
State-transition probabilities among massclasses also differed with
time of capture, and between sexes and among sites. Althoughbias in
estimates of survival probability is minimal when survival is high,
heterogeneity incapture probabilities among different classes of
individuals can bias estimates of pup growthrate and sex ratio. We
recommend measuring mass of individuals and incorporating thisand
perhaps other pertinent information into multistate mark–recapture
models when at-tempting to estimate survival and to determine the
effect of capture probability on estimatesof other life-history
parameters.
Key words: Arctocephalus forsteri, mark–recapture, multistate
model, New Zealand fur seal, pin-niped, survival, transition
Estimating survival probability in youngmammals has important
implications for theunderstanding of population dynamics,
es-pecially with regard to density-dependentprocesses (Sinclair
1996). However, obtain-ing precise estimates of survival
probabilityis often difficult because many time-
anddensity-dependent factors, such as bodymass and condition, can
affect 1st-year sur-vival. These individual covariates may
alsoaffect survival more extensively under con-
* Correspondent: [email protected]
ditions of fluctuating food availability,which has important
implications for life-history strategies (Hall et al. 2001).
Underexceptional circumstances, mammal popu-lations can be
monitored for the presenceor absence of nearly all individuals in
apopulation (Clutton-Brock 1988; Clutton-Brock et al. 1985), thus
allowing for thecalculation of precise estimates of
juvenilesurvival. For most mammals, however, thisis impractical, if
not impossible, and de-mands more intensive mark–recapture
mod-eling. Recent developments in mark–recap-
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66 Vol. 84, No. 1JOURNAL OF MAMMALOGY
ture modeling have allowed for the incor-poration of individual
covariates at the timeof initial capture into the estimation of
sur-vival (Hall et al. 2001; White and Burnham1999) and so provide
a powerful tool formodeling populations of mammals.
In addition, it is important to determineif there is
heterogeneity in capture ratesamong individuals or groups of
individuals(Gehrt and Fritzell 1996) because this het-erogeneity
can also bias estimates of pop-ulation parameters (Clobert 1995;
Johnsonet al. 1986; Nichols 1992; Pollock et al.1990; Trites 1991,
1993). Capture or recov-ery probabilities can vary among areas
andtimes (Cameron et al. 1999; Gehrt andFritzell 1996; Lindenmayer
et al. 1998;Pace and Afton 1999; Pradel et al. 1997);among size,
condition, or age classes (An-derson 1995; Pace and Afton 1999;
Pradelet al. 1997; Trites 1991, 1993); and betweenthe sexes
(Buskirk and Lindstedt 1989;Flatt et al. 1997; Gehrt and Fritzell
1996;Lindenmayer et al. 1998; Pradel et al. 1997;Prévot-Julliard
et al. 1998). If the assump-tion of homogenous capture
probabilities isviolated, then estimates of survival, growth,and
sex ratios may be biased.
Pinnipeds are suitable for the assessmentof individual
covariates on survival andcapture probabilities because body mass
orcondition can be assessed with relative easeand large sample
sizes can be obtained.This has been shown in phocid seals suchas
gray seals (Halichoerus grypus—Hall etal. 2001) and southern
elephant seals (Mir-ounga leonina—McMahon et al. 2000). Inthese
studies, survival probability increasedwith increasing body mass
(McMahon et al.2000) or body condition (Hall et al. 2001)at
weaning. However, little quantitative as-sessment of these
parameters has been ob-tained for otariid seals (fur seals and
sealions). This lack of rigorous testing maylead to bias in
population models for otariidseals and may confound the many
differentapplications of these models. Otariid sealshave been the
subject of extensive model-ing to estimate population size,
biomass,
and trends (Butterworth et al. 1987, 1995;Lander 1981;
Shaughnessy and Best 1982;Smith and Polacheck 1981; Wickens et
al.1992). Models have also been used to ex-amine the effects of
commercial harvests onpopulations (DeMaster 1981; Eberhardt1981;
Frisman et al. 1982; Lett et al. 1981;Smith and Polacheck 1981;
Trites and Lar-kin 1989) and to examine the effects of furseals
foraging on commercial fish stocks(Butterworth et al. 1995; Wickens
et al.1992). In addition, outputs of models usedto predict
population growth rates of furseals and food consumption rates are
sen-sitive to changes in age-related survival(Butterworth et al.
1995; Wickens and York1997). Wickens and York (1997) demon-strated
that survival to age at 1st reproduc-tion in fur seals was 50–80%
of adult sur-vival. Because juvenile survival in this tax-on is 1
of the most important parametersaffecting population growth models,
it isimperative to obtain precise and unbiasedestimates of survival
and other associatedparameters.
New Zealand fur seals (Arctocephalusforsteri) occur around New
Zealand, south-ern Australia, and the Australasian temper-ate and
subantarctic islands (Bradshaw etal. 2000b; Crawley 1990;
Shaughnessy etal. 1994). In the New Zealand region,breeding
colonies were once widespreadaround the coasts of all New Zealand
is-lands, but subsistence and commercialhunting by humans reduced
the populationto remnant pockets on remote islands by1830 (Lalas
and Bradshaw 2001; Mattlin1987). However, in recent years the
num-bers of A. forsteri in New Zealand have in-creased, and much of
their previous rangehas been recolonized (Bradshaw et al.2000c;
Lalas and Murphy 1998; Taylor etal. 1995).
New Zealand fur seals come ashore onrocky coastlines to breed
colonially frommid-November through early January, withmean pupping
in mid- to late December(Lalas and Harcourt 1995; Mattlin
1987).Mothers give birth to a single pup and re-
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February 2003 BRADSHAW ET AL.—MODELING SURVIVAL OF FUR SEAL PUPS
67
FIG. 1.—Study areas of New Zealand fur sealpups at Otago
Peninsula, South Island, NewZealand, showing the 3 colonies
sampled: Fuch-sia Gully (FG), Sandymount North (SMN), andTitikoraki
South (TKS).
main with it for a mean of 9 days beforegoing to sea to feed for
the 1st time sinceparturition (Crawley 1990; Mattlin 1987).Mothers
alternate between foraging trips atsea and time ashore to suckle
pups untilweaning occurs approximately 10 monthslater (Mattlin
1987). Early foraging tripslast 2–7 days, though subsequent trips
areprogressively longer as pups grow older(Harcourt et al. 2002).
Thus, pups have pro-gressively longer bouts of fasting whilemothers
are foraging, and solitary pups of-ten band together during these
times. Dur-ing the fasting period pups may be exposedto adverse
weather. There are no large landpredators in New Zealand; however,
occa-sional predation by New Zealand sea lions(Phocarctos hookeri)
has been recorded(Bradshaw et al. 1998).
Despite nearly 30 years of research onthe population dynamics
and behavior of A.forsteri in New Zealand, the recent substan-tial
increase in population size and the po-tential importance of this
species as a com-petitor with commercial fisheries (Harcourtet al.
2002; Lalas and Bradshaw 2001),there are still no regionally
replicated, pre-cise estimates of pup survival for A. for-steri.
Without reliable estimates of pup sur-vival, models attempting to
assess the lon-ger-term trends and potential impacts of thisspecies
on the local ecosystem can be in-adequate.
We use a multistate, mark–recapturemodel (Nichols et al. 1992;
Schwarz et al.1993) to estimate survival of A. forsteripups from
immediately after the breedingseason up to approximately 155 days
ofage. This type of model controls for indi-vidual characteristics
such as estimatedbody mass, which may influence the prob-ability of
recapture as shown in northern furseals, Callorhinus ursinus
(Trites 1993).The model structure also allows a covariatesuch as
body mass to be transformed into adiscrete input for each capture
session, thusmaximizing the data available. We also pro-vide a
correction to survival estimates fortags lost during the period of
the study and
investigate the effect of differential captureprobabilities on
estimates of survival. Wetest whether multistate
mark–recapturemodels provide insights into survival andgrowth rate
models that may be missedwhen data on mass change in growing
in-dividuals are not incorporated.
MATERIALS AND METHODS
Study sites, capture, and tagging.—We stud-ied New Zealand fur
seals on Otago Peninsula,South Island, New Zealand in 1997 and
1998.In 1997 we captured pups from Fuchsia Gully(Ohinepuha;
458509S, 1708459E; Fig. 1). In 1998we sampled Fuchsia Gully,
Sandymount North(458539S, 1708419E), and Titikoraki South(458519S,
1708449E; Fig. 1). Fuchsia Gully is a2,596-m2 site characterized by
rocks 0.6–5.0 min diameter on a mostly flat surface. Some
scrubvegetation populates the base of a 20-m cliffoverlooking the
colony. Sandymount North is a1,493-m2 site made up of rocks 1.3–5.0
m indiameter and is relatively flat. There are 2 mainsections of
the site separated by an area of smallpebbles that appears to be
used only by non-
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68 Vol. 84, No. 1JOURNAL OF MAMMALOGY
FIG. 2.—Relationship between body condition(loge[combined
condition index]) of pups of NewZealand fur seals and pup density
(loge[pups/100m2]) for colonies of New Zealand fur seals in sum-mer
at Otago Peninsula, New Zealand, in a) 1997and b) 1998 (data from
Bradshaw et al. 2000b).Straight line in a) represents mean
conditionamong colonies, and line in b) represents
negativerelationship between condition and density in thatyear (r2
5 0.25—Bradshaw et al. 2000b). The 3target colonies (Fuchsia Gully
[FG], SandymountNorth [SMN], and Titikoraki South [TKS]) areshown
in both graphs (mean 6 SE) as open circles,demonstrating that pup
density was similar amongcolonies and between years. Note
difference in y-axis scale in a) and b). Mean pup condition
wassignificantly lower in 1998 (Bradshaw et al.2000b); however, the
condition was similar amongthe 3 target colonies within a
particular year.
breeding fur seals. Titikoraki South is a smaller,907-m2 site
just to the north of Fuchsia Gully,backed by a 70-m cliff. The site
is characterizedby a narrow, rocky region above high tide
(ap-proximately 7 m) with rocks 1.3–2.5 m in di-ameter. The colony
is split into several sectionsby large rock embankments that pups
do not ap-pear to traverse easily until closer to the weaningperiod
(Bradshaw 1999; Bradshaw et al. 1999).
The 3 sites were chosen for their proximity toeach other to
control for potentially confoundingeffects due to characteristics
of the terrestrialand marine habitats, and population demograph-ics
(Bradshaw et al. 1999, 2000b). Using prin-cipal components derived
from terrestrial char-acteristics of each site (Bradshaw et al.
1999),we determined that the 3 target colonies, FuchsiaGully,
Sandymount North, and Titikoraki South,were similar in their
breeding terrain relative to23 other breeding colonies around South
Island,New Zealand. However, Sandymount North hadslightly smaller
rocks and lower rock densitythan did Fuchsia Gully and Titikoraki
South(Bradshaw et al. 1999). All sites were within 10-km swimming
distance from each other. We as-sume that lactating females from
each colonyhad approximately the same foraging habitatconditions
(Bradshaw et al. 2000b, 2002) be-cause it is known that they can
travel .100 kmfrom the colony when foraging (Harcourt et al.2002).
All 3 sites demonstrated similar pup den-sities (pups/100 m2) and
condition (observedmass/predicted mass—Bradshaw et al. 2000b) atthe
end of the breeding season (early January)in both 1997 and 1998
(Fig. 2). Although colo-nies had similar pup densities in both
years,mean pup condition was significantly lower in1998 for all
colonies (Fig. 2; Bradshaw et al.2000b). Breeding colonies have
occupied allsites since at least the early 1990s and have
beenincreasing annually since their inception (Brad-shaw et al.
2000c; C. Lalas, pers. comm.).
We captured pups on 4 occasions betweenJanuary and June during
both years (AppendixI). We placed individually numbered plastic
tags(Allflext ‘‘Mini’’ tags, 52 by 17 mm, Palmer-ston North, New
Zealand) in the connective tis-sue on the trailing edge of both
foreflippers onall pups captured. All pups received the sametype of
tag, and the tagging procedure did notvary among colonies (Bradshaw
et al. 2000a).Pups were also weighed to the nearest 0.1 kg(Bradshaw
et al. 2000b) using a 20-kg balance
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February 2003 BRADSHAW ET AL.—MODELING SURVIVAL OF FUR SEAL PUPS
69
(Pesolat, Baar, Switzerland). During each ses-sion we started at
1 end of the colony and cap-tured as many pups as possible while
moving tothe other end of the colony. We attempted tokeep human
disturbance to a minimum duringthe capture and tagging procedures.
We appliedtags once to all captured pups, and for each re-capture
session thereafter, we noted the status ofpreviously tagged animals
(i.e., tags present ormissing). Lost tags left a small notch in the
con-nective tissue of the flipper; in this way we wereable to
distinguish pups that had never been cap-tured from those that had
lost both tags (Brad-shaw et al. 2000a). To standardize capture
effortand procedures, one of us (CJAB) was presentduring all
capture sessions and weighed all pups.
Previous tagging of A. forsteri pups usingmetal tags
demonstrated 77% incomplete heal-ing; however, no difference in
mortality was ob-served between tagged and untagged pups (Mat-tlin
1978), nor was handling by humans a sig-nificant factor affecting
pup growth in that study(Mattlin 1978). Researchers have attempted
toassess these effects for other species of pinni-peds. Some have
suggested an increase in pupmortality due to the application of
metal tags(Chapman and Johnson 1968), whereas othershave suggested
that differences (mass, growthrate) between tagged and untagged
pups can beexplained by differences in capture probability(Trites
1991).
Each population of pups was assumed to begeographically
‘‘closed’’ (i.e., no emigration orimmigration of pups to or from
neighboring col-onies). Ninety-two percent of 75
mark–recaptureestimates around South Island indicated geo-graphic
closure, and for those that were consid-ered to be ‘‘open,’’ the
magnitude of the biaswas only 1.9% on average (Bradshaw et
al.2000b). The realistic assumption of populationclosure to births,
deaths, and immigration per-mits a more accurate estimation of the
probabil-ity of survival because mark–recapture modelscan only
provide estimates of apparent survival(the number of individuals
available for recap-ture). Although emigration is unlikely for
suck-ling pups, animals that emigrate from the pop-ulation appear,
in the model, to have died, henceunderestimating the true
probability of survival(Cormack 1972; White and Burnham 1999).
Allanimal treatment procedures were approved bythe University of
Otago Committee on Ethics inthe Care and Use of Laboratory Animals
(No.
83-95) and a New Zealand Department of Con-servation Permit to
Take Marine Mammals.
Data analysis, estimation, and model selec-tion procedures.—We
used 4 generalized linearmodels for each capture session to test
for theeffects of sex, site, and the interaction betweensex and
site (sex 3 site) on mass at capture. Weloge-transformed the mass
data to homogenizevariances among groups. All differences
wereconsidered significant at a rejection probability(P) ,0.05.
To assess the effects of sex, site, time, andmass class at each
capture session on apparentpup survival (f), capture probability
(p), andprobability of transition of pups from 1 massclass (state)
to another between capture sessions(c), we fitted a series of
mark–recapture modelswith different restrictions on model
parameters.Due to the large number of potential models (atotal of
6,877 possible models if all combina-tions of sex, time of capture,
mass at capture,and colony of capture on f, p, and c were test-ed),
we examined only those models that testedexplicit hypotheses
regarding the biology of A.forsteri pups and the sampling technique
used.
Given that terrain features and pup densitywere similar among
sites, we hypothesized thatsurvival could depend on sex (DeVilliers
andRoux 1992; Oosthuizen 1991) as well as onmass (Hall et al. 2001)
and sampling time. Wehypothesized that capture probability
wouldvary according to pup mass but that any differ-ences due to
sex would be explained adequatelyby mass. We also expected to find
a significanteffect due to site, even though the colonies didnot
differ markedly in the composition of theterrain (Bradshaw et al.
1999). Therefore, wetreated all sites and the extra year (1997)
atFuchsia Gully as separate levels of the same fac-tor. Capture
probability was also investigated fortime effects in addition to
the variation describedby pup mass. We expected nontrivial
differencesin the probability of mass-state transition overtime
because the pups were growing. Becauseall sites were ,10 km from
each other (Fig. 1),we assumed that differences in growth
trendsamong sites would be insignificant. However,because food
resources can vary markedly fromyear to year and have been
hypothesized to af-fect pup condition and possibly growth
rates(Bradshaw et al. 2000b), we expected that dif-ferences between
years at Fuchsia Gully wouldbe nontrivial.
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70 Vol. 84, No. 1JOURNAL OF MAMMALOGY
We used program MARK (White and Burn-ham 1999) to construct
reduced-parameter ver-sions of a multistate mark–recapture
model(Nichols et al. 1992; Schwarz et al. 1993). Thismodel
incorporated the effect of body mass onsurvival by categorizing
mass into 3 classes forall capture sessions: light (0 , mass # 6.8
kg),medium (6.8 , mass # 9.0 kg), and heavy(mass . 9.0 kg). The
mass classes were chosenso that an approximately equal proportion
ofpups occurred in each mass class at 1st capture.
Changes in mass class between sampling oc-casions were modeled
using a Markov chain inwhich the probability of moving from one
massclass to another (c) depends on the mass classoccupied at the
previous sampling occasion. Theuse of mass classes in a multistate
mark–recap-ture model allows the effect of time-varyingbody mass on
survival to be modeled despitemass not being observed at every
sampling oc-casion due to pups evading capture.
Categorizing mass results in a loss of infor-mation, and the
fewer the mass classes, thegreater is this loss of information.
However, be-cause each transition matrix in the model re-quires s(s
2 1) parameters, where s is the num-ber of mass classes, the number
of transitionprobabilities grows rapidly with an increasingnumber
of mass classes. Three classes were cho-sen to compromise between
having too few clas-ses (to capture the effect of mass
meaningfully)and too many (which would result in many poor-ly
estimated parameters and a reduced ability todetect effects of body
mass).
We allowed parameters to differ for the 2years at Fuchsia Gully,
the only site sampled for2 years. We did this by treating Fuchsia
Gullyin 1997 as a separate colony because the con-dition of pups
throughout South Island wasmuch higher in 1997 than in 1998 (Fig.
2; Brad-shaw et al. 2000b). We denoted the combinedeffect of year
and colony as yr/site. In addition,we allowed parameters to depend
on capturetime (t), mass (m), and sex (sex). To indicate theyear
effect on transition probabilities, which ap-plied only to Fuchsia
Gully, we used the nota-tion yr(FG). The symbol 3 between a pair
ofvariables indicates that the effect of one param-eter is
different at all levels of the other. Forexample, sex 3 t indicates
that the parameterconcerned varies from sample to sample, is
dif-ferent for male and female pups, and also variesfrom sampling
time to sampling time.
Thus, the parameters denoting apparent sur-vival (f) or capture
(p) were described as theprobability of a pup surviving or being
caught,respectively, from time i to i 1 1 for pups atsite j (j 5 1,
. . . , 4 sites) and of sex k (male orfemale) in body-mass state a
(light, medium, orheavy). The probability of mass-state
transition(c) was described as the probability that a pupat site j
and of sex k alive at time i in body-mass state a and alive at time
i 1 1 is in body-mass state b at time i 1 1. We incorporated
theterm c(yr(FG) 3 m 3 sex 3 t) in all the modelstested because
intersite differences in the growthrate of pups were assumed to be
trivial.
Model selection was based on a small-sampleversion of
quasi-likelihood adjusted Akaike’s in-formation criterion for
overdispersion, c(QAICc—Burnham and Anderson 1998). Weused a
2-stage model-selection procedure inwhich we first fitted a
sequence of 16 modelsthat incorporated all possible combinations
ofthe effects of yr/site, m, sex, and t on survivalprobabilities.
These models all included an ef-fect of yr/site, m, and t on
capture probabilitiesand of yr(FG), m, sex, and t on transition
prob-abilities. We denoted the most general model inthis sequence
as f(yr/site 3 sex 3 m 3 t)p(yr/site 3 m 3 t)c(yr(FG) 3 m 3 sex 3
t).
At the 2nd stage of model selection, we con-structed another
sequence of 8 models that be-gan with the best-fitting model from
the 1ststage of selection and that considered restric-tions on the
effects of yr/site, m, and t on captureprobabilities.
To compare models we adopted the selectionstrategy recommended
by Burnham and Ander-son (1998) for selecting the
best-approximatingmodel from a set of candidate models. Here,models
within 2 QAICc units (i.e., DQAICc #2) of the model minimizing
QAICc are con-sidered to have substantial support and shouldbe used
for making inferences. Models withDQAICc of 4–7 have considerably
less sup-port, and models with DQAICc .10 have nearlyno support.
QAICc weights and deviance scores(22 log-likelihood[current model]
2 2 log-like-lihood[saturated model]) are reported for eachmodel
fitted (McCullagh and Nelder 1989).QAICc weights are normalized to
sum to 1 toprovide the relative weight of evidence in favorof a
particular model being the best from a larg-er set of models
(Burnham and Anderson 1998).
An overdispersion factor was estimated to ac-
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February 2003 BRADSHAW ET AL.—MODELING SURVIVAL OF FUR SEAL PUPS
71
TABLE 1.—Probabilities of survival for New Zealand fur seal pups
at Otago Peninsula, New Zea-land, as indicated by f, apparent
47-day probability of survival up to about 5 months of age
(Ap-pendix I) under the multistate model, and Ŝ, estimates of
survival probability corrected for tag loss(using estimates of t,
probability of retaining at least 1 tag—Bradshaw et al. 2000a). The
multistatemodel is f((yr/site) 3 sex), p(m), c(yr(FG) 3 m 3 sex 3
t).
Site
Apparent survival(uncorrected)
f̂ SE
Probability of retaining atleast 1 tag
t̂ SE
Apparent survival(corrected for tag loss)
Ŝ SE
Fuchsia Gully1997
FemaleMale
0.9180.999
0.0390.017
0.9880.988a
0.0120.012
0.9291.000
0.0410.021
1998
FemaleMale
0.9040.917
0.0350.035
0.9170.917
0.0300.030
0.9861.000
0.0500.050
Sandymount North1998
Female 0.910 0.041 0.897 0.049 1.000 0.072Male 0.831 0.049 0.897
0.049 0.926 0.074
Titikoraki South1998
FemaleMale
0.7880.869
0.0510.048
0.9230.923
0.0370.037
0.8530.941
0.0650.064
a No sex-specific calculated (Bradshaw et al. 2000a).t̂
count for the unexplained variation in the data.This factor was
estimated by comparing themost general model considered in model
selec-tion with a model in which survival and captureprobabilities
were fully sex-, time-, site-, andmass-specific, and transition
probabilities weresite-, time-, and sex-specific (f((yr/site) 3
sex3 m 3 t), p((yr/site) 3 sex 3 m 3 t), c((yr/site)3 m 3 sex 3
t)). The ratio of the chi-squaregoodness-of-fit statistic to its
degrees of freedomwas used to estimate the overdispersion factor
c(c 5 1.0 indicates no overdispersion). For ourmost general model,
the estimated factor indi-cated some overdispersion (ĉ 5 1.50; x2
586.99, d.f. 5 58, P 5 0.008). Thus, we calcu-lated the estimates
of sampling variance by mul-tiplying the theoretical (model-based)
variancesby ĉ (Finney 1971).
Estimates of survival probability are confound-ed with the
probability that a pup loses both tags(Bradshaw et al. 2000a).
Arnason and Mills(1981) demonstrated that the estimated true
sur-vival rate (Ŝ) after correcting for tag loss is
f̂Ŝ 5
t̂
where is the estimated probability of retainingt̂at least 1 tag
(i.e., 1 2 the probability of losingboth tags—Bradshaw et al.
2000a). The varianceof Ŝ is estimated as
Var(f̂) Var(t̂)2ˆ ˆVar(S) 5 S 1
2 251 2 1 26f̂ t̂(Seber 1982). Although tag loss varied
amongsites, the Allflex ‘‘Mini’’ tags used provided $t̂0.90 during
the course of the study (Bradshawet al. 2000a). Nonetheless, we
used separate,colony-specific values of t to correct the surviv-al
probabilities estimated for each site.
RESULTS
We tagged 719 individual pups and ob-tained 1,650 masses of pups
(including re-weighings; Appendix I). Males were heavi-er than
females at all capture times, butthere was considerable variation
in meanmass between years at Fuchsia Gully (Fig.3). There was a
significant effect of sex oncapture mass in each capture session
(maleswere heavier than females; all rejection
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72 Vol. 84, No. 1JOURNAL OF MAMMALOGY
FIG. 3.—Mass of male and female New Zea-land fur seal pups at
Otago Peninsula, New Zea-land, for a) Fuchsia Gully (F) in 1997 and
1998and b) Sandymount North (S) and TitikorakiSouth (T) in 1998.
Symbols indicate means anderror bars, 1 SE.
probabilities # 0.021) and a significant ef-fect of site in all
capture sessions (all rejec-tion probabilities # 0.021) except the
initialcapture (F 5 5.029, d.f. 5 3, 493, P 5
0.109). In none of the 4 capture sessionswere the sex 3 site
interactions significant(all rejection probabilities $ 0.146).
In the 1st stage of model selection, thebest-approximating model
of the 16 modelsconsidered was f((yr/site) 3 sex)p((yr/site)3 m 3
t)c(year(FG) 3 m 3 sex 3 t);QAICc 5 2,645.17, K 5 95, deviance
5434.20. Under this model there are survivalprobabilities estimated
for male and femalepups at each yr/site combination (Table 1).This
model had a QAICc weight .0.999,so no subsequent models were
consideredin the 1st stage of selection.
The top model of the 8 models consid-ered in the 2nd stage of
model selectionwas f((yr/site) 3 sex)p(m)c(yr(FG) 3 m 3sex 3 t);
QAICc 5 2,645.17, K 5 72, de-viance 5 447.79. This model had a
QAICcweight of 0.974; therefore, no subsequentmodels were
considered. The model in-cludes a yr/site and sex effect on the
prob-ability of survival. Correcting for tag loss,the true
estimated survival (Ŝ) probabilitiesfor the 47 days (average)
between samplingintervals from postpupping to approximate-ly 155
days (about 5 months) for each yr/site combination were $0.850
(Table 1).
There was strong evidence of a mass ef-fect on the probability
of capture. Here, theheaviest mass class had the lowest
captureprobability (p̂ 5 0.540 6 0.026 SE), fol-lowed by the medium
class (p̂ 5 0.664 60.042) and the light class (p̂ 5 0.873 60.081).
The lack of a significant sex effecton capture probability can be
explained bythe relative difference in mass betweenmales and
females. Because males weighedmore at each capture time than did
females(Fig. 3), any difference in capture proba-bility between the
sexes would have beendue to differences in mass alone.
Transition probabilities ranged widelyunder the model term
c(yr(FG) 3 m 3 sex3 t). Transitions from lower to higher
statesrepresent a gain in mass between capturesi and i 1 1.
Transitions from higher to low-er states represent loss of mass.
Mean tran-sition probabilities revealed a higher prob-
-
February 2003 BRADSHAW ET AL.—MODELING SURVIVAL OF FUR SEAL PUPS
73
FIG. 4.—Probability of moving from 1 massstate (light, medium,
large) to another during thestudy period (mean state-transition
probabilities,c) among all sites, years, and capture times fora)
mass gain and b) mass loss (11 SE).
ability of mass gain for males than for fe-males (Fig. 4a).
However, males demon-strated a higher capacity to lose mass
oncethey attained the heavier mass classes (Fig.4b).
DISCUSSION
Pup survival from shortly after birth toage of approximately 155
days was highduring the period of our study (0.88 6 0.05;Table 2).
Expressed as a standardized, 50-day survival probability, our
estimates(mean Ŝ50 5 0.952 6 0.02) fall within theupper range of
pup survival estimated forother otariid seals (Wickens and York
1997;Table 2). There is some suggestion that theprobability of
surviving from immediatelyafter the breeding season to weaning
inotariids is higher than that from weaning tothe end of the 1st
year (DeVilliers and Roux1992; Mattlin 1978). However, there are
noconvincing empirical estimates of post-weaning survival of
juveniles for New Zea-land fur seals. If survival during this
periodis lower for A. forsteri in New Zealand,then our survival
estimates would overes-timate the survival of 1st-year pups.
Anoth-er reason for overestimating apparent sur-vival is that we
did not take into accountany mortality that occurred before the
ini-tial capture session (Lalas and Harcourt1995). Mortality during
this period cannotbe dismissed as negligible or unimportantbecause
in some populations early pup mor-tality (during the 1st month of
life) can beas high as 50% (DeVilliers and Roux 1992;Harcourt 1992;
Majluf 1992).
The significance of the yr/site term onis more likely to reflect
the higher sur-f̂
vival probabilities observed for pups fromFuchsia Gully in 1997
relative to the colo-nies sampled in 1998 (Table 1). Given thatpups
at the Fuchsia Gully colony in 1997were in much better physical
condition thanwere pups sampled from all 3 colonies in1998 (Fig.
2), and all colonies had essen-tially identical terrain and density
charac-teristics (Bradshaw et al. 1999), we suggestthat the year
difference in apparent survival
was attributable to the body condition ofpups alone.
We found evidence that survival proba-bilities between male and
female pups dif-fered even after controlling for body mass.However,
the difference was small (mean47-day interval Ŝfemale 5 0.942 6
0.033,Ŝmale 5 0.967 6 0.019). In all sites and
-
74 Vol. 84, No. 1JOURNAL OF MAMMALOGY
TA
BL
E2.
—M
ean
surv
ival
(pro
port
ion
ofpu
psbo
rnth
atsu
rviv
eor
prob
abil
ity
ofsu
rviv
al)
repo
rted
for
pups
ofsp
ecie
sof
the
genu
sA
rcto
ceph
alus
(see
also
Wic
kens
and
Yor
k19
97)
duri
ngsp
ecifi
cin
terv
als.
For
com
pari
son
wit
hth
isst
udy
and
for
ease
ofin
terp
reta
tion
,al
lpr
obab
ilit
ies
have
also
been
stan
dard
ized
toa
50-d
ayin
terv
al,
S50
5S
int(
50/i
nt) ,
whe
rein
t5
inte
rval
.
Spe
cies
Yea
rsIn
terv
al(d
ays)
Inte
rval
surv
ival
50-d
aysu
rviv
alna
Sou
rce
A.
gaze
lla
A.
gala
pago
ensi
sA
.tr
opic
alis
1978
–198
2b
1979
–198
2c
1979
–198
119
8219
87–1
988
;0
–40
;0
–40
0–3
00
–84
0–7
7
0.95
0.77
0.91
0.85
0.96
0.93
80.
721
0.85
50.
908
0.97
4
1,21
82,
002
202
10,8
98 248
Doi
dge
etal
.(1
984)
—S
chli
eper
Bay
Doi
dge
etal
.(1
984)
—B
ird
Isla
ndT
rill
mic
h(1
987)
Hes
and
Rou
x(1
983)
—A
mst
erda
mIs
land
Sha
ughn
essy
and
Gol
dsw
orth
y(1
990)
—H
eard
Isla
nd
A.
aust
rali
s
A.
pusi
llus
pusi
llus
A.
fors
teri
1996
1997
1984
–198
919
87–1
988
1987
–199
019
88–1
990
1988
–199
3
0–3
00
–15
0–
410
–55
0–3
00
–30
;0
–39
0.97
0.91
0.64
0.60
0.80
60.
03d
0.65
60.
01d
0.99
0.95
10.
730
0.58
00.
629
0.68
90.
488
0.98
7
443
331
8,30
93,
959
560
735
5,79
2e
Geo
rges
and
Gui
net
(200
0)—
Am
ster
dam
Isla
ndG
eorg
esan
dG
uine
t(2
000)
—A
mst
erda
mIs
land
Maj
luf
(199
2)H
arco
urt
(199
2)D
eVil
lier
san
dR
oux
(199
2)—
Atl
asB
ayD
eVil
lier
san
dR
oux
(199
2)—
Wol
fB
ayS
haug
hnes
syet
al.
(199
5)—
Kan
garo
oIs
land
1990
–199
319
93–1
994
1997
–199
8
;0
–39
;0
–55
;12
–155
0.98
0.92
0.88
60.
05g
0.97
40.
927
0.95
26
0.02
2,86
9e
142f
719h
,1,
650i
Sha
ughn
essy
etal
.(1
995)
—N
orth
Cas
uari
naL
alas
and
Har
cour
t(1
995)
Thi
sst
udy
aT
otal
num
ber
ofpu
psco
unte
dor
esti
mat
edov
eral
lye
ars
ofst
udy.
bE
xclu
ding
1979
.c
Exc
ludi
ng19
80.
dM
ean
amon
gye
ars.
eE
stim
ated
from
mar
k–re
capt
ure
tech
niqu
es.
fM
axim
umda
ily
coun
t.g
Mea
nam
ong
site
san
dye
ars
calc
ulat
edas
mea
nsa
mpl
ing
inte
rval
(X̄5
47da
ys)
Ŝto
the
pow
erof
3(3
sam
plin
gin
terv
als)
6ye
ar-s
ite
SE.
hN
umbe
rof
indi
vidu
alpu
psta
gged
.iN
umbe
rof
pups
caug
ht(i
nclu
des
reca
ptur
es).
-
February 2003 BRADSHAW ET AL.—MODELING SURVIVAL OF FUR SEAL PUPS
75
years except Sandymount North, where allfemales survived, the
probability of surviv-ing was lower for female pups (Table
1).Although some studies have found signifi-cant differences in
survival between thesexes in otariid seals (DeVilliers and
Roux1992; Oosthuizen 1991), others have not(Boltnev et al. 1998;
Georges and Guinet2000). When differences in survival be-tween the
sexes have been found in polyg-ynous mammal species, juvenile males
areusually reported as the sex with the lowestprobability of
survival (Hall et al. 2001;Ralls et al. 1980). It has been
suggested thatthis is due to the faster-growing sex (usuallymales)
suffering additional mortality due tonutritional stress
(Clutton-Brock 1991;Clutton-Brock et al. 1994; Stewart
1997).Clearly, this was not the case in this study.However, there
is evidence to suggest thatmale-dominated sex ratios are present
inpopulations of mammals that are not regu-lated by population
density (Kruuk et al.1999). Assuming that higher densities re-flect
lower per capita food availability, maleoffspring are expected to
show a relativelylower probability of survival (Kruuk et al.1999).
Bradshaw et al. (2000b) found anegative effect of density on the
conditionof fur seal pups at colonies around NewZealand but only
during years when foodresources were purported to be reduced.The
higher average survival probability ofmales in 1998 (a year when
pup conditionwas below a 3-year average—Bradshaw etal. 2000b)
suggests that population densityat these colonies had not yet
reached thelevel required to elicit regulation (Kruuk etal. 1999).
This is consistent with the obser-vation that colonies on the
eastern coast ofSouth Island are still increasing in numberand are
probably below carrying capacity(Bradshaw et al. 2000c).
We did not find any effect of mass attime of capture on
subsequent survivalprobability. Boltnev et al. (1998) demon-strated
that pup survival of C. ursinus cor-relates positively with mass at
birth, Cal-ambokidis and Gentry (1985) reported that
dead C. ursinus pups were lighter at birththan were the total
marked population, andMajluf (1992) found that pups of the
SouthAmerican fur seal (A. australis) that diedwere lighter at
birth than were those thatsurvived. Continual monitoring of pup
sur-vival at our study sites will be necessary todetermine if this
relationship appears duringyears when survival is lower.
There are potentially many reasons whypups of a certain size
class would have low-er or higher capture probabilities. We
foundthat large pups are less likely to be recap-tured, possibly
due to the increased mobil-ity of healthy pups (a pup in good
conditionwould be more likely to avoid capture thanwould a smaller,
weaker pup). Heteroge-neity in the spatial distribution of pups
ofdifferent size classes may also occur, al-though we endeavoured
to search as muchof each colony as possible. As pups age,specific
size classes may become more orless likely to be captured relative
to the restof the population. This warrants further
in-vestigation.
It has been shown previously that hetero-geneity in capture
probabilities can lead tobias in estimates of survival (Clobert
1995;Nichols 1992) and growth (Trites 1991,1993). This potential
influence of hetero-geneity, together with the results
reportedhere, highlights the importance of measur-ing individual
mass at time of each capture.If the assumption of homogenous
captureprobabilities is violated (Carothers 1973;Lebreton et al.
1992), then bias can becomeproblematic (Buckland 1982;
Prévot-Jul-liard et al. 1998), especially if recapturerates are
low. This usually results in under-estimating survival
probabilities (Prévot-Julliard et al. 1998).
When capture probability depends onmass at capture, estimates of
sex ratio alsowill be biased. For large-bodied mammals,we suggest
that researchers endeavour toweigh individuals at each capture
session inaddition to marking to account for this po-tential bias.
For instance, in the presentstudy the estimated true (adjusted)
number
-
76 Vol. 84, No. 1JOURNAL OF MAMMALOGY
of individuals of a particular sex (nadj) be-comes the observed
number of individualsof a particular sex (nobs) in mass class a
di-vided by the corresponding mass-specificcapture probability (pa)
and the sex-specificsurvival probability (Ssex) during the
sam-pling interval. As an example, the sex ratioof the last capture
sample (27 May 1997)at Fuchsia Gully in 1997 was 51 females to59
males (0.86; Table 1). Adjusting for dif-ferential capture
probability among massclasses and sex-specific survival
probabili-ty, the true sex ratio without differentialmortality and
capture rates becomes 116 fe-males to 108 males (1.07).
The mean transition probabilities be-tween mass states varied
significantly withcapture time and colony; however, cautionmust be
observed in the interpretation ofthese results because specific
hypotheses re-lating to the probabilities of transition be-tween
mass classes were not tested explic-itly. Nonetheless, overall
means indicatedthat male pups are more likely to gain massthan are
females, and they also are morelikely to lose mass once they have
reachedthe heavier mass classes (Fig. 4). The high-er transition
probabilities for males versusfemales from lower to higher mass
states(Fig. 4) suggest that males grew faster thanfemales. Varying
capture probabilities mayhelp to explain the conflicting evidence
fordifferential pup growth rates between thesexes for species of
the genus Arctocephal-us (Arnould et al. 1996; Georges and Gui-net
2001). Sex differences in growth pat-terns in terms of tissue
deposition (i.e., de-position of relatively more fatty or lean
tis-sue—Arnould et al. 1996; Georges andGuinet 2001) should also be
investigated tohelp interpret differences in survival andgrowth
under conditions of varying foodavailability.
There was an apparently different growthpattern in Fuchsia Gully
in 1997 relative tothe colonies measured in 1998 (Fig. 3).However,
it should be noted that the sam-pling time for the 3rd capture
session waslater in 1997 (late April) than in 1998 (early
April; see Table 1). Although it is impos-sible to determine,
the different growth pat-tern observed may have been an artifact
ofthis different sampling regime.
The multistate model highlighted effectsthat would have
otherwise been missed.The implications for the calculation of
in-dividual growth rate and sex ratios are ob-vious: if more
individuals of a specific bodymass class are caught relative to
others,then the number of individuals within a par-ticular grouping
(sex or mass class) will bebiased. Because heavier pups had
lowercapture probabilities, transitions to highermass states would
be underrepresentedfrom random pup captures. This has beenfound for
C. ursinus pups by Trites (1993).It is known that cross-sectional
samplingcan bias estimates of growth rate (Andersonand Fedak 1987;
Baptista et al. 2000; Lunnet al. 1993), thus modifying
conclusionsabout sex differences (Doidge and Croxall1989; Lunn et
al. 1993). However, evenlongitudinal sampling of individuals
fromfree-ranging populations for estimation ofgrowth rates can be
biased when captureprobabilities are heterogenous among
massclasses. Different probabilities of recaptur-ing individuals
within different mass clas-ses result in mean growth rates that are
bi-ased in the direction of the most commonlyrecaptured class. For
example, the presentstudy has demonstrated that random sam-ples of
fur seal pups would have underes-timated growth rate because
individuals thathave demonstrated maximal growth are lesslikely to
be recaptured in the final capturesession. For other mammals,
researchersshould endeavour to measure mass and oth-er parameters
thought to contribute to cap-ture probability for all recapture
sessions.
Transition probabilities provide informa-tion on the growth
process, and size-depen-dent capture probabilities can be used
tocorrect estimates of growth rate. The esti-mated true number of
individuals withineach mass class can be adjusted by applyingthe
corresponding probabilities of capture.This accounts for biases
attributed to sam-
-
February 2003 BRADSHAW ET AL.—MODELING SURVIVAL OF FUR SEAL PUPS
77
pling individuals from different mass clas-ses and provides a
more realistic parameterestimation for models estimating
populationsize, sex ratio, colonization processes, andfood
consumption rates.
ACKNOWLEDGMENTS
This research was funded by the University ofOtago. We also
thank Allflex New Zealand Ltd.(Palmerston North) for providing the
plastic tagsused to identify fur seal pups, Combined RuralTraders
Society Ltd. (Otago) for providing fieldequipment, and Cadbury
Confectionary Limitedfor field supplies. We particularly thank the
De-partment of Zoology (University of Otago) andthe Department of
Conservation (New Zealand)for logistic support. We thank C. Duncan,
C.Littnan, N. McNally, M. Wright, and the manyvolunteers who
assisted with data collection. Wethank A. J. Hall and J.-Y. Georges
of the NaturalEnvironment Research Council (NERC) SeaMammal
Research Unit (Scotland) and 2 anon-ymous reviewers for providing
helpful com-ments on the manuscript.
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Submitted 3 December 2001. Accepted 1 September2002.
Associate Editor was Thomas J. O’Shea.
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80 Vol. 84, No. 1JOURNAL OF MAMMALOGY
APPENDIX I
Capture dates, number of New Zealand fur seal pups captured, and
total number of pups newlytagged per colony and per capture session
at Otago Peninsula (South Island, New Zealand) colonies.
Capture details
Fuchsia gully
1997 1998
Sandymount north
1998
Titikoraki south
1998
1st capture
DateNumber of femalesNumber of malesTotal caughtNewly tagged
5 January7668
144144
5 January8169
150150
8 January5255
107107
6 January5347
100100
2nd capture
DateNumber of femalesNumber of malesTotal caughtNewly tagged
26 February7056
12645
25 February6658
12432
27 February38468440
26 February51469721
3rd capture
DateNumber of females
30 April52
8 April68
10 April41
9 April42
Number of malesTotal caughtNewly tagged
61113
26
55123
19
357619
448616
4th capture
DateNumber of femalesNumber of malesTotal caughtNewly tagged
27 May5159
1100
25 May455196
0
29 May312859
0
27 May272855
0
Grand total caughtGrand total tagged
493215
493201
326166
338137