Estimating survival rates of black bears

Estimating survival rates of black bears

Vanessa A. Sorensen and Roger A. Powell

Abstract: Capture–recapture, radiotelemetry (on a monthly and a yearly basis), and age-distribution methods were usedto estimate annual survival rates for black bears (Ursus americanus) in the southern Appalachians from 1981 to 1996.Using capture–recapture data, the Jolly–Seber estimator calculated the annual survival rate for all bears over all yearsto be 0.64 ± 0.04 (mean ± SE). Because of small sample sizes, this method did not produce yearly estimates or allowseparation of the data into age or sex classes. Both the Kaplan–Meier estimator (using monthly telemetry data) and thepercent survival estimator (using yearly telemetry data) computed an overall annual survival rate of 0.76 ± 0.04.Survival rates for the early years of the study (1981–1987) were significantly lower than in the late years (1988–1996).No significant difference in survival rate was detected between the sexes or among age-classes. Because it is difficultto capture and recapture large numbers of animals, radiotelemetry methods are preferable for large mammals such asblack bears. If bears wear their collars for at least a year, calculating survival from yearly telemetry data provides agood estimate of bear survival. Using monthly telemetry data, however, provided the most detailed understanding ofbear survival. Survival estimates produced by the age-distribution method were unreliable.

Résumé: Diverses techniques, capture–recapture, radio-télémétrie (données mensuelles ou annuelles) et méthodesbasées sur la réapartition en fonction de l’âge, ont servi à estimer les taux annuels de survie des Ours noirs (Ursusamericanus) dans le sud des Appalaches de 1981 à 1996. Le coefficient de Jolly–Seber utilisé avec les données decapture–recapture a permis d’évaluer à 0,64 ± 0,04 (moyenne± erreur type) le taux annuel de survie pour tous les oursau cours de toutes les années d’étude. À cause de la petite taille des échantillons, cette méthode n’a pas permisd’obtenir des taux de survie chaque année ni de regrouper les données en classes d’âge ou de sexe. Le coefficient deKaplan–Meier utilisé avec les données mensuelles de radiotélémétrie et le coefficient du pourcentage de survie utiliséavec les données annuelles de télémétrie ont évalué le taux annuel de survie global à 0,76 ± 0,04. Les taux de survieau cours des premières années (1981–1987) ont été significativement plus faibles que ceux des années subséquentes(1988–1996). Il n’y avait pas de différence significative entre les classes d’âge ou entre mâles et femelles quant autaux annuel de survie. Comme la capture–recapture de grands nombres de ces animaux est une opération difficile, lesméthodes radio-télémétriques sont préférables dans le cas de gros mammifères comme l’ours noir. Si les ours portentleur collier durant 1 an, le calcul de leur survie à partir de données obtenues par télémétrie est une bonne estimation.Ce sont cependant les données mensuelles de télémétrie qui permettent de concevoir le plus en détails la survie desours. Les estimations obtenues par la méthode basée sur la répartition en fonction de l’âge ne sont pas précises.

[Traduit par la Rédaction] Sorensen and Powell 1343

Survival is an important demographic parameter used bywildlife managers to make decisions about harvest rates(Taylor et al. 1987; Miller 1990) and to elucidate populationtrends (Knight and Eberhardt 1985; Powell et al. 1996). Al-though vital for these decisions, survival rates are difficult toestimate for long-lived, secretive mammals that occur at lowdensities (Lindzey et al. 1988). An example of such a spe-cies is the North American black bear (Ursus americanus).The life histories of all members of the family Ursidae arecharacterized by late maturation, long intervals betweenbirths, small litter sizes, and high adult survival rates. Con-sequently, bear populations may be greatly affected byoverharvesting, and recovery from low population densitiesis often slow because of low rates of increase (Taylor et al.1987). The total population of black bears across NorthAmerica appears to be stable, but concern exists for popula-

tions in the southeast United States, many of which are oftenconfined to “islands” of forested public lands (Pelton 1982,1986; Neal 1990). Accurate estimates of survival rates areespecially important to ensure sound management of theseisolated populations, and insights into survival rates of thesepopulations may contribute to conservation of other endan-gered ursids.

Numerous statistical estimators have been developed forcalculating survival rates of wildlife populations, includingestimators that use band-return data (Brownie et al. 1985),mark–recapture data (Jolly 1965; Seber 1965; Pollock et al.1990; Lebreton et al. 1992), life-table data (Caughley 1977),and radiotelemetry data (Kaplan and Meier 1958; Trent andRongstad 1974; Heisey and Fuller 1985; and Pollock et al.1989a, 1989b). To obtain accurate estimates of survival, it isnecessary to understand the costs and benefits of each data-collection method and subsequent statistical method and tochoose the most appropriate procedure for a given situation.The advantages and disadvantages of the various methodshave been elucidated (Pollock et al. 1989a, 1990; Caughley1977), but comparisons between methods using empiricaldata are rare (Boutin and Krebs 1986), especially for largemammals. We used mark–recapture data (Jolly–Seber esti-

Can. J. Zool.76: 1335–1343 (1998) © 1998 NRC Canada

1335

Received September 18, 1997. Accepted February 23, 1998.

V.A. Sorensen and R.A. Powell.Department of Zoology,Box 7617, North Carolina State University, Raleigh,NC 27695, U.S.A. (e-mail: [email protected]).

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mator), monthly and yearly radiotelemetry data (Kaplan–Meier and percent-survival estimators), and age-at-capturedata (life-table analyses) to estimate survival rates of blackbears in the Pisgah National Forest of North Carolina from1981 to 1996. By comparing these methods we provide in-sight into which are the most practical and reliable.

The Jolly–Seber model yields estimators that use mark–recapture data from open populations. It estimates popula-tion size at each sampling time and estimates birth (plus im-migration) numbers and survival rates between samplingtimes. Survival-rate estimates are based on the ratios of theestimated numbers of marked animals at successive sam-pling times. Also, if emigration occurs, this method esti-mates the complement of mortality plus emigration, ratherthan survival.

The Jolly–Seber model requires the following assump-tions when estimating survival: (i) equal probability of cap-ture, (ii ) equal probability of survival for all marked animalsfrom one sampling time until the next, (iii ) permanence ofmarks, (iv) instantaneous sampling and release, and (v) noemigration (or if it occurs, all emigrants die). To extrapolateestimates from marked animals to a whole population, onemust assume that survival rates of marked and unmarked an-imals are equal.

Although commonly used to estimate animal locations,radiotelemetry also provides data for studying survival. Re-searchers typically locate individuals at regular intervals,which allows determination of animals’ fates. To estimatesurvival from telemetry data, a researcher must determine,for each location time, whether an animal is alive, dead, orout of radio contact (the animal is then considered “cen-sored”). Loss of contact includes transmitter failure, emigra-tion, and collar loss.

We used the staggered-entry Kaplan–Meier method to es-timate survival from monthly radiotelemetry data (Pollock etal. 1989a). Many of the statistical methods proposed for cal-culating survival using radiotelemetry data are modificationsof the Mayfield method for estimating nesting success andthey assume a constant survival rate during the whole periodof sampling (Mayfield 1961, 1975; Trent and Rongstad1974; Heisey and Fuller 1985). The Kaplan–Meier methodis more general and does not assume a constant survival rate(Bunck et al. 1995). This method yields a survival function,St, that is the probability of an individual surviving fortunits of time from the beginning of the study (Pollock et al.1989a). If hj is the probability of survival from timej – 1 totime j, given that it is alive atj – 1, then

[1] S htj

t

j==Π

1

The estimate of$St is obtained as the product of the esti-mated conditional probabilities of surviving for each timeunit. Large mammals (e.g., bears) are often difficult to trapand collar in large numbers at one time. To accommodatethis problem, Pollock et al. (1989a) proposed a staggered-entry design that allows gradual entry of animals into thestudy.

The staggered-entry Kaplan–Meier method assumes thefollowing: (i) random sampling of individuals, (ii ) independ-ent fates for all animals, (iii ) no influence of the radio tag on

survival, (iv) censoring unrelated to an animal’s fate,(v) homogeneous survival rates (newly tagged animals havethe same survival function as previously tagged animals),and (vi) animals present are located with probability 1. If ananimal is not located during a sampling period, it must becensored but added back to the risk group when locatedagain (Bunck et al. 1995).

Another statistical method that uses radiotelemetry datawhich is commonly employed to calculate annual survival iswhat we will call the percent-survival method. This methodis a simple ratio of those individuals that survive for oneyear to the total number of individuals present at the begin-ning of that year. For this method, censored animals aredropped from both the numerator and the denominator. Thismethod is analogous to the Kaplan–Meier estimator, but isapplied to annual rather than monthly tracking data. The as-sumptions of this method are (i) random sampling of indi-viduals, (ii ) independent fates for all animals, (iii ) noinfluence of the radio tag on survival, (iv) censoring not re-lated to animals’ fates, and (v) animals present are locatedwith probability 1.

Both radiotelemetry estimators also assume that the prob-ability of survival is equal for animals in all groups that arepooled.

Caughley (1977) presented several methods of estimatingsurvival from demographic data. A method once commonlyused (e.g., Tabor and Wight 1977; Dapson et al. 1979) calcu-lates survival from the standing age distribution of a popula-tion using the following equation:

[2] ,x = Sxe rx

where,x is survivorship to agex, Sx is the relative proportionof individuals of agex in the population (calculated so thatthe number of newborns is 1.00), andr is the intrinsic rateof increase in population size. The age-specific annual sur-vival rate, px, is then estimated as,x+1/,x. We refer to thismethod as the age-distribution method. This method as-sumes that the calculated age distribution is stable (constantage-specific survival and fecundity rates) and the populationsize is stable (r = 0). To calculate age distribution from trap-ping data requires the additional assumption that trappingsamples the population randomly.

This approach interested us particularly because the popu-lation of bears in this study met one of the assumptions thatis often difficult to meet in wild populations. Powell et al.(1992, 1996; unpublished data through 1996) found that theintrinsic rate of increase was not significantly different from0. Although the stability of the age distribution was un-known and sampling may not have been random, we won-dered if this simplistic approach could yield reasonableestimates for a population exhibiting overall stability over15 years.

Study areaWe collected data from a black bear population in the Pisgah

Bear Sanctuary and adjacent lands in the Pisgah National Forest,North Carolina, from 1981 to 1996, except for a hiatus in 1991 and1992. The sanctuary and the non-sanctuary area together totaledover 400 km2 in the southern Blue Ridge Mountains. Elevations

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1336 Can. J. Zool. Vol. 76, 1998



range from 650 to over 1800 m. The Blue Ridge Parkway (Na-tional Park Service) runs along Pisgah Ridge at approximately1500 m elevation. The area is managed for multiple use, includingtimber, wildlife, and recreation. Bear hunting is illegal within theSanctuary and along the Blue Ridge Parkway corridor (Powell etal. 1996, 1997). Bears roam in and out of the sanctuary at will.

Trapping and radiotelemetryWe livetrapped bears beginning in May and ending in June or

July. We used Aldrich foot snares modified for bear safety (John-son and Pelton 1980) or culvert traps, and immobilized the bearswith a combination of Ketaset (ca. 7 mg/kg) and Rompun (ca.3 1/2 mg/kg) (Cook 1984), administered with a jab stick or blow-gun. We tagged, tattooed, and measured bears and then extracted afirst upper premolar to estimate age. We also recorded the sex,body mass, and reproductive condition of each bear.

From 1981 to 1996, we trapped 151 bears 251 times and outfit-ted 112 with transmitters (Table 1). We used 5 types of transmit-ters. Before 1987, bears were fitted with Telonics 800-g motion-sensitive radio collars or ear-tag transmitters (Telonics Inc., Mesa,Arizona) broadcasting at 150–152 mHz. Motion-sensitive transmit-ters returned to the non-active pulse rate if activity did not occurwithin 5 min. From January 1987 through early June 1988, trans-mitters were removed from bears because poachers were using ra-diotelemetry to find bears (Powell et al. 1992). In August 1988,undercover enforcement officers arrested over 40 poachers in west-ern North Carolina, northern Georgia, and western Tennessee (Op-eration Smoky). Officers indicated that one female bear waspoached using telemetry (Powell et al. 1992). From June 1988through 1990, bears were outfitted with 900-g transponder collarsthat could be programmed to turn on and off at designated timesand transmitted on a previously unused frequency band not moni-tored by poachers. From 1993 to 1996, bears received eitherTelonics motion-sensitive breakaway collars or Lotek motion-sensitive collars. Bears were followed to their dens to change col-lars or to replace batteries whenever possible (Powell et al. 1992,1996, 1997)

We located radio-collared bears using a Telonics receiver (Mesa,Ariz.) and an eight-element Yagi antenna mounted on a truck, oron foot using a two- or three-element antenna. During 1981–1982and 1986–1996, bears were located at 2-h intervals for 8-h periodsstaggered to begin at 32-h intervals, as permitted by the trappingschedule. In 1983–1985, bears were located at 2-h intervals for

24 h at the beginning of each week and at 2-h intervals for 12 h atthe end of each week (Powell et al. 1996, 1997).

Jolly–Seber estimatorJolly–Seber mark–recapture analysis included all bears>1 year

old. Out of 251 total captures, 213 were suitable for analysis (outof 251 captures, 7 were cub captures and 31 were recaptures in thesame year) (Table 2). We analyzed capture data using the programJOLLY (Pollock et al. 1990), which uses the full Jolly–Seber model(model A, year-specific survival and capture probabilities) (Jolly1965; Seber 1965), as well as two modifications (Jolly 1982):model B (constant survival but year-specific capture probabilities)and model D (constant survival and capture probabilities). Ideally,JOLLY computes goodness-of-fit tests and tests between models thatallow the researcher to choose the most appropriate model. For ourstudy, however, neither model A nor model B produced reliable es-timates, owing to the lack of recaptures in some years. Model Dprovided one annual estimate of survival based on the assumptionthat survival was constant across all years. We also attempted touse model D to estimate survival in the early and late years. Wewere unable to calculate survival for the early years because thenumerical optimization procedure inJOLLY did not converge.

Kaplan–Meier estimatorWe used the staggered-entry Kaplan–Meier method (Pollock et

al. 1989a) to calculate survival rates on a monthly basis for bears≥1 year old. If a bear received and wore a collar for more than halfthe month, we added the bear at the beginning of the month. Other-wise it was added the next month. Also, if radio contact was lostduring the first half of the month, the bear was censored the previ-ous month. Survival was calculated on a monthly instead of aweekly basis for several reasons. Although attempts were made tolocate each bear weekly, not all bears were found each week. Also,because bears are long-lived we do not believe that the detailgained from a weekly estimate of survival rather than a monthlyestimate would appreciably change the annual estimate.

We included in the analysis all bears that wore transmitters andwe included censored animals in the risk group until the time ofsignal loss (Vangilder and Sheriff 1990). If we censored a bear in agiven month but found it again later, we counted it as censored andadded it back into the risk group at the appropriate time (Bunck etal. 1995). For some individuals there was strong evidence that cen-soring coincided with death, and these cases were counted asdeaths even though death was not actually documented (for exam-ple, when a bear was not reported as harvested but its cut collarwas found in the woods or river or found with a bullet hole in thetransmitter) (Powell et al. 1996). Treating strongly suspecteddeaths in this manner possibly produced a small negative bias inour estimates of survival from telemetry data (Powell et al. 1996).

We pooled data for all bears in all years to calculate an overallestimate of annual survival. Telemetry effort often varied from Jan-uary through May; consequently, we used only data collected dur-ing periods with weekly location effort. We further grouped databy the early years (1981–1987) and late years (1988–1996) of thestudy. Both groups included 7 years of data (no trapping or teleme-try occurred in 1991 and 1992) and we wished to learn whetherlaw-enforcement activity against poaching in 1988 affected sur-vival rates. (During all years, almost all mortality occurred duringfall. Arrests from Operation Smoky occurred in August 1988. Wetherefore analyzed 1998 data with the “late” years. Because telem-etry began on a regular basis in May in the late years, we used sur-vival estimates from May to December for comparisons betweenearly and late years.

Finally, we grouped data for analyses by sex and age class ofthe bears. We estimated annual survival (January–December) sepa-rately for males and females. Although we estimated age-class sur-

© 1998 NRC Canada

Sorensen and Powell 1337

YearNo. of bearsmonitored

No. ofdeaths Cause of death

1981 1–5 2 2 poached1982 5–12 3 2 poached, 1 legal kill1983 5–13 8 3 poached, 4 legal kills, 1

unknown1984 4–10 1 1 poached1985 7–16 4 4 poached1986 1–16 7 3 poached, 4 legal kills1987 2–4 1 1 legal kill1988 1–3 01989 4–7 01990 4–10 01993 6–10 1 1 poached1994 4–19 01995 12–23 01996 15–23 0

Table 1. Numbers of radio-tagged bears and causes of mortalityin North Carolina from 1981 to 1996.



vival rates using only data from May to December (June–December for 1-year-olds), we consider these to be age-specificannual survival rates (px) because we never recorded death for anybear from January to May (except the one bear poached usingtelemetry). We calculatedpx values for the early and late yearsand for each sex. We used log-rank tests to test for differences insurvival rates between the early and late years, between the sexes,among age-classes, and between the early and late years for eachsex (Pollock et al. 1989a). A z test was used to determine ifpx val-ues differed between the early and late years of the study or be-tween the sexes (Pollock et al. 1989a):

[3] zp p

p pi j

i j

=−+

$ $

$ $var var

Pollock et al. (1989a) proposed two methods for estimating thevariance of the survival estimate for the staggered-entry Kaplan–Meier method (Cox and Oakes 1984). We calculated both estimatesand only Greenwood’s (1926) formula produced a reliable estimate(the other method produced estimates of variance that were highlysensitive to the sample size in the last month). Thus, the varianceof all Kaplan–Meier estimates of survival was calculated as

[4] var ( $ ) ( $ )( )

S Sd

r r dt t

j

j j jj

t

=−=

∑2

1

where $St is the probability of survival to timet, dj is the number ofdeaths in monthj, and rj is the number of individuals at risk inmonth j.

Percent survival estimatorWe estimated age-specific annual survival rates by calculating

the proportion of radio-tagged bears surviving from each age to thenext, beginning at age 1 year. Only individuals that survived atleast to January of the following year were counted as survivors.The first partial year a bear wore a collar was included as “sur-vival.” This could produce a small positive bias because bears thatdied before trapping season in May and June would not be in-cluded in the analysis. Most bears (80%), however, wore their col-lars for more than half the first year and we never documented adeath before May (except the one bear poached using telemetry). If

a bear wore a transmitter but contact was lost before the end of De-cember, it was censored for that year. Again, individuals for whichstrong evidence indicated that being censored coincided with deathwere counted as dead. Powell et al. (1996) used this method to es-timate survival for the same bear population from 1981 through1990.

We calculated an overall estimate of annual survival by poolingall bears over all years. We also grouped data by early and lateyears and by sex and age class.

We calculated variances for all estimates by using the formulafor the variance of a binomial (Sokal and Rohlf 1981):

[5] var ( $)$( $)

SS S

n= −1

where $S is the estimated annual survival rate andn is the numberof bear years.

Age distribution estimatorWe estimated the age distribution,Sx, each year using capture

data.Sx is usually expressed as the number of animals in an age-class (Fx) relative to the number of newborns (F0): Sx = Fx/F0. WecalculatedSx for each year by counting the number of bears in eachage-class captured that year and averaged theSx values in order tocalculatepx. Because very few bears in age-class 0 were captured,Sx was calculated as the number of animals in an age-class (Fx) rel-ative to the number of 1-year-olds (F1): Sx = Fx/F1. This did not af-fect estimation ofpx.

From the annual bait station population index, Powell et al.(1992, 1996) calculated that the intrinsic rate of increase,r, wasnegative but not significantly different from 0 (SAS regression,testing for both linear and exponential relationship,P > 0.4 forboth tests). Ifr is known to be 0 (stationary population) and theage distribution is stable, then,x = Sx andpx can be calculated as

[6] pSS

xx

x

= +1

Using model D (which assumes constant survival andcatch probabilities), the Jolly–Seber estimate of annual sur-

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1338 Can. J. Zool. Vol. 76, 1998

1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1993 1994 1995 1996

1981 1 2 1 1 1 0 0 0 0 0 0 0 01982 0 0 0 0 0 0 0 0 0 0 0 01983 3 1 0 0 0 0 0 0 0 0 01984 4 4 1 1 0 1 0 0 0 01985 3 1 0 0 0 0 0 0 01986 0 2 0 0 1 0 0 01987 3 1 1 0 0 0 01988 4 1 1 0 1 01989 1 0 0 0 01990 1 2 1 11993 5 5 31994 2 11995 11996Caught 11 13 12 16 15 16 8 17 9 20 23 18 21 14Marked 0 1 2 4 6 8 2 6 5 4 3 7 9 6Unmarked 11 12 10 12 9 8 6 11 4 16 20 11 12 8Released 11 13 12 15 15 15 8 17 9 19 23 18 20 13

Table 2. Capture–recapture data for black bears in North Carolina from 1981 to 1996.



vival over all bears and all years was 0.62 ± 0.04 (estimate ±SE) and the estimate for the late years was 0.75 ± 0.06 (anestimate for the early years was not possible because ofsmall sample sizes during that time). Both estimates werelower than the Kaplan–Meier and percent-survival estimates,although the estimate for all years was not significantlylower. For all analyses, the Kaplan–Meier and straight-percentage estimates were very similar and did not differsignificantly (Table 3).

The Kaplan–Meier annual survival estimate of all bears inthe early years was significantly lower than for the late years(χ2 = 22.70, 1 df,P < 0.05) (Fig. 1). Survival rates were sig-nificantly lower in the early years for both sexes (females:χ2 = 15.84, 1 df,P < 0.05; males:χ2 = 8.33, 1 df,P < 0.05)and for bears aged 1 year (P = 0.019, df = 1), 3 years (P <0.001, df = 1), 4 years (P = 0.002, df = 1), and 6+ years (P <0.001, df = 1) (Table 3). No difference in survival was foundbetween males and females (χ2 = 0.66, 1 df, P > 0.05)(Fig. 2), among age-classes (χ2 = 1.47, 1 df,P > 0.05) (Ta-ble 3), or between the sexes in a given age-class (P > 0.05,df = 1) (Table 3).

The age-distribution method did not yield valid estimatesof annual survival. Estimates of survival rates by age-classwere as follows: 1.04 for 1-year-olds; 0.61 for 2-year-olds;0.66 for 3-year-olds; 0.52 for 4-year-olds; 0.5 for 5-year-olds; 1.33 for 6-year-olds; 0.75 for 7-year-olds; 0.83 for 8-year-olds; and 0.20 for 9-year-olds. The estimate of the sur-vival of yearlings and 6-year-olds exceeded 1.0 because wecaptured fewer 1-year-olds than 2-year-olds and fewer 6-year-olds than 7-year-olds. Thus, the age distribution of ourpopulation may not have been stable, or sample sizes mayhave been too small and nonrandom.

Comparison of survival estimatorsIf a researcher is interested in estimating survival, two

questions must be considered. First, what is the most effi-cient method of data collection? For black bears, there arecosts and benefits of capture–recapture and ratiotelemetrymethods for estimating survival. The main benefit ofcapture–recapture is that it does not require any time to beexpended in monitoring. The large amount of capture–recapture data required for estimating survival, however,greatly decreases the potential use of this method for largemammals such as the black bear. Using capture–recapturemethods we were unable to compare survival between thesexes, age-classes, and early and late years, owing to small

© 1998 NRC Canada


px (mean± SE)

Jolly–Seberestimator

Kaplan–Meierestimator

% survivalestimator

All yearsa 0.64±0.04 0.76±0.04 0.76±0.04Early years

(1981–1987)b,c*0.58±0.07 0.59±0.06

Late years (1988–1996)b

0.74±0.06 0.98±0.02 0.98±0.02

Femalesa 0.73±0.06 0.73±0.06Malesa 0.78±0.06 0.78±0.06Femalesb*

Early years 0.48±0.10 0.50±0.09Late years 0.97±0.03 0.96±0.04

Malesb*


1-year-olds (p1)d 0.80±0.10 0.77±0.12

2-year-olds (p2)b 0.82±0.07 0.80±0.08

3-year-olds (p3)b 0.64±0.12 0.71±0.10

4-year-olds (p4)b 0.73±0.12 0.69±0.13

5-year-olds (p5)b 0.90±0.09 0.88±0.12

6+-year-olds (p6)b 0.77±0.08 0.77±0.08

1-year-olds (p1)d*


2-year-olds (p2)b


3-year-olds (p3)b*


4-year-olds (p4)b*


5-year-olds (p5)b


6+-year-olds (p6)b*


1-year-olds (p1)d

Females 0.83±0.15 0.71±0.18Males 0.77±0.14 0.71±0.17

2-year-olds (p2)b

Females 0.76±0.12 0.77±0.12Males 0.88±0.08 0.83±0.11

3-year-olds (p3)b

Females 0.73±0.14 0.80±0.12Males 0.62±0.16 0.64±0.15

4-year-olds (p4)b

Females 0.75±0.15 0.71±0.17Males 0.67±0.19 0.67±0.19

5-year-olds (p5)b

Females 0.80±0.18 0.75±0.22Males 1.00 ±0.00 1.00±0.00

6+-year-olds (p6)b

Females 0.67±0.12 0.67±0.12

Table 3. Annual survival estimates for black bears in NorthCarolina from 1981 to 1996.

px (mean± SE)

Jolly–Seberestimator

Kaplan–Meierestimator

% survivalestimator

Males 0.88±0.08 0.87±0.09aEstimated survival from January to December.bEstimated survival from May to December.cSurvival rate could not be calculated because the numerical

optimization procedure inJOLLY did not converge.dEstimated survival from June to December.*Significant difference between Kaplan–Meier estimates.

Table 3 (concluded).



numbers of recaptures. The main costs of using radiotelemetryare the initial expense of tracking equipment and the timeassociated with tracking. However, telemetry allows one toestimate survival and make comparisons with data on fewerindividuals than are needed for capture–recapture. Many lo-cations are possible at a low cost per location compared withthe cost per capture for mark–recapture methods.

Another important factor when considering how to collectdata is sampling frequency. Although sampling on a monthlyversus a yearly basis did not affect survival estimates in thisstudy, sampling frequency has the potential to bias estimatesof survival rates. Both the Kaplan–Meier (for which we usedmonthly telemetry data) and the percent-survival (for whichwe used annual telemetry data) methods divided the numberof deaths by the number of animals at risk, but estimates us-ing yearly data had smaller annual sample sizes because ofloss of contact with bears before the end of the year. For in-stance, if a bear wore a transmitter from May through Au-

gust but then dropped it in September, the Kaplan–Meiermethod would include this bear in the risk group for thesemonths, while the percent-survival method would censor thebear for the entire year. Although this type of censoring didnot greatly affect the survival estimate in this study, if sam-ple sizes are small, owing to censoring, and mortalities arecommon, a negative bias could result. Sampling on a yearlybasis provides only annual estimates of survival, whereasmonthly sampling yields a more detailed understanding ofsurvival throughout the year. An advantage of sampling on ayearly basis, however, is that estimates are relatively easy tocompute and yearly sampling requires less telemetry effortthan does monthly sampling. In addition, the estimates pro-duced using yearly data are not sensitive to small monthlysample sizes.

The second question a researcher interested in estimatingsurvival must consider is how the estimators appropriate foreach data-collection method perform? When comparing the

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1340 Can. J. Zool. Vol. 76, 1998

Fig. 1. Cumulative monthly estimates of survivorship using the staggered-entry Kaplan–Meier method for black bears radio-tagged inNorth Carolina from 1981 to 1987 (early years) and from 1988 to 1996 (late years). Vertical bars show the standard error.

Fig. 2. Cumulative monthly estimates of survivorship using the staggered-entry Kaplan–Meier method for female and male black bearsradio-tagged in North Carolina from 1981 to 1996. Vertical bars show the standard error.



utility of several survival estimators, it is necessary to under-stand the assumptions of each method and how violation ofthese assumptions might affect estimates. The assumptionthat emigration does not occur, which is required for Jolly–Seber estimates of survival, was violated, and violation ofthis assumption leads to underestimation of survival (thisstudy; snowshoe hares, Boutin and Krebs 1986; polar bears,Derocher and Stirling 1995). Survival is underestimated un-less it can be assumed that emigration is negligible or allemigrants die (Pollock et al. 1990). In this study, however,bears were free to leave the study area and we know fromharvest records that many survived for many years. There-fore, the Jolly–Seber estimate of annual survival was nega-tively biased.

In our study, the only model inJOLLY that produced an es-timate of survival assumed constant capture probability andconstant survival for the duration of the study. Carothers(1973, 1979) suggested that the Jolly–Seber method wasfairly robust to heterogeneous capture probabilities and thatheterogeneity produced only a small negative bias. Violationof the assumption of constant survival, however, probablyhad a large effect on the survival estimate in this study. TheKaplan–Meier method showed that the survival rate waslower during the first half of the study than during the sec-ond. Thus, the estimate produced by Jolly–Seber model Dfor the entire period should be interpreted with caution.

The assumptions of both radiotelemetry methods weresimilar, and the following four were particularly importantto our study. First is the assumption of equal survival for allgroups pooled. Although we found no differences betweenthe sexes or among age-classes, our sample sizes may havebeen too small to allow differences to be detected. In addi-tion, survival differed between the early and late years of thestudy, potentially biasing estimates that pooled data from theearly and late years. Second, the assumption that a transmit-ter does not influence survival was known to have been vio-lated for one bear. During Operation Smoky, one female waspoached using telemetry but at most only two additionalbears could have been poached in this way (Powell et al.1992). This violation gave our survival estimates a negligi-ble negative bias. Third, we assumed random sampling ofbears in the study area. If sampling was not random, sur-vival estimates were biased towards survival of that categorywhich was sampled more often. In addition, our methodswere more likely to sample bears inside than outside theSanctuary. Powell et al. (1992, 1996) found that bears out-side the Sanctuary had lower survival rates than bears resi-dent within it. Thus, our results likely overestimate survivalof bears in the region. Finally, censoring may not have beenindependent of survival. Because bears that emigrated out-side the Sanctuary were more likely to be censored and be-cause bears outside the Sanctuary had lower survivorshipthan bears resident in the Sanctuary (Powell et al. 1992,1996), our survival estimates may have had a positive bias.

Overall, the assumptions of the estimators using radio-telemetry versus capture–recapture data were fairly similar.Both assumed random sampling, no influence of the mark orcollar on survival, and equal probability of survival fornewly and previously marked animals. Several of the as-sumptions that differed, however, were those that were vio-lated, and herein lies the most important comparison. The

most problematic assumption for the estimators using telem-etry data was that censoring, generally caused by transmitterfailure or emigration, should be unrelated to an animal’sfate. Using the Jolly–Seber model to estimate survival re-quired the assumption that emigration did not occur. Thus,when using an estimator that uses telemetry data, one mustassume equal survival only for bears that do and do not emi-grate, whereas when using the Jolly–Seber estimator, onemust assume that the survival rate for all bears which emi-grate is 0. The latter assumption is not realistic.

The results obtained using the age-distribution methodshow that this method is suspect, even when the overall pop-ulation growth rate is 0, as in our study. Researchers mustverify that the estimated age distribution is stable, otherwisethis method can produce wildly inaccurate results. We cau-tion against using this method when the stability of the agedistribution is unknown. This method is also highly depend-ent upon the assumption of random sampling, which maynot have been met in this study. If the age distribution wasknown to be stable and nonrandom sampling was the causeof survival rates greater than 1, the problem could be cor-rected provided the extent of sampling bias for certain age-classes was known. We explored methods of eliminatingcapture bias in the hope of alleviating problems of samplingerror on our estimates of age distribution. We attempted touse a minimum number alive approach (Krebs 1966; Hilbornet al. 1976) to reconstruct the age distribution of the popula-tion for each year. To do this we included bears we knew tobe alive in the study area, owing to capture at a later date,and bears wearing collars that were not captured. Thismethod produced age distributions with extreme bias. In-cluding bears known to be in the study area because theywere captured at later dates led to underestimation of sur-vival, while including bears known to be alive because theywore transmitters caused overestimation of survival.

Overall, radiotelemetry methods allowed estimation andcomparisons of survival rates with data on fewer individualsthan are needed for capture–recapture methods. If telemetrydata can be collected on a regular (monthly) basis, and if aresearcher is interested in the distribution of mortality withinthe year, then monthly sampling yields the most detailed un-derstanding of annual survival. If, however, the researcher isonly interested in annual estimates of survival and truncationof data is not great (i.e., most surviving animals wear theirtransmitters for more than a year), then annual sampling pro-vides accurate survival estimates using fewer tracking occa-sions. The assumption that emigration does not occur, whichis required by the Jolly–Seber estimator in order to calculatesurvival, was more restrictive than assumptions for estima-tors that used radiotelemetry data.

Survival of Pisgah bearsThe difference in survival between the early and late years

is striking and suggests that management practices (Opera-tion Smoky) had an important impact and increased the sur-vival of bears. The main sources of mortality for bears in thestudy area were hunting and poaching (Powell et al. 1992,1996). Most bears were trapped inside the Pisgah Bear Sanc-tuary. Nevertheless, many were harvested legally outside theSanctuary and many were poached both inside and outsidethe Sanctuary. Poaching decreased markedly after 1988. The

© 1998 NRC Canada




lack of differences in survival between the sexes and amongage-classes, estimated using the Kaplan–Meier method, sug-gests that hunting and poaching were not sex- or age-specific and appears to contradict the idea that males aged1–3 years often have relatively low survival rates as theydisperse (Jonkel and Cowan 1971; Elowe and Dodge 1989).If young males in our study area dispersed long distances, sothat we failed to find them using telemetry, we counted themas censored in our analyses. Consequently, our estimate ofp1 for males is actually an estimate of the annual survivalrate of yearlings that remained in the study area, and any ef-fect of dispersal on survival would be difficult to detect. Thelack of differences in survival between the sexes and amongage-classes may also be due to small sample sizes.

Powell et al. (1996) estimated age-specific annual survivalrates for the same population from 1981 through 1990 usingthe percent-survival method. Their survival estimates werelower, consistent with our results, which show that survivalimproved in the later years of the study. Powell et al. (1996)also used Monte Carlo analyses of Leslie matrices to suggestthat the bear population in the Sanctuary would be stableonly if cub survival was greater than 0.7. Using the survivalestimates from this study, this value is now 0.6. Carrel(1994) recently found almost exactly this value for survivalof cubs in Arizona (p0 = 0.62).

Future researchTo improve our understanding of the demography of bear

populations, further research is needed on cub survival(Jonkel and Cowan 1971; Bunnell and Tait 1985; Elowe andDodge 1989; LeCount 1987; Powell et al. 1996), whichPowell et al. (1996) found to have the greatest effect on pop-ulation growth of bears in Pisgah National Forest. Future re-search must also assess survival of young males, who oftendisperse long distances. Knowledge about survival of dis-persing males is important for understanding the genetic di-versity of small subpopulations and for modelingmetapopulation dynamics. Finally, estimates of both cub andyearling survival are needed to produce accurate life tablesfor black bears.

We thank Mike Fritz, Peggy Horner, Adrienne Kovach,Mike Mitchell, John Noel, Erran Seaman, Gordon Warbur-ton, and John Zimmerman, who, as graduate students,helped collect telemetry data on black bears. We also thanknumerous student interns, volunteers, and approximately 300Earthwatch volunteers who assisted with fieldwork. CavellBrownie, Ted Simons, Ken Pollock, Jim Gilliam, GeorgeFarnsworth, and two anonymous reviewers provided con-structive comments. Financial and logistic support was pro-vided by Robert Bacon, Joseph Bussen, Citibank Corp.,Earthwatch, Federal Aid in Wildlife Restoration Project W-57 administered through the North Carolina Wildlife Re-source Commission, the Geraldine R. Dodge Foundation, theInternational Association for Bear Research and Manage-ment, Ginger and Dick King, the Max McGraw WildlifeFoundation, McIntire Stennis funds, the National Geo-graphic Society, the National Park Service, the National Ri-fle Association, the North Carolina Agricultural Research

Service, North Carolina State University, Port Clyde andStinson Canning Companies, 3M Co., the U.S. Forest Ser-vice, the Wildlands Research Institute, Wil-Burt Corp., andWildlink, Inc.

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Estimating survival rates of black bears