estimating survival and capture probability of fur …€¦ · differences in capture probability...

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-

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-

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-


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


(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.


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-


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


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-


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


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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


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-


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.


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


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


27 May5159

1100

25 May455196

0

29 May312859

0

27 May272855

0

Grand total caughtGrand total tagged

493215

493201

326166

338137

estimating survival and capture probability of fur …€¦ · differences in capture probability...

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