Polar Bear Population Status in the 

Southern Beaufort Sea

Open-File Report 2006–1337

U.S. Department of the Interior

U.S. Geological Survey

Polar Bear Population Status in the 

Southern Beaufort Sea

By Eric V. Regehr and Steven C. Amstrup, U.S. Geological Survey; and Ian 

Stirling, Canadian Wildlife Service

Open-File Report 2006-1337

U.S. Department of the Interior 

U.S. Geological Survey
U.S. Department of the Interior

DIRK KEMPTHORNE, Secretary

U.S. Geological Survey

Mark D. Myers, Director

U.S. Geological Survey, Reston, Virginia: 2006

For product and ordering information:

World Wide Web: http://www.usgs.gov/pubprod

Telephone: 1-888-ASK-USGS

For more information on the USGS--the Federal source for science about the Earth, its natural and living resources, 

natural hazards, and the environment:

World Wide Web: http://www.usgs.gov

Telephone: 1-888-ASK-USGS

Any use of trade, product, or firm names is for descriptive purposes only and does not imply endorsement by the 

U.S. Government.

Although this report is in the public domain, permission must be secured from the individual copyright owners to 

reproduce any copyrighted materials contained in this report.

Suggested citation:

Regehr, E.V., Amstrup, S.C., and Stirling, Ian, 2006, Polar bear population status in the southern Beaufort Sea: U.S. 

Geological Survey Open-File Report 2006-1337, 20 p. 
iii

Contents

Abstract...........................................................................................................................................................1

Introduction.....................................................................................................................................................1

Methods...........................................................................................................................................................2

Capture-Recapture Analysis...............................................................................................................2

Goodness-of-Fit.....................................................................................................................................3

Estimating Survival Rate and Population Size .................................................................................4

Cub Production and Physical Stature ...............................................................................................5

Results5

Goodness of Fit......................................................................................................................................5

Estimating Survival Rate and Population Size .................................................................................7

Cub Production and Physical Stature ...............................................................................................8

Discussion.....................................................................................................................................................11

Capture-Recapture Analyses ...........................................................................................................11

Cub Production and Physical Stature .............................................................................................12

Conclusions...................................................................................................................................................14

Acknowledgments.......................................................................................................................................14

References Cited..........................................................................................................................................14

Appendix A. Description of Sex Composition, Age Composition, and Other Summary 

Statistics for Polar Bears Captured in the Southern Beaufort Sea, 2001–06 ......................17

Appendix B. Description of Model Notation, and the Model Selection Table for 

Cormack-Jolly-Seber (CJS) Models Fitted to Capture-Recapture Data for Polar 

Bears in the Southern Beaufort Sea, 2001–06...........................................................................18

Appendix C. Secondary Capture-Recapture Analysis to Investigate a posteriori

Hypotheses......................................................................................................................................19

Appendix D. Statistical Properties of Parameter Estimates and the Model Selection 

Process ............................................................................................................................................20
iv

Figures

Figure 1. Map showing distribution of polar bear captures from 2001 to 2006 that were 

included in capture-recapture estimates of survival and population size............ 3

Figure 2. Graph showing total size of the southern Beaufort Sea polar bear population ... 8

Tables

Table 1. Total number and proportion each sex and age class of polar bears 

captured by standard search and radiotelemetry in the Southern Beaufort Sea 

by the U.S. Geological Survey, 2001–06, and by the Canadian Wildlife Service, 

2003–06 ....................................................................................... 6

Table 2. Model-averaged estimates of total apparent survival probability for polar 

bears in the southern Beaufort Sea ...................................................... 7

Table 3. Cub production rates for polar bears in the southern Beaufort Sea, 1967–89 

and 1990–2006 .............................................................................. 9

Table 4. Cub production rates for polar bears in the southern Beaufort Sea, 1967–89 

and 1990–2006 .............................................................................. 9

Table 5. Litter sizes of dependent young polar bears in the southern Beaufort Sea, 

1967–89 and 1990–2006 ..................................................................... 10

Table 6. Sum of skull length and skull width measurements (cm) for polar bears in the 

southern Beaufort Sea, 1967–89 and 1990–2006 ....................................... 10

Table 7. Scale weights (kg) for polar bears in the southern Beaufort Sea, 1967–89 and 

1990–2006 .................................................................................... 10
Conversion Factors, and Abbreviations, Acronyms, and 

Symbols

Conversion Factors

Multiply By To obtain

kilometer (km) 0.6214 mile (mi)

meter (m) 3.281 foot (ft) 

meter (m) 1.094 yard (yd) 

Abbreviations, Acronyms, and Symbols

Abbreviations, Acronyms, and 

Symbols Meaning

AIC Akaike’s information criterion

CI confidence interval

CJS Cormack-Jolly-Seber

COYs cubs of the year

CWS Canadian Wildlife Service

GOF goodness-of-fit

PRB percent relative bias

QAIC quasi-likelihood adjustment of AIC

SE standard error

SBS southern Beaufort Sea

USGS U.S. Geological Survey
vi

This page left intentionally blank
Abstract

Polar bears depend entirely on sea ice for survival. In 

recent years, a warming climate has caused major changes in 

the Arctic sea ice environment, leading to concerns regarding 

the status of polar bear populations. Here we present findings 

from long-term studies of polar bears in the southern Beaufort 

Sea (SBS) region of the U.S. and Canada, which are relevant 

to these concerns. We applied open population capturerecapture models to data collected from 2001 to 2006, and 

estimated there were 1,526 (95% CI = 1,211; 1,841) polar 

bears in the SBS region in 2006. The number of polar bears 

in this region was previously estimated to be approximately 

1,800. Because precision of earlier estimates was low, our 

current estimate of population size and the earlier ones cannot 

be statistically differentiated. For the 2001–06 period, the 

best fitting capture-recapture model provided estimates of 

total apparent survival of 0.43 for cubs of the year (COYs), 

and 0.92 for all polar bears older than COYs. Because the 

survival rates for older polar bears included multiple sex and 

age strata, they could not be compared to previous estimates. 

Survival rates for COYs, however, were significantly lower 

than estimates derived in earlier studies (P = 0.03). The 

lower survival of COYs was corroborated by a comparison 

of the number of COYs per adult female for periods before 

(1967–89) and after (1990–2006) the winter of 1989–90, when 

warming temperatures and altered atmospheric circulation 

caused an abrupt change in sea ice conditions in the Arctic 

basin. In the latter period, there were significantly more COYs 

per adult female in the spring (P = 0.02), and significantly 

fewer COYs per adult female in the autumn (P < 0.001). 

Apparently, cub production was higher in the latter period, but 

fewer cubs survived beyond the first 6 months of life. Parallel 

with declining survival, skull measurements suggested that 

COYs captured from 1990 to 2006 were smaller than those 

captured before 1990. Similarly, both skull measurements 

and body weights suggested that adult males captured from 

1990 to 2006 were smaller than those captured before 1990. 

The smaller stature of males was especially notable because 

it corresponded with a higher mean age of adult males. Male 

polar bears continue to grow into their teens, and if adequately 

nourished, the older males captured in the latter period should 

have been larger than those captured earlier. In western 

Hudson Bay, Canada, a significant decline in population 

size was preceded by observed declines in cub survival and 

physical stature. The evidence of declining recruitment 

and body size reported here, therefore, suggests vigilance 

regarding the future of polar bears in the SBS region.

Introduction

Polar bears are entirely dependent on sea ice as a 

platform to access the marine mammals that provide their 

nutritional needs (Amstrup, 2003). In recent years, a warming 

climate and changing atmospheric circulation patterns have 

resulted in major changes in the Arctic sea ice environment 

(Comiso, 2002; Rigor and others, 2002; Comiso and 

Parkinson, 2004; Rigor and Wallace, 2004; Stroeve and others, 

2005). Polar bears residing in the southern Beaufort Sea (SBS) 

region of the U.S. and Canada have been studied since 1967. 

Results of these studies provide insights into how changes in 

the environment may affect the status of polar bears in this 

region.

Radiotelemetry data collected from female polar 

bears during the mid-1980s suggested that the SBS region 

contained a single population of polar bears, extending 

from west of Barrow, Alaska, to east of Paulatuk, Northwest 

Territories, Canada (Amstrup and others, 1986; Amstrup and 

DeMaster, 1988). In response to that finding, an agreement 

was established between U.S. and Canadian user groups to 

cooperatively manage the hunting of polar bears throughout 

the entire SBS region (Brower and others, 2002).

To determine sustainable harvest levels, early polar 

bear research in the SBS region was focused on estimating 

population size and developing indices of recruitment and 

survival which could be used to evaluate trends in population 

status. The size of the SBS polar bear population was 

first estimated to be approximately 1,800 animals in 1986 

(Amstrup and others, 1986). Survival rates of adult females 

and dependent young were estimated from radiotelemetry data 

collected from the early 1980s to the mid-1990s (Amstrup 

Polar Bear Population Status in the Southern Beaufort Sea

By Eric V. Regehr1, Steven C. Amstrup1, and Ian Stirling2

1

U.S. Geological Survey

2

Canadian Wildlife Service
and Durner, 1995). Throughout the 1980s and early 1990s, 

empirical observations such as the frequency of encounters of 

polar bears during research flights over the sea ice, increased 

sightings of polar bears near onshore human settlements, 

and increasing numbers of maternal dens observed on 

land, suggested that the population of the SBS region was 

increasing. Because of interest among user groups in a larger 

harvest, population size and trend were re-assessed in the late 

1990s (Amstrup and others, 2001a; McDonald and Amstrup, 

2001). That analysis was limited to female polar bears because 

research objectives resulted in the under-sampling of males 

in some years. The estimate of 1,180 females (95% CI = 635; 

1,725) for the late 1980s was consistent with the previous 

estimate of at least 1,800 total polar bears (i.e., females and 

males) in the SBS region at that time (Amstrup and others, 

1986). For the late 1990s, the estimated number of females 

developed by Amstrup and others (2001a) suggested that 

the total population may have increased to as many as 2,500 

polar bears. However, because of interannual variation in 

sample size and other sources of heterogeneity within the data 

for the late 1990s, the estimate of 2,500 polar bears was not 

considered reliable. Therefore, managers took a conservative 

approach and harvest decisions continued to be based on a 

total population size of 1,800 polar bears in the SBS region.

We initiated a new study in 2001, to re-assess the status 

of the SBS polar bear population and to address the potential 

effects, on polar bear status, of changing sea ice conditions 

in the Arctic basin. Here we present estimates of survival 

and population size derived from capture-recapture data 

collected from 2001 to 2006, and compare these estimates 

to those developed earlier. We also document changes in the 

productivity and physical stature of polar bears using data 

collected from the late 1960s through the present.

Methods

Polar bear research began in the SBS region in 1967, 

and has continued through 2006. We captured polar bears by 

injecting the drugs tiletamine hydrochloride plus zolazepam 

hydrochloride (Telazol®, Warner-Lambert Co.), using 

projectile syringes fired from helicopters (Stirling and 

others, 1989). All captured polar bears were ear-tagged with 

a unique identification number, and tattooed on both sides 

of the inner surface of the upper lip. We determined body 

weight of captured bears with a spring or dynamometer 

scale and recorded various body measurements, including 

the condylobasal length and zygomatic width of the skull. 

Age was determined for all captured bears. Cubs-of-theyear (COYs; approximately 3 months old in spring) were 

always with their mothers and could be visually aged without 

error (Ramsay and Stirling, 1988). A vestigial premolar 

was extracted from other captured polar bears and age was 

estimated by counting cementum annuli (Calvert and Ramsay, 

1998). Beginning in 1981, selected adult females were 

fitted with radio-tracking collars that allowed us to relocate 

them from aircraft. All capture and marking protocols were 

approved by independent animal care and welfare committees.

Capture-Recapture Analysis

For the purpose of estimating population size and survival 

rates in this study, we captured polar bears in coastal areas of 

the SBS region, from Point Barrow, Alaska (about 157°W) 

to Cape Parry, Northwest Territories, Canada (about 125°W). 

Capture-recapture data were collected by the U.S. Geological 

Survey (USGS) in the U.S. portion of the SBS region, from 

late March through early May of 2001–06, and in October 

and November of 2001. Additional capture-recapture data 

were collected by the Canadian Wildlife Service (CWS) in 

the Canadian portion of the SBS region in April and May 

of 2003–06 (fig. 1). In each year from 2001 to 2006, our 

objectives were to maximize sample size, maximize the 

geographic distribution of capture effort throughout the SBS 

region, and ensure that all polar bears in the study area were 

equally exposed to capture efforts. Sample sizes in many years 

before 2001 were approximately equivalent to those of 2001–

06, but sampling strategies and time-frames of capture varied 

among many early years of study. Therefore, all animals 

were not subjected to equal capture effort in many of those 

early years. Previous studies have shown the difficulties of 

estimating demographic parameters from data collected under 

a non-random sampling protocol that varied among years, and 

did not include the entire study area (Amstrup, 1995; Amstrup 

and others, 2001a; McDonald and Amstrup, 2001). Therefore, 

we limited the current capture-recapture analyses to data 

collected from 2001 to 2006.

In our analysis of survival and population size for the 

2001–06 period, we included data for polar bears encountered 

by standard search methods (polar bears encountered 

randomly, while flying in polar bear habitat), and data for 

polar bears encountered by radiotelemetry. We use the term 

“capture” to refer to the physical capture of a polar bear, or the 

visual sighting of a polar bear for which the individual identity 

was known via radiotelemetry. Although some polar bears 

were captured multiple times per year, we used a maximum of 

one capture per bear per year in our analyses.

The data for each polar bear were summarized as an 

individual capture history and covariates. For example, bear 

20579 had the capture history {101100}, where 0 indicates not 

captured at sampling occasion j, and 1 indicates captured and 

released alive at sampling occasion j (j = 1, 2... k). Individual 

covariates for this polar bear included sex = female, age

(at-first-capture) = 0 yr, and agency = U.S., based on which 

agency originally captured bear 20579. The time-dependent 

covariate radio indicated when adult female polar bears were 

 Polar Bear Population Status in the Southern Beaufort Sea
available for recapture by radiotelemetry, based on radiocollar 

deployment information and real-time satellite telemetry data 

(Harris and others, 1990). Dependent young that accompanied 

radiocollared females also were considered to be available for 

recapture by radiotelemetry.

To investigate the potential relationship between sea 

ice and polar bear survival, we quantified spatiotemporal 

trends in sea ice coverage from 2001 to 2006 using sea 

ice concentration data for 25 × 25 km grid cells, derived 

from passive microwave imagery using the NASA Team 

algorithm (National Snow and Ice Data Center, Boulder, 

Co., ftp://sidads.colorado.edu/pub/). First, we defined an 

area of preferred polar bear habitat as all grid cells in the 

SBS population boundary with an ocean depth of less than 

300 m (International Bathymetric Chart of the Arctic Ocean, 

http://www.ngdc.noaa.gov/mgg/bathymetry/arctic/arctic.

html). We then averaged daily ice concentrations in the area 

of preferred habitat, and calculated the number of days during 

each calendar year j that the mean ice concentration was 

less than 50% (xj). We derived the covariate icej for use in 

capture-recapture models, by standardizing xj via the formula: 

ice x x SD x j j = − ( )/ ( ), where x is the mean and SD(x) is the 

standard deviation of xj for j = 2000–05 (Franklin, 2001).

Goodness-of-Fit

The valid estimation of demographic parameters from 

capture-recapture data requires an analysis of goodness-of-fit 

(GOF), to determine how well the data meet the assumptions 

of the model being used (Lebreton and others, 1992; Cooch 

and White, 2005, Chapter 5; McDonald and others, 2005). 

Because no single method is sufficient in practice, we used 

multiple methods to obtain a thorough consideration of 

GOF. First, we partitioned the data into sex- and age-based 

strata and used program RELEASE (Burnham and others, 

1987) to investigate patterns in the data. Second, we used the 

parametric bootstrap procedure in program MARK (White 

and Burnham, 1999) to evaluate the fit of a general model, ak20-0049_Figure 01

Figure 1. Distribution of polar bear captures from 2001 to 2006 that were included in capture-recapture estimates of 

survival and population size.

Methods 
and to estimate a bootstrapped value of the variance inflation 

factor cˆ (White and others, 2001). We also used MARK 

to estimate a value of median cˆ (Cooch and White, 2005: 

Chapter 5). Third, we estimated a “biological” cˆ based on 

the lack of independence among the fates of adult female 

polar bears and their dependent young, via the formula: 

c n ˆ /(n n ) c = − , where n is the total number of captures, and 

nc is the number of captures of dependent young (Taylor and 

others, 2002). Finally, we note that radiotelemetry captures 

present methodological difficulties for program RELEASE 

and the parametric bootstrap, and were excluded from the 

GOF analysis. However, it is unlikely that this lead to an 

underestimation of cˆ, because all reasonable capture-recapture 

models explicitly allowed for telemetry-based variation 

in recapture probabilities by incorporating the individual 

covariate radio.

Estimating Survival Rate and Population Size

We estimated survival using Cormack-Jolly-Seber (CJS) 

models (Lebreton and others, 1992) fitted to the data with 

R-language software for the “general regression” approach to 

capture-recapture (McDonald and others, 2005, http://www.

west-inc.com). The CJS model conditions on first capture, 

and estimates the probabilities of survival (φ) and recapture 

(p) most likely to produce the observed capture histories. 

Estimates of φj represent total apparent survival, which is the 

cumulative probability of remaining alive and in the study area 

between sampling occasions j and j+1.

We considered models that allowed φ to vary by time, 

sex, and four age classes: COYs, yearlings, subadults (2–4 yr), 

and adults (5+ yr). We modeled φj as a function of icej and 

icej-1, to investigate the hypothesis that reduced sea ice 

coverage would affect polar bear survival by limiting access 

to the biologically productive waters over the continental 

shelf. We also fitted models with a generic linear trend that 

allowed for a monotonic change in survival. Finally, we 

considered an additive effect in φ following the occasion 

of first capture for male subadults and adults, based on the 

indication of “transient” males within the population from 

program RELEASE (Pradel and others, 1997). Transients are 

defined as individuals that entered the study population, were 

captured once, and subsequently emigrated. In theory, the 

influence of these individuals on estimates of apparent survival 

can be mitigated using a parameterization for φ that allows the 

transients to “die” (i.e., leave the study area) following first 

capture.

For recapture probability (p), we considered models 

that included the individual covariate agency, and the 

covariate effort, which was based on the annual number of 

helicopter hours flown in capture operations. For example, an 

interaction between agency and effort produced estimates of 

pj for “U.S.” bears as a function of USGS capture effort, and 

separate estimates of pj for “Canadian” bears as a function of 

CWS capture effort. This approach was based on evidence 

that individual polar bears exhibit geographic fidelity in the 

SBS region (Amstrup and others, 2004, 2005), which we 

hypothesized would lead to a correlation between where an 

individual was originally captured, and where it was available 

for recapture. We considered models with time-dependence in 

p, and with interactions between time-dependence and agency. 

This reflected the hypothesis that pj varied as a cumulative 

function of sampling effort, general fidelity patterns, and 

unknown ecological phenomena (e.g., interannual variation in 

the spatial distribution of polar bears, as influenced by sea ice 

conditions). We also considered models with an intermediate 

form of time-dependence in p, based on observations by the 

CWS that polar bear densities in the eastern portion of the 

SBS region were dramatically lower in 2006 than in other 

years. Finally, in nearly all models the covariate radio allowed 

for an additive effect in p for polar bears that were available 

for recapture by radiotelemetry.

Model selection was based on Akaike’s information 

criterion (AIC) (Burnham and Anderson, 2002), as well as 

considerations of biological plausibility and other statistical 

issues (e.g., the number of parameters in the model that could 

be estimated). We adjusted AIC for overdispersion (i.e., 

QAIC) based on the GOF analysis, and evaluated 152 CJS 

models representing all combinations of the hypothesized 

parameterizations for φ and p. We derived final parameter 

estimates by averaging across models in the candidate set 

with ∆QAIC ≤ 7.0. We used this cutoff because ∆QAIC 

= 7.0 corresponds to a normalized Akaike weight (wi) of 

approximately 0.01, below which the impact on modelaveraged estimates is negligible. This approach ensured that 

model selection uncertainty was reflected in all real parameter 

estimates, and their associated variances (Burnham and 

Anderson, 2002).

We estimated population size (N) from the modelaveraged estimates of recapture probability (p) derived 

from the CJS models, via a Horvitz-Thompson estimator 

(McDonald and Amstrup, 2001). This approach has several 

advantages over traditional Jolly-Seber methods (McDonald 

and others, 2005). First, it retains the flexibility of the 

CJS modeling framework. Second, it is straightforward to 

estimate N from models in which p is a function of individual 

covariates. Third, it is straightforward to estimate N from 

model-averaged estimates of p. We estimated the variance 

of N by bootstrapping (Manly, 1997), because conventional 

variance estimators for the HT approach (e.g., the Laake 

estimator in Taylor and others, 2002) require estimates of the 

covariance among p for all strata, which were not available 

for the model-averaged estimates. The bootstrap procedure 

involved re-sampling the individual capture histories (and 

covariates) to generate 1,000 new datasets, fitting each dataset 

with all models in the original candidate set with ∆QAIC 

≤ 7.0, and deriving model-averaged parameter estimates 

for each iteration. We then estimated the variance of N

by assuming that the distribution of bootstrapped, modelaveraged ˆNj represented the sampling distribution of true 

population size.

 Polar Bear Population Status in the Southern Beaufort Sea
Cub Production and Physical Stature

We analyzed numbers of young accompanying adult 

female polar bears captured each spring in 1967–79, 1982–92 

(except 1990) and 1998–2006, and each autumn in 1981–86, 

1988, 1989, 1994, 1997, and 1998–2001. We analyzed 

physical stature using skull size and body weight data for 

polar bears captured in the spring only. For both analyses, we 

compared data from two periods: 1967–89 and 1990–2006. 

This comparison was motivated by dramatic changes in the 

polar basin sea ice beginning in 1989–90 (Rigor and others, 

2002). We hypothesized that these changes would affect 

the nutritional condition of polar bears, resulting in altered 

production and survival of cubs, and altered physical stature 

for all polar bears (Stirling and others, 1999).

We compared data between the two periods using logistic 

regression, the Kruskal-Wallis rank sum test, and contingency 

tables. Cub production and survival were assessed using the 

proportion of adult females accompanied by litters, and the 

number of dependent young (COYs, yearlings, and 2-yearolds) per female. Because the comparison of indices requires 

the assumption of equal detectability among years, we limited 

our analysis of spring cub production rates to data collected in 

April and May. In early years of the study, COYs were undersampled because much of the field work occurred in March 

before new family groups emerged from their dens (Amstrup 

and DeMaster, 1988; Amstrup, 1995). Almost all females with 

COYs, however, had emerged from dens by the first week in 

April (Amstrup and Gardner, 1994).

Results

The combined 2001–06 USGS data, and 2003–06 CWS 

data, consisted of 1,099 captures of 843 individual polar bears 

(table 1, fig. 1). Approximately 90 percent of captures were for 

polar bears encountered by standard search, and 10 percent of 

captures were for polar bears encountered by radiotelemetry. 

Approximately 87 percent of captures occurred during the 

annual spring capture seasons (mean date of capture April 

14), and 7 percent of captures occurred during the autumn 

capture season by the USGS in 2001 (mean date of capture 

October 30). The remaining 6 percent of captures occurred as 

visual sightings during winter aerial radiotelemetry surveys. 

Appendix A includes a statistical description of the sex and 

age composition of the capture sample, information regarding 

marked polar bears that were harvested, and other summary 

statistics.

A total of 45 individual polar bears occurred in both 

the USGS and CWS samples: 38 “U.S.” bears (i.e., bears 

originally captured by the USGS) appeared in the Canadian 

sample, while 7 “Canadian” bears appeared in the U.S. 

sample. Although the larger number of U.S. bears in the 

Canadian sample may reflect the deployment of more marks 

into the U.S. portion of the SBS region, it also may reflect a 

distributional phenomenon. Annual encounter rates with polar 

bears were higher in Canada than in the U.S., except in 2006.

The covariate icej was based on sea ice concentration 

data for 2000–05, because we hypothesized that ice conditions 

in year j could predict polar bear survival in year j+1, and 

because CJS models cannot estimate survival following the 

final sampling occasion (i.e., 2006). For j = 2000, 2001... 

2005: icej = {-1.03, -0.89, -0.71, 0.41, 1.13, 1.09}, where 

larger values indicate a longer ice-free period. A simple linear 

regression on the covariate (prior to standardization) indicated 

that the mean number of days with less than 50 percent ice 

concentration in the SBS region of preferred habitat increased 

from approximately 82 days in 2000, to 138 days in 2005 

( ˆ

β = 11.29 d/yr, SE ( ˆβ) = 1.84, P = 0.004).

Goodness of Fit

Program RELEASE investigates whether capturerecapture data meet the assumptions of the standard CJS 

model φ ( )t p( )t , which allows φ and p to vary independently 

with time for a single stratum (see appendix B for a detailed 

description of model notation). We found no evidence 

for lack of fit in the female data (overall χ2 = 14.23, df = 

12, P = 0.29). In contrast, the male data did not fit model 

φ ( )t p( )t due entirely to a lack of fit in the program 

RELEASE component TEST3.SR (χ2 = 25.45, df = 4, 

P < 0.001). The directionality of TEST3.SR indicated a lower 

future recovery rate of newly marked male animals, which 

is often caused by age-specificity in φ (Choquet and others, 

2002). However, the lack of fit in the male data persisted 

despite progressive subsetting on age (i.e., from polar bears 

of all ages, to adults only), and despite the complete removal 

of harvested polar bears, which could exacerbate lack of fit 

due to a male bias in the harvest. Therefore, it is possible 

that the lack of fit in the male data represented a biological 

phenomenon, such as the presence of “transient” individuals 

(Cooch and White, 2005, Chapter 8).

In theory, program RELEASE can be used to estimate 

cˆ for a global model that is equivalent to independently 

fitting model φ ( )t p( )t to multiple strata in the data (Sendor 

and Simon, 2003). In this study, small sample size resulted 

in estimation problems for highly parameterized models 

that incorporated sex × time and age × time interactions 

in both φ and p. Therefore, we estimated cˆ using an 11-

parameter model that was sufficiently general to allow for 

major hypothesized sources of variation, but did not suffer 

from estimation problems, and thus was a reasonable starting 

point for model selection. The 11-parameter general model 

estimated time-constant φ for three strata: COYs of both sexes, 

female polar bears older than COYs, and male polar bears 

older than COYs. Recapture probabilities were time-dependent 

Results 
Table 1. Total number and proportion each sex and age class of polar bears captured by standard 

search and radiotelemetry in the Southern Beaufort Sea by the U.S. Geological Survey, 2001–06, and by 

the Canadian Wildlife Service, 2003–06.

Females captured Males captured

Number Proportion Number Proportion

2001

Adult1 without dependent young 21 0.15 21 0.15

Adult with dependent young 36 0.26 NA 0.00

Subadult1 5 0.04 2 0.01

Two-year-old 4 0.03 1 0.01

Yearling 16 0.12 11 0.08

Cub-of-the-year 11 0.08 9 0.07

2002

Adult without dependent young 21 0.19 20 0.18

Adult with dependent young 24 0.21 NA 0.00

Subadult 5 0.04 3 0.03

Two-year-old 4 0.04 7 0.06

Yearling 2 0.02 6 0.05

Cub-of-the-year 11 0.10 10 0.09

2003

Adult without dependent young 14 0.08 55 0.32

Adult with dependent young 33 0.19 NA 0.00

Subadult 9 0.05 11 0.06

Two-year-old 7 0.04 8 0.05

Yearling 3 0.02 7 0.04

Cub-of-the-year 10 0.06 13 0.08

2004

Adult without dependent young 39 0.14 70 0.25

Adult with dependent young 48 0.17 NA 0.00

Subadult 27 0.09 20 0.07

Two-year-old 15 0.05 10 0.04

Yearling 9 0.03 9 0.03

Cub-of-the-year 17 0.06 21 0.07

2005

Adult without dependent young 47 0.19 67 0.27

Adult with dependent young 39 0.16 NA 0.00

Subadult 17 0.07 13 0.05

Two-year-old 12 0.05 7 0.03

Yearling 9 0.04 7 0.03

Cub-of-the-year 14 0.06 17 0.07

2006

Adult without dependent young 28 0.19 49 0.34

Adult with dependent young 22 0.15 NA 0.00

Subadult 6 0.04 6 0.04

Two-year-old 7 0.05 0 0.00

Yearling 10 0.07 1 0.01

Cub-of-the-year 8 0.06 8 0.06

1

Adult (≥5 yr); Subadult (3-4 yr).

 Polar Bear Population Status in the Southern Beaufort Sea
with an interactive agency effect, which allowed independent 

estimates of pj for U.S. versus Canadian polar bears. Program 

MARK gave a bootstrap cˆ = 1.45 and a median cˆ = 1.21 

(SE = 0.01) for this model, which indicated a moderate 

amount of overdispersion. The “biological” cˆ based on the 

number of dependent young in the capture sample was 1.34, 

which was similar to the statistically based estimates. Because 

there was no clear theoretical basis for deciding which value 

of cˆ to select, we used the arithmetic mean of the three values, 

which gave cˆ = 1.33.

As noted above, the simulation-based estimates of cˆ

were derived for a model that was a compromise between 

an ideal (i.e., very general) global model, and limitations 

in the data. The parameterization for φ in that model also 

was influenced by the practical difficulty of bootstrapping 

in MARK with complex group structure. In the actual CJS 

analysis, we considered several models with more general 

parameterizations for φ. It is therefore possible that the 

simulation-based estimate of cˆ was larger than necessary.

Estimating Survival Rate and Population Size

The low-QAIC model included a simple parameterization 

for φ that estimated time-constant survival for two groups: 

COYs versus all polar bears older than COYs (model No. 1, 

table B1, appendix B). This model provided estimates of 

“average” φ for 2001–05, which could be compared to 

time-constant estimates of φ published for other polar bear 

populations. Estimates of total apparent survival probability 

( φ) from the low-QAIC model were 0.43 (SE = 0.11) for 

COYs, and 0.92 (SE = 0.04) for all polar bears older than 

COYs.

Although the low-QAIC model estimated time-constant 

φ for two groups, there also was support in the data for models 

that included other sex- and age-based groups, and allowed 

for temporal variation in φ (table B1, appendix B). Because 

all these models represented valid biological hypotheses, 

we derived estimates of φ by averaging across models in 

the candidate set with ∆QAIC ≤ 7.0, with two exceptions. 

First, we excluded model No. 13 (∆QAIC = 4.0) because of 

difficulty in interpreting the transient effect for male subadults 

and adults (see appendix C). Second, we excluded model 

No. 14 (∆QAIC = 6.0), which was the only model with a 

time-dependent parameterization for φ, because it resulted in 

confounded estimates of p2006 for some individuals.

We report model-averaged estimates of survival 

probability for three groups: COYs, female polar bears older 

than COYs, and male polar bears older than COYs (table 2). 

Although some models considered for model-averaging 

included additional groupings (e.g., subadult females separated 

from adult females), the resulting differences in parameter 

estimates were limited to the third or fourth significant digit, 

and therefore are not reported. The unconditional standard 

errors in table 2 reflect both the sampling variance of each 

model, and the additional variance associated with model 

selection uncertainty (Buckland and others, 1997). The 

percent variation due to model selection uncertainty was 

approximately 14 percent for COYs, 20 percent for females 

older than COYs, and 32 percent for males older than COYs.

All CJS models with ∆QAIC ≤ 7.0 included a single 

parameterization for p, with the exception of model No. 15 

(table B1, appendix B). Recapture probabilities differed 

between U.S. and Canadian polar bears, and were timeconstant with the exception of p2006 for Canadian bears. Also, 

an additive effect was allowed for polar bears that were 

available for recapture by radiotelemetry. We derived final 

estimates of p by model-averaging over the same candidate 

model set as considered for survival. We used this approach 

because the point estimates of p varied slightly among 

models, due to interdependence with φ. The model-averaged 

estimates of p were 0.14 (SE = 0.02) for U.S. bears, 0.20 

(SE = 0.04) for Canadian bears in 2004 and 2005, 0.06 

(SE = 0.02) for Canadian bears in 2006, and 0.49 (SE = 0.07) 

for all polar bears available for recapture by radiotelemetry. 

Overall, approximately 4 percent of the variation in recapture 

probability was due to model selection uncertainty.

We estimated N by applying the HT estimator to modelaveraged estimates of p (fig. 2). Valid estimates of population 

size were available for 2004–06 only, because of interactions 

between sampling design, the parameterization for p, and 

properties of the CJS model. The explanation is as follows. 

First, the CJS model cannot produce estimates of N in the first 

year of the study (i.e., 2001). Second, 2002 Nˆ was biased low 

because it only represented polar bears in the portion of the 

SBS region that was sampled by the USGS. Third, 2003 Nˆ also 

was biased, because 2003 was the first year of sampling by the 

CWS, and therefore the estimate of p2003 for Canadian bears 

Table 2. Model-averaged estimates of total apparent survival 

probability for polar bears in the southern Beaufort Sea.

Year

COYs of 

both sexes

Females older 

than COYs

Males older

than COYs

φ SE(φ) φ SE(φ) φ SE(φ)

2001 0.47 0.14 0.92 0.05 0.94 0.05

2002 0.45 0.13 0.92 0.05 0.94 0.05

2003 0.43 0.12 0.92 0.05 0.93 0.05

2004 0.39 0.14 0.90 0.05 0.92 0.06

2005 0.37 0.16 0.90 0.07 0.91 0.07

Results 
was not valid. Finally, we note that 2006 Nˆ represents a valid 

estimate, because all models considered for model-averaging 

had time-constant parameterizations for φ, which allowed for 

the estimation of non-confounded p2006.

The best estimate of the total size of the SBS polar bear 

population in 2006 (denoted *

2006 Nˆ ) was 1,526 (95% 

CI = 1,211; 1,841). We estimated *

2006 Nˆ by taking the 

arithmetic mean of the model-averaged point estimates 

of N from 2004 to 2006. This approach was based on the 

observation that interannual variability in Nˆ from 2004 to 

2006 was within the limits of sampling variation, and most 

likely not a reflection of real changes in population size 

(fig. 2). We estimated SE( *

2006 Nˆ ) using the standard deviation 

of the mean, model-averaged population size estimates from 

2004 to 2006, for the 1,000 bootstrap iterations. Appendix D

provides additional results from the bootstrap procedure 

regarding the statistical properties of the parameter estimates 

and model selection process.

Cub Production and Physical Stature

We compared numbers of young accompanying adult 

female polar bears captured between 1967 and 1989, to those 

accompanying females captured between 1990 and 2006. 

The spring data consisted of 788 captures of adult females 

(age ≥ 5 yr) located by standard search during April and 

May (table 3). The proportion of adult females accompanied 

by COYs increased from 0.15 for the earlier period, to 0.22 

for the later period (logistic regression; period model versus 

intercept-only model, G = 5.8, df = 1, P = 0.016). The 

number of COYs per adult female also increased, from 0.25 

to 0.39 (Kruskal-Wallis test; χ2 = 6.35, df = 1, P = 0.012). In 

contrast to the pattern observed for COYs, indices of yearling 

production declined between the two periods, although the 

changes were not statistically significant. The proportion of 

adult females accompanied by yearlings decreased from 0.22 

to 0.19 (G = 1.28, df = 1, P = 0.258), while the number of 

yearlings per adult female decreased from 0.34 to 0.26 

(χ2= 1.90, df = 1, P = 0.168).

The autumn data, which consisted of 190 captures 

of adult females during October and November, showed a 

different pattern than the spring data (table 4). The proportion 

of adult females accompanied by COYs in autumn decreased 

from 0.40 to 0.16 (G = 14.53, df = 1, P < 0.001), while the 

number of COYs per adult female decreased from 0.61 to 

0.25 (χ2 = 12.70, df = 1, P < 0.001). Similarly, although 

the differences were not significant, the proportion of adult 

females accompanied by yearlings decreased from 0.33 to 0.23 

(G = 2.39, df = 1, P = 0.122) and the number of yearlings per 

adult female decreased from 0.47 to 0.34 (χ2 = 2.13, 

df = 1, P = 0.144).

Litter sizes in the two periods were not statistically 

different (table 5). For the spring data, COY litters were 

slightly larger in the later period (2 × 3 contingency table of 

litter sizes versus period; χ2 = 2.49, df = 2, P = 0.288), while 

yearling litters were somewhat smaller (χ2 = 5.60, df = 2, 

P = 0.061). For the autumn data, litter size was similar 

between periods for both COYs (χ2 = 0.43, df = 1, P = 0.511) 

and yearlings (χ2 = 0.10, df = 1, P = 0.750).

We compared the physical stature of polar bears between 

the two periods using data for COYs, yearlings of both sexes, 

and adults (age ≥ 5 yr) of both sexes that were captured 

by standard search and radiotelemetry, from March-May. 

Statistically significant decreases in skull measurements were 

observed for COYs and adult males (table 6). Body weight 

decreased significantly for adult males (table 7). Because male 

polar bears continue to grow into their teen years (Derocher 

and others, 2005), it was possible that changes in skull 

measurements and body weight were related to changes in age 

structure. However, the mean age of adult male polar bears in 

the 1990–2006 capture sample—10.9 (SE = 0.30) years—was 

greater than the mean age—9.4 (SE = 0.23) years—in the 

1967–89 capture sample (Kruskal-Wallis test; χ2 = 15.62, 

df = 1, P < 0.001). Given equal nutrition, the older male 

bears captured in more recent years should have been larger. 

Therefore, it is likely that the observed changes in physical 

stature reflected a real shift towards smaller adult male polar 

bears in the SBS region.

Figure 2. Total size of the southern Beaufort Sea polar bear 

population. Squares are annual, model-averaged estimates of 

population size with bootstrapped 95% confidence intervals. 

Heavy dashed line is the mean population size from 2004 to 2006 

with bootstrapped 95% confidence intervals.

 Polar Bear Population Status in the Southern Beaufort Sea

500

1000

1500

2000

2500

2004 2005 2006

POPULATION SIZE

YEAR
Table 3 Cub production rates for polar bears in the southern Beaufort Sea, 1967–89 and 1990–2006. 

[Data are included for polar bears captured by standard search in the spring (April-May)]

Adult 

female age 

(yr)

1967–89 1990–2006

Number 

of adult 

females

Prop. with 

COYs

COYs 

per adult 

female

Prop. with 

yearlings

Yearlings 

per adult 

female

Prop. with 

2-yearolds

2-yearolds per 

adult 

female

Number 

of adult 

females

Prop. with 

COYs

COYs 

per adult 

female

Prop. with 

yearlings

Yearlings 

per adult 

female

Prop. with 

2-yearolds

2-yearolds per 

adult 

female

5 68 0.09 0.15 0.02 0.03 0.00 0.00 38 0.18 0.26 0.00 0.00 0.03 0.036 58 0.16 0.21 0.16 0.21 0.02 0.03 28 0.29 0.43 0.04 0.04 0.04 0.047 50 0.12 0.14 0.30 0.46 0.12 0.14 34 0.15 0.27 0.27 0.29 0.03 0.038 48 0.19 0.27 0.33 0.44 0.13 0.23 18 0.11 0.22 0.33 0.44 0.00 0.009 38 0.16 0.29 0.24 0.42 0.26 0.32 25 0.16 0.32 0.24 0.32 0.04 0.04

10 33 0.09 0.18 0.33 0.52 0.18 0.27 16 0.25 0.50 0.44 0.50 0.00 0.0011 26 0.27 0.54 0.15 0.23 0.12 0.12 17 0.41 0.77 0.18 0.18 0.12 0.1812 17 0.35 0.59 0.24 0.35 0.12 0.12 23 0.30 0.35 0.17 0.22 0.04 0.0413 19 0.05 0.11 0.42 0.68 0.21 0.32 20 0.20 0.35 0.20 0.25 0.10 0.1514 13 0.23 0.39 0.23 0.39 0.08 0.15 14 0.14 0.36 0.29 0.43 0.14 0.2115 15 0.33 0.60 0.33 0.67 0.13 0.20 11 0.18 0.36 0.18 0.27 0.18 0.3616 20 0.20 0.40 0.20 0.25 0.25 0.35 18 0.39 0.72 0.28 0.50 0.06 0.1117 9 0.11 0.22 0.22 0.33 0.22 0.33 9 0.11 0.22 0.33 0.44 0.11 0.2218 5 0.00 0.00 0.40 0.80 0.20 0.40 10 0.40 0.80 0.20 0.30 0.10 0.1019 3 0.00 0.00 0.33 0.33 0.00 0.00 5 0.40 0.80 0.00 0.00 0.20 0.4020+ 13 0.08 0.15 0.15 0.31 0.08 0.15 32 0.13 0.25 0.19 0.28 0.19 0.31

Overall1 437 0.15 0.25 0.22 0.34 0.11 0.16 351 0.22 0.39 0.19 0.26 0.07 0.11

1Overall counts include data for 2 (1967–89) and 33 (1990–2006) females that were field-aged as adults, but did not have cementum-derived ages.

Table 4. Cub production rates for polar bears in the southern Beaufort Sea, 1967–89 and 1990–2006. [Data are included for polar bears captured by standard search in the autumn (October-November)]

Adult female 

age (yr)

1967–89 1990–2006

Number of 

adult females

Proportion 

with COYs

COYs per 

adult female

Proportion 

with 

yearlings

Yearlings per 

adult female

Number of 

adult females

Proportion 

with COYs

COYs per 

adult female

Proportion 

with 

yearlings

Yearlings per 

adult female

5-9 54 0.35 0.48 0.30 0.37 36 0.06 0.08 0.19 0.31

10-14 30 0.40 0.60 0.33 0.53 26 0.35 0.58 0.19 0.2715-19 17 0.47 0.88 0.47 0.71 8 0.00 0.00 0.38 0.63

20+ 6 0.67 1.00 0.17 0.33 10 0.20 0.30 0.40 0.50

Overall1 107 0.40 0.61 0.33 0.47 83 0.16 0.25 0.23 0.34

1Overall counts include data for 3 (1990–2006) females that were field-aged as adults, but did not have cementum-derived ages. 

Results   
Table 5. Litter sizes of dependent young polar bears in the southern Beaufort Sea, 1967–89 and 1990–2006. 

[Data are included for polar bears captured by standard search in the spring (April-May) and autumn (October-November)]

Season

COY litter size Yearling litter size Two-year-old litter size

1 2 3 1 2 3 1 2 3

1967–89

Spring 23 44 0 47 48 2 29 21 0

Autumn 22 22 0 19 15 2 1 0 0

Both 45 66 0 66 63 4 30 21 0

1990–2006

Spring 21 55 2 44 23 0 11 14 0

Autumn 5 8 0 10 8 3 1 1 0

Both 26 63 2 54 31 3 12 15 0

Overall 71 129 2 120 94 7 42 36 0

Table 6. Sum of skull length and skull width measurements (cm) for polar bears in the southern Beaufort Sea, 1967–89 

and 1990–2006. 

[Data are included for all polar bears captured in the spring (March-May)]

1967–89 1990–2006 ANOVA

n Mean SD n Mean SD F df P versus 

equal means

COY males and females 70 27.8 1.8 191 26.8 1.8 16.2 1 0.000

Yearling males 34 44.6 2.4 43 44.5 2.2 0.1 1 0.771

Yearling females 26 42.2 1.9 57 41.5 2.1 2.5 1 0.121

Adult males 137 65.3 4.2 315 64.3 4.7 4.9 1 0.028

Adult females 234 55.4 1.9 425 55.3 2.6 0.6 1 0.431

Table 7. Scale weights (kg) for polar bears in the southern Beaufort Sea, 1967–89 and 1990–2006. 

[Data are included for all polar bears captured in the spring (March-May)]

1967–89 1990–2006 ANOVA

n Mean SD n Mean SD F df P versus

 equal means

COY males and females 66 14.1 4.0 164 13.2 3.9 2.4 1 0.124

Yearling males 13 85.8 16.2 16 94.5 25.2 1.2 1 0.286

Yearling females 11 74.9 17.6 29 74.8 15.1 0.0 1 0.988

Adult males 38 367.6 80.6 83 329.0 89.0 5.2 1 0.024

Adult females 92 185.3 28.3 180 184.1 27.6 0.1 1 0.731

10 Polar Bear Population Status in the Southern Beaufort Sea
Discussion

Capture-Recapture Analyses

The survival estimates derived from the 2001 to 

2006 capture-recapture data appear lower than previously 

published estimates for this population. Amstrup and Durner 

(1995) derived precise estimates of survival for COYs (0.65, 

95% CI = 0.610–0.675), yearlings (0.86, 95% CI = 0.751–

0.903), and adult females (0.97, 95% CI = 0.952–0.983) in the 

SBS region by following radiocollared females. Comparison 

of the earlier estimates with those from the current study, 

however, is complicated by strata-related issues. The 

comparison also is complicated by the fact that estimates of 

apparent survival from capture-recapture studies reflect both 

biological survival and the probability of remaining in the 

study area, whereas estimates of survival from radiotelemetry 

data reflect biological survival only. In the current study, 

estimates of apparent survival from the best fitting model 

were 0.43 (95% CI = 0.21–0.65) for COYs and 0.92 (95% 

CI = 0.84–1.00) for all polar bears older than COYs. 

Identifying a stratum that includes all bears older than COYs 

represented a compromise between actual sex- and age-based 

variation in survival, and the ability to detect this variation 

in the data using capture-recapture models. For example, 

we know from the life history of polar bears that recently 

weaned subadults generally have lower survival than prime 

age adults. Hence, a single estimate of survival for all polar 

bears older than COYs represents an average over biologically 

distinct strata. This issue, and the distinction between apparent 

survival and biological survival, precluded a meaningful 

comparison of current survival estimates for adult females 

with those derived previously.

Differences in COY survival between the two studies, 

however, can be meaningfully compared. Adult females with 

COYs are less mobile than other polar bears (Amstrup and 

others, 2000), and therefore more likely to remain in the study 

area. Estimates of apparent survival for COYs, therefore, 

should be similar to biological survival. Also, assuming 

that survival rates for adult females have not changed 

dramatically since the early 1990s, the difference between 

the radiotelemetry-based survival estimate for adult females 

(0.97, Amstrup and Durner, 1995) and the current estimate of 

apparent survival for all polar bears older than COYs (0.92) 

sets an upper limit on the emigration component of apparent 

survival for COYs. Because COYs are completely dependent 

on their mothers and cannot leave the study area on their own, 

the maximum emigration component of apparent survival 

for COYs cannot exceed 0.05. Finally, the actual emigration 

component has to be less than 0.05, because the current 

estimate of 0.92 was an average survival rate, derived for both 

adult females and other polar bears with lower biological 

survival (e.g., subadults, senescent adults).

In contrast to the maximum possible emigration 

component of <0.05, the difference between the 

radiotelemetry-based survival estimate for COYs (Amstrup 

and Durner, 1995) and the current estimate of apparent 

survival for COYs was 0.22 (i.e., 0.65–0.43). This difference 

was statistically significant (P versus the null hypothesis of 

equal or increasing survival = 0.03), and clearly represents 

a decline in biological survival since the early 1990s. The 

decline in COY survival is consistent with the statistically 

significant changes in COY and yearling production that we 

report here.

In our capture-recapture analysis, we used a weight 

of evidence approach (Burnham and Anderson, 2002) that 

allowed us to derive estimates of survival by averaging over 

multiple, well supported models. Model-averaged estimates 

of apparent survival were different for three sex and age 

groups. All three exhibited declining survival for the years 

2001–05 (table 2). Because the best fitting (i.e., low-QAIC) 

model estimated time-constant survival, these declines in 

model-averaged survival are not “statistically significant” 

in the classical sense of testing versus the null hypothesis of 

no trend. However, the declines do reflect the existence of 

a similar degree of support in the data for several models, 

some of which estimated survival probabilities that changed 

over the course of the study. The evidence ratio between two 

models can be calculated as the ratio of normalized Akaike 

weights (wi) (Burnham and Anderson, 2002). For example, the 

evidence ratio for the low-QAIC model versus model No. 3, 

which estimated survival as a function of sea ice conditions, 

was 0.18/0.12 = 1.5 (table B1, appendix B). In other words, 

the low-QAIC model was approximately 1.5 times as well 

supported as model No. 3. This low evidence ratio indicates 

considerable ambiguity as to which model was actually a 

better representation of the data (Burnham and Anderson, 

2002). Therefore, we cannot simply overlook the suggestion of 

a declining trend in survival.

Estimates of survival are generally robust to model 

assumption violations (Williams and others, 2002, Chapter 

17). Because estimates of survival derived from CJS models 

represent “total apparent survival,” however, changes in 

survival can arise from interactions between study design 

and animal movement patterns, as well as from changes in 

biological survival. In the SBS region, radiotelemetry data 

confirm that polar bears do not restrict their movements to 

the areas that we can access during helicopter supported 

capture efforts (Amstrup and others, 2000, 2004) . Over 

periods of multiple years, every bear in the population spends 

considerable time in the sampling region. However, the 

shorter the time-frame considered for sampling, the greater 

the probability that previously marked polar bears will be 

located outside of the effective study area, and not available 

for recapture prior to the end of the study. Thus, the declines 

we observed in model-averaged survival rates may reflect an 

increase in the number of “emigrants” toward the end of the 

study, and not an actual decrease in biological survival.

Discussion 11
Our model selection process did not support a transient 

effect in survival for male subadults and adults. We were, 

however, curious whether there might be sex or age specific 

differences in recapture probability. Therefore, we performed 

a limited amount of secondary modeling to investigate this 

and other a posteriori hypotheses (appendix C). Although 

inference regarding transience remained equivocal, the 

secondary modeling provided some evidence for differential 

movement patterns between males and females, and 

emphasized that this is a topic worthy of further investigation.

In our analysis of the 2001–06 data, we did not find clear 

evidence for a relationship between sea ice coverage in the 

SBS region (i.e., the covariate ice) and survival. However, 

this should be interpreted in light of the short duration of the 

study and the limitations of the data. Polar bears are longlived mammals that are well adapted to periods of resource 

shortage. Our study may not have been long enough, and may 

not have included enough interannual variation in sea ice, 

to detect a significant relationship between changing sea ice 

and survival. This also may be due to our inability to resolve 

survival patterns for subadult and senescent polar bears, which 

may be most affected by annual changes in sea ice conditions 

(Regehr and others, unpub. data, 2006). Because polar bears 

are entirely dependent on sea ice for foraging, reduced access 

to sea ice translates directly into reduced feeding opportunity. 

In other parts of the polar bear range, reductions in the 

spatiotemporal availability of sea ice have been shown to 

negatively impact polar bear stature, productivity, and survival 

of juvenile, subadult and senescent animals (Stirling and 

others, 1999; Stirling, 2002).

Our best estimate of the population size for the SBS 

region was 1,526 polar bears (95% CI = 1,211; 1,841). We 

believe that this estimate—the mean for the period 

2004–06—is relatively unbiased for several reasons. First, it 

was derived from capture-recapture data that were, for the first 

time, collected throughout the entire SBS region under a welldefined and consistent sampling protocol. Second, a thorough 

GOF analysis suggested that the data met the most important 

capture-recapture assumptions. The CJS models fitted to the 

data included covariates for all major sources of variation of 

which we were aware, and the resulting coefficient estimates 

were biologically plausible. Third, estimates of population 

size were insensitive to model selection, as evidenced by the 

low percent variation in recapture probability associated with 

model selection uncertainty (appendixes C and D). Finally, 

the point estimates of population size were relatively stable 

for 2004–06 (i.e., the years for which valid estimates could be 

derived).

Stability in point estimates for 2004–06 is further 

evidence that they reflect the total number of polar bears in 

the SBS region. In each year of the study, some individuals 

probably were located outside of the effective sampling 

area. However, the estimates of population size derived from 

CJS models represent the total number of individuals that 

had a finite probability of being exposed to sampling (i.e., 

the “superpopulation”), whether or not they were actually 

accessible to the USGS or CWS in every year (Kendall and 

others, 1997). The stability of estimated population sizes 

for the latter years of the study, when both agencies were 

performing field work, indicates that new individuals were not 

continuing to be “recruited” into the superpopulation as they 

cycled through the area exposed to sampling efforts.

Amstrup and others (2001a) estimated that there were 

1,180 (95% CI = 635; 1,725) female polar bears in the SBS 

region in the late 1980s. Sample sizes during this period 

were similar to those in the 2001–06 study, which allows for 

a reasonable comparison of estimated population sizes. If 

the sex ratio of the population in the late 1980s was similar 

to what (54 percent female) we estimated for the 2001–06 

period, the Amstrup and others (2001a) female-only estimate 

corresponded to a total population size in the late 1980s of 

approximately 2,185 polar bears. Because the estimate and 

confidence interval were calculated for females only, however, 

we do not know the statistical variance associated with this 

estimate of the total population size. We do know, however, 

that the variance associated with the estimate of the total 

population was necessarily greater than the variance for the 

female-only estimate (SE = 278). Therefore, the confidence 

interval around the total population size estimate of 2,185 

must have exhibited considerable overlap with the confidence 

interval around the current estimate of 1,526 (95% CI = 

1,211; 1,841). This overlap, in conjunction with the similarity 

between the current estimate and the original Amstrup and 

others (1986) estimate of 1,800 (95% CI not available), 

precludes a statistical determination that the total number of 

polar bears in the SBS region has changed in recent years.

Estimating the size of wildlife populations is inherently 

difficult (e.g., Pollock and others, 1990; Pledger and Efford, 

1998). This is especially true for animals that occur at low 

densities in remote regions, because of the potential for bias 

introduced by heterogeneity in recapture probability (e.g., 

due to differences in distribution, behavior, sightability). 

We believe that the estimated population sizes for 2004–06 

are accurate. However, evaluation of long-term trends in 

population size via post hoc comparison with previous 

analyses is clearly a challenge. To address this issue more 

thoroughly, we are preparing an integrated analysis of historic 

and current data for polar bears in the SBS region, including 

both capture-recapture and radiotelemetry data.

Cub Production and Physical Stature

The changes we observed in cub production between 

the early (1967–89) and latter (1990–2006) time periods 

appear to reflect a decrease in the survival of polar bear cubs 

during their first 6 months of life. Polar bears have a multiyear reproductive cycle (Amstrup, 2003). Females give birth 

in January and emerge from the maternal den with new cubs 

in March or early April. Young typically accompany their 

mother for 2.3 years while they learn the methods of survival 

12  Polar Bear Population Status in the Southern Beaufort Sea
in the Arctic (Amstrup, 2003). For polar bears captured 

during the autumn, the number of COYs per adult female 

declined significantly (P < 0.001) from a mean of 0.61 in 

the early period to a mean of 0.25 in the latter period. This 

decline can only be explained by lower survival of cubs after 

den emergence. In contrast to the autumn data, the numbers 

of COYs per adult female captured in the spring increased 

between the two periods. This reflects a shortened inter-birth 

interval for the recent period. Apparently, more females are 

losing their cubs shortly after den emergence, breeding again 

shortly after losing their cubs, denning again the following 

autumn, and emerging with another litter the following spring. 

In short, numerous cubs are currently being born in the SBS 

region, but many of them are not being recruited into the 

population.

The evaluation of changes in cub production requires 

the recognition of possible sampling differences between the 

early and latter study periods. Amstrup and DeMaster (1988) 

and Amstrup (1995) suggested that COYs were often undersampled in spring captures. In the early period, this undersampling was reflected by a higher proportion of yearlings 

than COYs in spring captures, and by a higher proportion of 

COYs captured in the autumn than in the spring. Because it 

is not possible for actual cub production to increase between 

the spring and autumn of a single year, a higher proportion of 

females with cubs in the autumn must represent a bias in the 

index. Two sampling issues may contribute to the bias against 

the spring capture of COYs. First, polar bear families often do 

not emerge from the maternal den until early April (Amstrup 

and Gardner, 1994). Because family groups located in dens 

are not available for capture, capture efforts conducted in 

March are likely to under-sample females with COYs. Second, 

Amstrup and Gardner (1994) showed that many female 

polar bears in the Beaufort Sea denned on the far offshore 

pack ice. Females emerging from dens far offshore may be 

less available to capture by research crews operating from 

logistical bases onshore.

In our analysis of cub production data, we controlled for 

the first source of bias by excluding capture data from March. 

For the 1967–89 period, however, spring samples still included 

a higher proportion of yearlings than of COYs. This suggests 

that the under-representation of COYs in the spring sample 

for the early period was due to bears that denned far offshore. 

Indeed, new analyses of the distribution of denning in the U.S. 

portion of the SBS region confirm that more bears denned 

in far offshore regions in early years of polar bears studies 

than in the recent decade (Fischbach and others, unpub. data, 

2006). We attribute this shift in denning distribution to sea ice 

conditions that have become less suitable as a substrate for 

denning.

The suspected shift over time towards more onshore 

denning cannot account for the profound decline in the 

number of COYs per adult female captured in the autumn 

(0.61 versus 0.25). During the freeze-up period of our autumn 

sampling, polar bears in the SBS region are concentrated in 

the nearshore areas (Durner and others, 2004) where they are 

highly vulnerable to capture by shore-based research crews. 

Therefore, the observed decline in the number of COYs per 

adult female captured in the autumn must reflect an actual 

decline in the survival of cubs between den emergence and 

the autumn sampling period, and not a sampling artifact. This

decline in turn appears to be the principal cause of the increase 

in COYs and decrease in yearlings that we observed in the 

spring capture data after 1989.

Observed changes in the physical stature of polar bears 

in the SBS region appear to parallel declines in recruitment. 

Declines in skull size for both COYs and adult males were 

significant. The decline in body weight for adult males was 

significant. Such changes in physical stature may suggest 

different impacts of reduced summer sea ice on adult male 

and female polar bears. In the spring, adult males often forgo 

foraging opportunities and focus their efforts on locating 

females for mating. Therefore, adult males enter the summer 

period in relatively poorer nutritional condition. They may 

then be more vulnerable to summer sea ice retreats, which 

can separate polar bears from foraging habitats thought to be 

the most productive (Amstrup and others, 2006). Conversely, 

reduced foraging opportunity for adult females usually is first 

reflected in poorer survival of young. Although the average 

body weight of COYs did not decline significantly between 

the two periods, their weights were slightly lower in the latter 

period. Evidence from other portions of the polar bear’s range 

suggest lower weights, combined with significantly smaller 

skull sizes, may be related to the poorer survival we observed 

for COYs in recent years. In western Hudson Bay, Canada, 

which is near the southern extreme of the species range, 

declines in cub survival and physical stature were recorded for 

years (Stirling and others, 1999; Derocher and others, 2004) 

before a statistically significant decline in population size was 

confirmed. In western Hudson Bay, we associated the decline 

in population size with reduced survival of juvenile polar bears 

and adults that were beyond prime ages. Poorer survival of 

animals in those age classes was directly related to the reduced 

availability of sea ice (Regehr and others, unpub. data, 2006). 

The situation in western Hudson Bay offers insight into the 

future status of polar bears in more northern regions such as 

the SBS, because recently observed declines in the area and 

extent of sea ice are predicted to continue throughout the polar 

basin (Overpeck and others, 2005; Stroeve and others, 2005)

Evidence of declining physical stature and poorer 

survival of COYs in the SBS region is consistent with other 

observations, which suggest that changes in the sea ice may 

be adversely affecting polar bears. Previously, human harvest 

accounted for most documented polar bear mortalities in the 

SBS region (Amstrup and Durner, 1995). In contrast, several 

recently observed mortalities were directly related to sea ice 

retreat, or appeared related to changes in food availability 

that may be associated with sea ice retreat. In autumn of 

Discussion 13
2004, four polar bears were observed to have drowned while 

attempting to swim between shore and the distant pack ice. 

Despite offshore surveys extending back to 1987, similar 

observations had not previously been recorded (Monnett and 

Gleason, 2006). During winter and early spring of 2004, three 

observations were recorded of polar bears hunting, killing, 

and consuming other polar bears in the Beaufort Sea (Amstrup 

and others, 2006). Similar observations had not been recorded 

in that region despite studies extending back for decades. In 

spring of 2006, three adult female polar bears and one yearling 

were found dead. Two of these females and the yearling had 

depleted their lipid stores and apparently starved to death. 

Although the third adult female was too heavily scavenged 

to determine a cause of death, her death appeared unusual 

because prime age females have had very high survival 

rates in the past (Amstrup and Durner, 1995). Similarly, the 

yearling that was found starved was the offspring of another 

radiocollared prime age female that had recently disappeared 

from the airwaves. Annual survival of yearlings, given survival 

of their mother, was previously estimated to be 0.86 (Amstrup 

and Durner, 1995). Therefore, the probability that this yearling 

died while its mother was still alive was only approximately 

14 percent. These anecdotal observations, in combination with 

both the changes in survival of young and in physical stature 

reported here, suggest mechanisms by which a changing sea 

ice environment can affect polar bear demographics and the 

status of populations.

Conclusions

Information on changes in survival and physical stature, 

reported here, indicate that the status of polar bears in the 

SBS region is changing. Annual survival rates of COYs 

estimated from the 2001 to 2006 capture-recapture study 

were lower than survival rates estimated in previous studies. 

The increased loss of cubs during the first 6 months of life 

may be associated with the smaller physical stature of COYs 

observed in recent years. The smaller physical stature of COYs 

was paralleled by a smaller physical stature of adult males, 

even though the average age of adult males has increased. 

Despite these indicators of a declining status for the SBS polar 

bear population, our best estimate of the current size of the 

population does not show a statistically significant decline. 

This may mean there has been no change in numbers in recent 

years, or it could reflect insufficient precision in current and 

past estimates to resolve such a change.

Although our 2001–06 capture-recapture study did not 

provide evidence for a change in the size of the SBS polar bear 

population, significant changes in cub survival and physical 

stature must ultimately have population level effects. Lowered 

body weight has been implicated in declining survival of polar 

bear cubs in western Hudson Bay, Canada. There, reduced 

cub survival, associated with declines in physical stature 

caused by reduced foraging opportunity, was recorded long 

before a statistically significant decline in population size was 

confirmed. The relationship between decreased availability 

of sea ice and declining population size in western Hudson 

Bay, which is near the southern extreme of polar bear range, 

is cause for concern regarding the future status of polar bears 

in more northern regions such as the SBS. Because more 

profound declines in sea ice area and extent are predicted for 

these northern regions, continued monitoring and conservative 

management of the SBS polar bear population is warranted.

Acknowledgments

Principal funding for the intensive capture-recapture 

effort in 2001–06 was provided by the U.S. Geological Survey, 

Science Support Partnership program, which is dedicated to 

fulfilling current research needs of the U.S. Fish & Wildlife 

Service, and by the Canadian Wildlife Service, the Department 

of Environment and Natural Resources of the Government 

of the Northwest Territories, and the Polar Continental Shelf 

Project, Ottawa, Canada. Funding for capture-recapture 

efforts was also provided by BP Exploration Alaska, Inc., 

Conoco-Phillips Alaska, Inc., and the ExxonMobil Production 

Company, Inc. through the National Fish and Wildlife 

Foundation. Our long-term studies of polar bears in the 

SBS region have been supported by U.S. Geological Survey 

(formerly the research division of the U.S. Fish and Wildlife 

Service), the Canadian Wildlife Service, the Government of 

the Northwest Territories (Department of Resources, Wildlife, 

and Economic Development) and the Polar Continental Shelf 

Project. To a large degree, our understanding of the past and 

present status of the SBS polar bear population is owed to the 

continued, cumulative support of these agencies. We thank 

T.L. McDonald, J.A. Schmutz, and M.S. Udevitz for their 

reviews which substantially improved this report. We also 

thank K. Simac for assistance with literature citations.

References Cited

Amstrup, S.C., 1995, Movements, distribution, and population 

dynamics of polar bears in the Beaufort Sea: Fairbanks, 

Alaska, University of Alaska, Ph.D. dissertation. 

Amstrup, S.C., 2003, Polar bear, in Feldhammer, G.A., 

Thompson, B.C., and Chapman, J.A. (eds.), Wild 

mammals of North America: Biology, Management, and 

Conservation, 2nd edition: Baltimore, Maryland, Johns 

Hopkins University Press, p. 587-610.

Amstrup, S.C., and DeMaster, D.P., 1988, Polar Bear – Ursus 

maritimus, in Lentfer, J.W. (ed.), Selected marine mammals 

of Alaska: species accounts with research and management 

recommendations: Marine Mammal Commission, 

Washington, D.C., p. 39-56.

14  Polar Bear Population Status in the Southern Beaufort Sea
Amstrup, S.C., and Durner, G.M., 1995, Survival rates of 

radio-collared female polar bears and their dependent 

young: Canadian Journal of Zoology, v. 73, p. 1312-1322.

Amstrup, S.C., and Gardner, C., 1994, Polar bear maternity 

denning in the Beaufort Sea. Journal of Wildlife 

Management, v 58, no. 1, p. 1-10.

Amstrup, S.C., Durner, G.M., McDonald, T.L., Mulcahy, 

D.M., and Garner, G.W., 2001b, Comparing movement 

patterns of satellite-tagged male and female polar bears: 

Canadian Journal of Zoology, v. 79, p. 2147-2158.

Amstrup, S.C., Durner, G.M., Stirling, I., Lunn, N.J., and 

Messier, F., 2000, Movements and distribution of polar 

bears in the Beaufort Sea: Canadian Journal of Zoology, 

v. 78, no. 6, p. 948-966.

Amstrup, S.C., Durner, G.M., Stirling, I., and McDonald, T.L., 

2005, Allocating harvests among polar bear stocks in the 

Beaufort Sea: Arctic, v. 58, no. 3, p. 247-259.

Amstrup, S.C., McDonald, T.L., and Durner, G.M., 2004, 

Using satellite radiotelemetry data to delineate and manage 

wildlife populations: Wildlife Society Bulletin, v. 32, no. 3, 

p. 661-679.

Amstrup, S.C., McDonald, T.L., and Stirling, I., 2001a, 

Polar bears in the Beaufort Sea: a 30-year mark-recapture 

case history: Journal of Agricultural, Biological, and 

Environmental Statistics, v. 6, p. 221-234.

Amstrup, S.C., Stirling, I., and Lentfer, J.W., 1986, Past and 

present status of polar bears in Alaska. Wildlife Society 

Bulletin, v. 14, no. 3, p. 241-254.

Amstrup, S.C., Stirling, I., Smith, T.S., Perham, C., and 

Thiemann, G.W., 2006, Recent observations of intraspecific 

predation and cannibalism among polar bears in the 

southern Beaufort Sea: Polar Biology, v. 29, no. 11, 

p. 997-1002, doi:10.1007/s00300-006-0142-5.

Boyce, M.S., 1984, Restitution of r- and K- selection as a 

model of density-dependent natural selection: Annual 

Review of Ecology and Systematics, v. 15, p. 427-447.

Brower, C.D., Carpenter, A., Branigan, M.L., Calvert, W., 

Evans, T., Fischbach, A.S., Nagy, J.A., Schliebe, S., and 

Stirling, I., 2002, The polar bear management agreement 

for the southern Beaufort Sea: An evaluation of the first ten 

years of a unique conservation agreement: Arctic, v. 55, 

no. 4, p. 362-372.

Buckland, S.T., K.P. Burnham, and N.H. Augustin. 1997. 

Model selection: An integral part of inference. Biometrics. 

53, p. 603-618.

Burnham, K.P., and Anderson, D.R., 2002, Model selection 

and multimodel inference, 2nd edition: New York, 

Springer-Verlag.

Burnham, K.P., Anderson, D.R., White, G.C., Brownie, C., 

and Pollock, K.H, 1987, Design and analysis methods 

for fish survival experiments based on release-recapture: 

American Fisheries Society Monograph No. 5, Bethesda, 

Md.

Calvert, W., and M.A. Ramsay. 1998, Evaluation of age 

determination of polar bears by counts of cementum growth 

layer groups: Ursus 10, p. 449-453.

Choquet, R., A.-M. Reboulet, R. Pradel, O. Gimenez, 

and Lebreton, J.-D.,2002, User’s manual for U-CARE, 

Mimeographed document: CEFE/CNRS, accessed at http://

ftp.cefe.cnrs.fr/biom/Soft-CR/, Montpellier, France.

Comiso, J.C., 1986, Characteristics of Arctic winter sea ice 

from satellite multispectral microwave observations: Journal 

of Geophysical Research, 91(C1). p. 975-994.

Comiso, J.C., 2002, A rapidly declining perennial sea ice 

cover in the Arctic: Geophysical Research Letters, 29(20), 

p. 1956-1959.

Comiso, J.C., and Parkinson, C.L., 2004, Satellite-observed 

changes in the Arctic: Physics Today, 57(9), p. 38-44.

Cooch, E., and White, G., 2005, Program MARK - A 

gentle introduction. Fifth edition (Web Page), accessed 

August 2006 at http://www.phidot.org/software/mark/docs/

book/.

Derocher, A. E., Andersen, M., and Wiig, Ø. 2005, Sexual 

dimorphism of polar bears: Journal of Mammalogy, 86(5), 

p. 895-901.

Derocher, A.E., Lunn, N.J., and Stirling, I., 2004, Polar bears 

in a warming climate: Integrative and Comparative Biology, 

44m, p. 163-176.

Durner, G. M., Amstrup, S.C., Nielson, R., and McDonald, 

T., 2004: Using discrete modeling to generate resource 

selection functions for female polar bears in the Beaufort 

Sea, p. 107-120 in S. Huzurbazar, ed.: Resource 

Selection Methods and Applications, Proceedings of 

the 1st International Conference on Resource Selection, 

Omnipress, Madison, Wis.

Franklin, A.B. 2001, Exploring ecological relationships in 

survival and estimating rates of population change using 

program MARK, p. 290-296 in Field, R., Warren, R.J., 

Okarma, H., and Sievert, P.R. eds.: Wildlife, Land, and 

People, Priorities for the 21st Century, Proceedings of 

the Second International Wildlife Management Congress, 

Bethesda, Md.

Harris, R.B., Fancy, S.G., Douglas, D.C., Garner, G.W., 

Amstrup, S.C., McCabe, T.R., and Pank, L.F., 1990, 

Tracking wildlife by satellite: current systems and 

performance: U.S. Fish and Wildlife Service Technical 

Report 30.

References Cited 15
Kendall, W. L., Nichols, J.D., and Hines, J.E., 1997, 

Estimating temporary emigration using capture-recapture 

data with Pollock’s robust design: Ecology,78, p. 563-578.

Lebreton, J.-D., Burnham, K.P. , Clobert, J., and Anderson, 

D.R., 1992, Modeling survival and testing biological 

hypotheses using marked animals: a unified approach with 

case studies: Ecological Monographs 62, p. 67-118.

Manly, B.F. 1997, Randomization, Bootstrap, and Monte Carlo 

Methods in Biology, Second ed.: Chapman and Hall.

McDonald, T. L., and Amstrup, S.C., 2001, Estimation of 

population size using open capture-recapture models: 

Journal of Agricultural, Biological, and Environmental 

Statistics 6, p. 206-220.

McDonald, T. L., Amstrup, S.C., Regehr, E.V., and Manly, 

B.F.J., 2005, Examples, p. 196-265 in Amstrup, S.C., 

McDonald, T.L. and Manly, B.F.J. eds.: Handbook of 

Capture-Recapture Analysis, Princeton University Press, 

New Jersey.

Monnett, C., and Gleason, J.S., 2006, Observations of 

mortality associated with extended open-water swimming 

by polar bears in the Alaskan Beaufort Sea [online]: Polar 

Biology 29(8), p.681-687, doi:10.1007/s00300-005-0105-2.

Overpeck, J.T., Sturm, M., Francis, J.A., Perovich, D.K., 

Serreze, M.C., Benner, R., Carmack, E.C., Chapin III, F.S., 

Gerlach, S.C., Hamilton, L.C., Hinzman, L.D., Holland, 

M., Huntington, H.P., Key, J.R., Lloyd, A.H., MacDonald, 

G.M., McFadden, J., Noone, D., Prowse, T.D., Schlosser, 

P., and Vörösmarty, C., 2005, Arctic system on trajectory 

to new, seasonally ice-free state: Earth Observing System 

86(34)309, p. 312-313.

Pledger, S., and Efford, M., 1998, Correction of bias due to 

heterogeneous capture probability in capture-recapture 

studies of open populations: Biometrics 54, p. 888-898.

Pollock, K.H., Nichols, J.D., Hines, J.E., and Brownie, 

C., 1990, Statistical inference for capture-recapture 

experiments: Wildlife Monographs No. 107.

Pradel, R., Hines, J.E., Lebreton, J.-D., and Nichols, J.D., 

1997, Capture-recapture survival models taking account of 

transients: Biometrics 53, p. 60-72.

Ramsay, M.A., and Stirling, I., 1988, Reproductive biology 

and ecology of female polar bears (Ursus maritimus):

Journal of Zoology (London) 214, p. 601-634.

Rigor, I.G., and Wallace, J.M., 2004, Variations in the age 

of Arctic sea-ice and summer sea-ice extent: Geophysical 

Research Letters. 31:L09401.

Rigor, I.G., Wallace, J.M., and Colony, R.L., 2002, Response 

of sea ice to the Arctic Oscillation: Journal of Climate 

15(18), p. 2648-2663.

Sendor, T., and Simon, M., 2003, Population dynamics of the 

pipistrelle bat: effects of sex, age and winter weather on 

seasonal survival: Journal of Animal Ecology 72, 

p. 308-320.

Stirling, I., Andriashek, D., and Calvert, W., 1981, Habitat 

preferences and distribution of polar bears in the western 

Canadian arctic: Prepared for Dome Petroleum Limited, 

Esso Resources Canada Limited, and the Canadian Wildlife 

Service

Stirling, I., 2002, Polar bears and seals in the eastern Beaufort 

Sea and Amundsen Gulf: A synthesis of population trends 

and ecological relationships over three decades: Arctic 

55(supplement 1), p.59-76.

Stirling, I., Lunn, N.J., and Iacozza, J., 1999, Long-term trends 

in the population ecology of polar bears in western Hudson 

Bay in relation to climatic change: Arctic 52, p. 294-306.

Stirling, I., Spencer, C., and Andriashek, D., 1989, 

Immobilization of polar bears (Ursus maritimus) with 

Telazol® in the Canadian Arctic: Journal of Wildlife 

Diseases 25, p. 59-168.

Stroeve, J.C., Serreze, M.C., Fetterer, F., Arbetter, T., Meier, 

W., Maslanik, J., and Knowles, K., 2005, Tracking the 

Arctic’s shrinking ice cover: Another extreme September 

minimum in 2004 [online]: Geophysical Research Letters, 

32:L04501, doi:10.1029/2004GL021810.

Taylor, M.K., Laake, J., Cluff, H.D., Ramsay, M., and Messier, 

F., 2002, Managing the risk from hunting for the Viscount 

Melville Sound polar bear population: Ursus 13, p. 185-202.

White, G.C., and Burnham, K.P., 1999, Program MARK: 

Survival estimation from populations of marked animals: 

Bird Study 46(supplement): p. s120-s138.

White, G.C., Burnham, K.P., and Anderson, D.R., 2001, 

Advanced features of program MARK, p. 368-377 in

Field, R., Warren, R.J., Okarma, H., and Sievert, P.R. 

eds., Wildlife, Land, and People: Priorities for the 21st 

Century, Proceedings of the Second International Wildlife 

Management Congress: Wildlife Society, Bethesda, Md.

Williams, B.K., Nichols, J.D., and Conroy, M.J., 2002, 

Analysis and Management of Animal Populations:

Academic Press, San Diego, Ca.

16  Polar Bear Population Status in the Southern Beaufort Sea
We summarized the sex composition, age composition, 

and proportion of marked versus unmarked bears using 

captures of polar bears encountered by standard search only, 

because polar bears encountered by radiotelemetry consisted 

mostly of adult females and dependent young. Trends were 

described using standard regression techniques (e.g., Boyce, 

1984; Comiso, 1986). For example, we assessed temporal 

variation in the sex ratio by computing a likelihood ratio 

test for a logistic model with an intercept only (H0), versus 

a logistic model with an intercept and five design variables, 

which allowed the proportion of females to differ among years 

(HA).

Table A1 summarizes the proportion of adult polar 

bears in the capture sample that were previously marked. 

The proportion of females in the capture sample was variable 

among years (logistic regression; time-dependent model 

versus time-constant model, G = 19.22, df = 5, P = 0.002), due 

to the difference between a high proportion of females in 2001 

and a low proportion of females in 2003 (Tukey-type multiple 

comparison test for proportions; q2001-2003 = 1.07, SE 

(q2001-2003) = 0.25). The high in 2001 reflects the fact 

that autumn sampling occurred in that year of the study. 

Historically, autumn samples have included high proportions 

of females and young. The overall proportion of females in the 

capture sample was 0.54 (SE = 0.02).

The overall age class composition of the capture sample 

was 0.12 (SE = 0.03) COYs, 0.09 (SE = 0.03) yearlings, 0.07 

(SE = 0.03) 2-year-olds, 0.12 (SE = 0.03) subadults, and 0.60 

(SE = 0.02) adults. The proportion of females in each age 

class was 0.47 for COYs, 0.55 for yearlings, 0.62 for 2-yearolds, 0.56 for subadults, and 0.55 for adults. The proportion 

of adult polar bears in the capture sample was stable among 

years (logistic regression; time-dependent model versus 

time-constant model, G = 6.62, df = 5, P = 0.251), with an 

overall value of 0.60 (SE = 0.02). The age of adult (i.e., age 

≥ 5 yr) females was stable among years (Kruskal-Wallis test; 

χ2

 = 4.16, df = 5, P = 0.527), with a mean value of 11.8 yr 

(SE = 0.33). The age of adult males was stable among years 

(Kruskal-Wallis test; χ2 = 6.18, df = 5, P = 0.289), with a 

mean value of 10.8 yr (SE = 0.33).

From 2001 to 2006, 37 previously marked polar bears 

were killed as part of a legal, regulated harvest by Inuit 

hunters in the SBS region (table A2). Because CJS models 

are appropriate for live-recapture data only, we excluded these 

deaths and 15 natural deaths (i.e., polar bears that we found 

dead on the sea ice, or cubs that were presumed dead because 

their mothers were later observed alone) from the data. We 

included death records for two research-related mortalities that 

occurred from 2001 to 2006, which the CJS model effectively 

handles by right-censoring the individual capture histories 

of animals not released back into the population following 

capture.

Appendix A. Description of Sex Composition, Age Composition, and Other 

Summary Statistics for Polar Bears Captured in the Southern Beaufort Sea,

2001–06. 

Table A1. Proportion of adult (age ≥ 5 yr) polar bears with a 

previous capture in the current study. 

[Data are for polar bears captured by standard search in the southern Beaufort 

Sea by the U.S. Geological Survey, 2001–06, and the Canadian Wildlife 

Service, 2003–06]

Year Total captures Recaptures Proportion 

recaptures

2001 73 0 0.00

2002 50 10 0.20

2003 93 12 0.13

2004 157 29 0.18

2005 146 45 0.31

2006 100 39 0.39

Table A2. Previously marked polar bears harvested in the 

southern Beaufort Sea, 2001–06.

Female Male

Adult1 7 13

Subadult 1 10

Two-year-old 5 1

Yearling 0 0

Cub-of-the-year 0 0

1

Adult (≥5 yr ); Subadult (3-4 yr)

Appendix A 17
The model notation used in table B1 is an extension 

of the standard CJS notation developed by Lebreton and 

others (1992). We fitted models that allowed survival (φ) and 

recapture (p) probability to vary as functions of individual, 

group, and environmental covariates. Time-constant and 

time-dependent parameterizations were denoted (.) and (t), 

respectively. In the parameterization for φ, we considered four 

age classes: cubs-of-the-year (i.e., COYs, 0 yr; denoted a1), 

yearlings (1 yr; a2), subadults (2-4 yr, a3), and adults (5+ yr; 

a4). We denoted combinations of age classes using the letter 

“a” followed by several integers. For example, an aggregate 

age class comprising COYs (a1) and yearlings (a2) was 

written a12. Age structure was written in square brackets. For 

example, the model φ([a12, a3, a4]) estimated time-constant 

survival probabilities for three age classes: a12, a3, and a4. 

We denoted models that included both additive (“+”) and 

interactive (“×”) effects using nested brackets. For example, 

model φ(al + {[a2, a3, a4] × sex}) estimated a single survival 

probability for COYs, but included age × sex interactions for 

yearlings, subadults, and adults. The environmental covariates 

icej,φj and icej,φj+1 were used to relate the sea ice conditions 

in the year j to survival probabilities in the year j and j+1, 

respectively. The covariate linear represented a generic linear 

trend in φ. The covariate trans represented transience, which 

was parameterized as an additive effect in φ following the 

occasion of first capture for subadult and adult male polar 

bears.

In the parameterization for p, the covariate effort

represented the number of helicopter hours flown in capture 

operations each year. The individual covariate agency

indicated whether each polar bear was first captured by the 

USGS or CWS. We used the notation agency* to indicate a 

parameterization for p that estimated time-constant p for U.S. 

and Canadian bears, but allowed p2006 to differ for Canadian 

bears. The time-dependent individual covariate radio indicated 

whether each polar bear was available for recapture by 

radiotelemetry.

Appendix B. Description of Model Notation, and the Model Selection Table for 

Cormack-Jolly-Seber (CJS) Models Fitted to Capture-Recapture Data for Polar 

Bears in the Southern Beaufort Sea, 2001–06.

Table B1. Model selection table for CJS models fitted to capture-recapture data for polar bears in 

the southern Beaufort Sea, 2001–06. 

[QAIC = Akaike’s information criterion adjusted for on a variance inflation factor ( cˆ ) of 1.33; dev = model 

deviance, np = number of estimated parameters, and wi = normalized Akaike weight. Of the 152 total CJS models 

fitted in the analysis, only models with ∆QAIC ≤ 7.0 (which corresponds to approximately wi ≥ 0.01) were considered 

for model averaging, and are shown here]

No. Survival Recapture np dev QAIC wi

1 φ([a1,a234]) p(agency*+radio) 6 1416.10 1076.73 0.18

2 φ([a1+{[a234]×sex}] p(agency*+radio) 7 1414.06 1077.20 0.14

3 φ([a1,a234]+icej, φj+1) p(agency*+radio) 7 1414.51 1077.54 0.12

4 φ([a1,a234]+linear) p(agency*+radio) 7 1414.75 1077.73 0.11

5 φ([a1,a234]+icej, φj+1) p(agency*+radio) 7 1414.94 1077.86 0.10

6 φ({a1× icej, φj+1}+[a234]) p(agency*+radio) 7 1415.82 1078.53 0.08

7 φ({a1× linear}+[a234]) p(agency*+radio) 7 1415.96 1078.64 0.07

8 φ({a1× icej, φj

}+ [a234]) p(agency*+radio) 7 1415.98 1078.65 0.07

9 φ([a1,a234]) p(agency*+radio) 7 1416.03 1078.68 0.07

10 φ([a1+{[a2a3a4]×sex}] p(agency*+radio) 9 1413.20 1080.56 0.03

11 φ [a1a2a3a4] p(agency*+radio) 8 1415.99 1080.65 0.03

12 φ([a12,a34]) p(agency*+radio) 6 1423.30 1082.15 0.01

13 φ([a1,a2,a34]+trans) p(agency*+radio) 8 1416.02 1080.68 NA1

14 φ([a1,a2,a3,a4]+t p(agency*+radio) 10 1413.45 1082.74 NA1

15 φ([a1,a234]+icej, φj+1) p(radio) 5 1428.00 1083.68 0.01

1

Models No. 13 and 14 were excluded from model averaging; see Results: Estimating survival rate and population 

size. 

18  Polar Bear Population Status in the Southern Beaufort Sea
After completing the main analysis, we performed a 

secondary analysis to investigate sex-specificity in recapture 

probability. This was motivated by the a posteriori hypothesis 

that females with dependent young may avoid male polar 

bears by limiting their use of preferred habitats (Stirling 

and others, 1981), which also were the habitats that we 

searched most intensively in our capture efforts. We began by 

modifying the most general model from the main analysis, 

to include an additive sex effect in p for subadult and adult 

males. After including this more general parameterization 

for p, we found that the data supported a “transient” effect 

in φ for subadult and adult males. Transience had been 

considered in the main analysis, but was poorly supported at 

that time (table B1, appendix B). Because differential capture 

probabilities between males and females and transience 

among males were both reasonable biological hypotheses, 

we evaluated their impact by continuing with a complete 

secondary model selection process.

The low-QAIC model from the secondary analysis was 

identical to the low-QAIC model from the main analysis, 

except that for subadult and adult males it included both the 

additive effect in p ( ˆ

β = 0.78, SE ( ˆβ) = 0.23; likelihood ratio 

test versus null model without ˆ

β: χ2

 = 13.37, df = 1, 

P < 0.001), and the additive transient effect in φ ( ˆ

β = -2.23, 

SE ( ˆ

β) = 0.83; likelihood ratio test versus null model without ˆ

β: χ2

 = 7.06, df = 1, P = 0.008). The magnitude of the sex 

effect in p was such that subadult and adult males had nearly 

twice the recapture probability of other polar bears (e.g., 0.21 

versus 0.11 for “U.S.” polar bears). Although a higher p for 

males was consistent with our hypothesis of sex-based habitat 

segregation, the magnitude of this effect was not realistic. 

Apparently, the estimated p for males was exaggerated by 

interaction with the transient effect (see below).

Evidence for transience was consistent with the GOF 

analysis, which indicated that the data contained an unusually 

large number of subadult and adult males that were captured 

once, and never recaptured. These polar bears were considered 

“transients” based on the assumption that they were present in 

the study area for a relatively short period (during which they 

were exposed to sampling efforts), after which they emigrated 

permanently. The transient parameterization of the CJS model 

handles this by estimating a different survival probability 

following first capture. From a modeling perspective, this 

allows transient individuals to “die” (i.e., to leave the study 

population), and therefore minimizes their impact on the 

estimates of apparent survival for non-transient individuals. 

We considered that this approach might be reasonable, 

because the annual use areas of highly mobile polar bears were 

potentially large with respect to the study area (Amstrup and 

others, 2000).

Both the GOF analysis and the secondary modeling 

indicated that transience was limited to male polar bears, 

which suggests differential movement patterns between males 

and females. This finding may be significant, because although 

there are few movement data for male polar bears, the limited 

information that is available suggests that movements of 

male and female polar bears are similar (Amstrup and others, 

2001b). The low-QAIC model from the secondary analysis 

estimated that φ was 0.63 (SE = 0.10) for newly marked 

subadult and adult males. The estimated value of φ for all 

other polar bears older than COYs (i.e., females, and males 

subsequent to their first capture) was 0.94 (SE = 0.04). This 

“transient-corrected” value of φ was higher than the estimate 

of 0.92 (SE = 0.04) from the main analysis, and likely 

represents an intermediate value between apparent survival 

and biological survival. We used the ratio of the two survival 

probabilities from the low-QAIC model to derive a rough 

estimate of the proportion of transients among newly-captured 

subadult and adult males: 1 – 0.63 / 0.94 = 0.33 (Cooch and 

White, 2005, Chapter 8).

Aside from the inclusion of the two effects discussed 

above, model selection was similar for the main and secondary 

analyses. Also, the mean of the 2004–06 model-averaged 

estimates of population size from the secondary analysis 

was 1,523, which is nearly identical to the estimate of 1,526 

from the main analysis. However, the inclusion of a sex 

effect in p in the secondary analysis resulted in a strongly 

skewed sex ratio in the subadult and adult components 

of the population (approximately 0.70 female). This was 

unrealistic, and largely an artifact of model structure. The 

CJS model that allowed for both sex-specificity in p and 

transience in φ for males, effectively estimated values of p

(and consequently N) that applied only to the males in the 

population that were considered “residents.” However, the 

delineation of “transients” versus “residents” was somewhat 

arbitrary, because it was a cumulative function of study 

duration, movement patterns, and other unknown phenomena. 

Furthermore, valid estimation of population size requires the 

assumption that estimated recapture probabilities apply to all 

animals in the population, which is clearly not the case here. 

In conclusion, the 2001–06 capture-recapture data suggested 

the potential for differences in movement patterns for males 

and females. Ultimately, these differences were beyond the 

ability of the data to resolve.

Appendix C. Secondary Capture-Recapture Analysis to Investigate a posteriori 

Hypotheses.

Appendix C 19
The bootstrap procedure that we used to estimate the 

variance in ˆNj also allowed us to investigate some statistical 

properties of the real parameter estimates, and of the model 

selection procedure. For survival, mean percent relative bias 

(PRB) was less than 1% between the model-averaged point 

estimates, and the mean values of the bootstrapped estimates. 

For population size, mean PRB was -1% between the 

model-averaged point estimates, and the mean values of the 

bootstrapped estimates. Mean PRB was 17% between 

SE( ˆNj) derived from the Laake estimator (Taylor and others, 

2002) for the low-QAIC model, and SE( ˆNj) estimated from 

the distribution of the model-averaged bootstrapped estimates. 

This suggests reasonable agreement between theoretical and 

simulation-based variance estimators. Finally, we found that 

model selection frequencies from the bootstrap procedure 

were similar to the QAIC weights for models with ∆QAIC 

≤ 7.0 (Burnham and Anderson, 2002) (table D1).

Appendix D. Statistical Properties of Parameter Estimates and the Model 

Selection Process

Table D1. Comparison between QAIC weights 

and bootstrapped model selection frequencies 

for the CJS models as defined in table B1.

No. QAIC weight Frequency

1 0.18 0.25

2 0.14 0.29

3 0.12 0.14

4 0.11 0.06

5 0.10 0.07

6 0.08 0.04

7 0.07 0.02

8 0.07 0.02

9 0.07 0.00

10 0.03 0.05

11 0.03 0.01

12 0.01 0.03

13 NA NA

14 NA NA

15 0.01 0.04

20 Polar Bear Population Status in the Southern Beaufort Sea
For more information concerning the research in this report, contact 

Director, Alaska Science Center

U.S. Geological Survey

1011 East Tudor Road

Anchorage, Alaska 99503

http://alaska.usgs.gov/
OFR 2006-1337 Regehr and others Polar Bear Population Status in the Southern Beaufort Sea