Evaluating the demographic buffering hypothesis with

vital rates estimated forWeddell seals from 30 years of

mark–recapture data

Jay J. Rotella1*,WilliamA. Link2, Thierry Chambert1, Glenn E. Stauffer1 andRobert A. Garrott1

1Department of Ecology, Montana State University, Bozeman,MT 59717, USA; and 2U.S. Geological Survey, Patuxent

Wildlife Research Center, MD 20708, USA

Summary

1. Life-history theory predicts that those vital rates that make larger contributions to population

growth rate ought to be more strongly buffered against environmental variability than are those

that are less important. Despite the importance of the theory for predicting demographic responses

to changes in the environment, it is not yet known how pervasive demographic buffering is in ani-

mal populations because the validity of most existing studies has been called into question because

of methodological deficiencies.

2. We tested for demographic buffering in the southern-most breeding mammal population in the

world using data collected from 5558 known-age female Weddell seals over 30 years. We first esti-

mated all vital rates simultaneously with mark–recapture analysis and then estimated process

variance and covariance in those rates using a hierarchical Bayesian approach. We next calculated

the population growth rate’s sensitivity to changes in each of the vital rates and tested for evidence

of demographic buffering by comparing properly scaled values of sensitivity and process variance

in vital rates.

3. We found evidence of positive process covariance between vital rates, which indicates that all

vital rates are affected in the same direction by changes in annual environment. Despite the positive

correlations, we found strong evidence that demographic buffering occurred through reductions in

variation in the vital rates to which population growth rate was most sensitive. Process variation in

vital rates was inversely related to sensitivity measures such that variation was greatest in breeding

probabilities, intermediate for survival rates of young animals and lowest for survival rates of older

animals.

4. Our work contributes to a small but growing set of studies that have used rigorous methods on

long-term, detailed data to investigate demographic responses to environmental variation. The

information from these studies improves our understanding of life-history evolution in stochastic

environments and provides useful information for predicting population responses to future envi-

ronmental change. Our results for an Antarctic apex predator also provide useful baselines from a

marine ecosystem when its top- and middle-trophic levels were not substantially impacted by

human activity.

Key-words: demography, environmental canalization,Leptonychotes weddellii, marinemammal,

pinniped, population dynamics

Introduction

Theory predicts that variation in a population’s annual

growth rate (k) will typically increase extinction probability

(Lewontin & Cohen 1969). In perennial organisms, k varies

because vital rates vary and covary. However, different vital

rates make different contributions to k; and thus, similar

degrees of temporal variation in different vital rates are

expected to induce different consequences for variation in the

annual multiplication rate of a lineage (Morris & Doak

2004). Accordingly, Pfister (1998) and Gaillard et al. (2000)

developed the demographic buffering hypothesis: life histo-

ries should evolve to minimize the effects of environmental

variation on fitness by favouring traits that buffer important*Correspondence author. E-mail: rotella@montana.edu

Journal of Animal Ecology 2012, 81, 162–173 doi: 10.1111/j.1365-2656.2011.01902.x

� 2011TheAuthors. Journal of Animal Ecology � 2011 British Ecological Society

vital rates from temporal environmental variation. In long-

lived iteroparous species with delayed maturity, analyses of

data from a variety of turtles, birds and ungulates have

shown that changes in adult survival rate cause greater varia-

tion in k than do changes in juvenile survival or reproduction

(Heppell 1998; Pfister 1998; Gaillard, Festa-Bianchet &

Yoccoz 1998; Gaillard et al. 2000; Sæther & Bakke 2000;

Reid et al. 2004; Jenouvrier et al. 2005). Given this informa-

tion on which vital rates have the greatest potential impact

on k, the demographic buffering hypothesis predicts that, for

long-lived animals, environmental variation should have the

least effect on adult survival and greater impacts on repro-

duction and survival of younger animals.

Recent research has, however, shown that life-history evo-

lution in stochastic environments might be more complex

than previously hypothesized (Boyce et al. 2006). Empirical

results from a rigorous, 17-year study of a long-lived seabird

indicated that the vital rate to which kwasmost sensitive was

not the vital rate with the lowest temporal process variation

(Doherty et al. 2004). Several explanations have now been

put forth for why demographic buffering is not always

expected. Negative covariation between vital rates can, under

some circumstances, actually lead to selection for variation in

some parameters (Doak et al. 2005). Further, nonlinear rela-

tionships between vital rates and environmental conditions

can promote demographic lability rather than buffering

under certain conditions (Koons et al. 2009).

Another difficulty in evaluating the empirical support for

demographic buffering hypothesis relates to approach.

Doherty et al. (2004) noted three deficiencies in the methods

employed for much of the work performed on the demo-

graphic buffering hypothesis: (i) estimates of vital rates might

be biased because they did not account for detection proba-

bility, (ii) biological process variation and sampling variation

were not distinguished and partitioned and (iii) measures of

k’s response to changes in vital rates might not have been

properly scaled, especially for vital rates such as survival rates

and breeding probabilities that are bounded between 0 and 1.

Morris & Doak (2004) emphasized that proper analyses

require estimates of vital rates whereas many studies to date,

including foundational work by Pfister (1998), have not had

access to the requisite data and therefore relied on less-desir-

able alternatives. Finally, as shown by Coulson, Gaillard &

Festa-Bianchet (2005) and Doak et al. (2005), covariation

between vital rates can have important implications, but it

has largely been ignored in past work.

There is clearly a need for further empirical studies of the

demographic buffering hypothesis. By implementing

advanced estimation methods on data from long-term stud-

ies, we can improve our understanding of life-history evolu-

tion in variable environments. Such understanding has

important theoretical and applied implications (Boyce et al.

2006; Tuljapurkar, Gaillard & Coulson 2009; Nevoux,

Weimerskirch & Barbraud 2010). Accordingly, several recent

studies have addressed the topic using long-term data and at

least some of the suggestions for improved analyses (e.g.

Altwegg, Schaub & Roulin 2007; Forcada, Trathan &

Murphy 2008; Frederiksen et al. 2008; Karell et al. 2009).

However, more such studies are needed, especially across

diverse taxa and life histories (Koons et al. 2009; van de Pol

et al. 2010).

Data collected to date on the Erebus Bay population of

Weddell seals (Leptonychotes weddellii Lesson) provide an

excellent opportunity to investigate demographic buffering

in a long-lived mammal in a variable environment. This

southern-most population of breeding mammal has been the

subject of an on-going mark–resight research program since

1968 (Stirling 1969; Siniff et al. 1977) and contains a large

number and proportion of known-age animals for which

annual rates of survival and reproduction can be estimated

(Hadley et al. 2006; Hadley, Rotella &Garrott 2007). Recent

analyses indicate that survival rates and breeding probabili-

ties vary not only by age and breeding state, but also among

years. Recent advances in hierarchical modelling (Link &

Barker 2010) now make it possible to estimate process varia-

tion and covariation among the population’s vital rates with

all rates being estimated simultaneously from a multi-decade

data set. Accordingly, we conducted this study to evaluate

the empirical support for the demographic buffering

hypothesis while employing recent suggestions for improved

analyses (Link & Doherty 2002; Doherty et al. 2004; Morris

& Doak 2004; Doak et al. 2005). We used rigorous estimates

of all vital rates and their process variation and covariation

as well as properly scaledmeasures of k’s response to changesin vital rates in our evaluation.

Materials andmethods

STUDY AREA AND POPULATION

The study population occupies Erebus Bay, located in the western

Ross Sea, Antarctica ()77Æ62� to )77Æ87�S, 166Æ3� to 167Æ0�E; seeCameron & Siniff 2004 for details). Each spring, c. 10 pupping colo-

nies form along perennial cracks in the sea ice created by tidal move-

ment of fast ice against land or glacial ice. Females generally have

their first pup at about 7 years of age and have a pup in two of every

3–4 years thereafter (Hadley et al. 2006; Hadley, Rotella & Garrott

2007). Pupping occurs on the fast ice surface from late October to

November (Stirling 1969).Mothers and pups are highly visible on the

ice, typically close to one another and spend much of their time

hauled out on the sea ice, especially in the few weeks immediately

following birth. Females who have not yet had a pup (pre-breeders)

or those who are skipping pupping also haul out in the study area

each year and are readily visible.

DATA COLLECTION

Weddell seals have been individually marked and resighted in

Erebus Bay annually since 1968 (Siniff et al. 1977). The majority

of the tagging effort occurred from approximately 15 October to

15 November each year, during parturition when colonies were

visited every few days to tag new-born pups. Beginning in early

November, 6–8 resighting surveys were performed every 3–5 days

each year. Seals could be readily approached within 0Æ5 m, such

that observers were able to read tags on all resighted animals.

Nearly all females that use the study area during the pupping

Demographic buffering inWeddell seals 163

� 2011 TheAuthors. Journal ofAnimal Ecology� 2011 British Ecological Society, Journal of Animal Ecology, 81, 162–173

season are detected at least once during annual surveys (Rotella

et al. 2009). High fidelity to breeding colonies (Cameron et al.

2007) and high recapture rates (Hadley et al. 2006) allow con-

struction of comprehensive encounter histories that include

annual breeding state for each marked animal.

DATA ANALYSIS OVERVIEW

The analysis consisted of four major components: (i) estimation of

vital rates with a mark–recapture analysis of data collected over

30 years, (ii) hierarchical modelling of mark–recapture estimates

to decompose variances and develop estimates of mean vital rates

and process variance–covariance of vital rates, (iii) matrix model-

ling of the vital rates to estimate population growth rate’s sensitiv-

ity to changes in vital rates and (iv) evaluation of the

demographic buffering hypothesis through comparisons of process

variation in vital rates and sensitivity values. Mark–recapture

modelling of annual vital rates was performed with a multi-state

model (Williams, Nichols & Conroy 2002), and subsequent hierar-

chical modelling was performed with a Bayesian approach. Our

evaluation of the demographic buffering hypothesis incorporated

a variety of recent suggestions for improving investigations of the

hypothesis. In particular, we (i) conducted all analyses at the level

of the vital rates rather than matrix elements (Morris & Doak

2004), (ii) estimated all vital rates from a single, long-term study,

which allowed us to have rigorous estimates of process variance–

covariance (Doak et al. 2005) and (iii) used variance-stabilized

measures of sensitivity (Link & Doherty 2002).

MARK–RECAPTURE MODELL ING OF VITAL RATES

We conducted multi-state capture–recapture analysis that (i) took

advantage of Hadley et al.’s (2006) and Hadley, Rotella & Gar-

rott’s (2007) modelling results for annual rates of apparent sur-

vival, recruitment and breeding for female seals during 1979–2003

and (ii) incorporated data from an additional 5 years. Hadley

et al. (2006) provided strong evidence of annual variation in sur-

vival and recruitment rates for pre-breeding females of different

ages. However, annual variation in breeding probabilities for

females that had already recruited to the pup-producing portion

of the population was ignored by Hadley et al. (2006) and evalu-

ated in a subsequent analyses that used data only from recruited

females (Hadley, Rotella & Garrott 2007). Thus, both previous

analyses evaluated a variety of possible sources of variation in

vital rates, but neither considered all of the data simultaneously.

Accordingly, analyses have not yet evaluated whether vital rates

for pre-breeders and recruited females might covary annually,

which is a distinct possibility given that c. 62–87% of pre-breeders

and recruited females are typically present in the study area dur-

ing the pup-rearing season and thus experience the same environ-

mental conditions for at least part of the year (Hadley et al. 2006;

Rotella et al. 2009). In the analyses reported here, we used data

from 30 years to evaluate several combinations of multi-state

model structures identified by Hadley et al. (2006) as useful for

pre-breeders and by Hadley, Rotella & Garrott (2007) for

recruited females to investigate possible covariation in vital rates

for pre-breeders and recruited females. All analyses were per-

formed in program MARK (White & Burnham 1999).

The multi-state model included three types of parameters: appar-

ent survival probability (/), capture probability (p) and conditional

transition probability (wrs) between any pair of states r and s. We

considered four breeding states: pre-breeder (P), first-time mother

(F), experienced mother (E) and skip breeder (S). We were able to

identify these states accurately for females in our study population

because detection rate for mother–pup pairs is 1Æ0 (Hadley et al.

2006). Within each state, we used the same age and ⁄ or experienceclasses as those found by Hadley et al. (2006) and Hadley, Rotella &

Garrott (2007) to be most parsimonious among a variety of potential

classes and age-related patterns in rates for fixed-effects-only multi-

state models. For females in state P, we used three age classes for /(pups, yearlings, ‡2 years old); 4 age classes for p (1, 2, 3–6 and

‡7 years old); and 7 age classes for w (5, 6, …, 10, ‡11 years old). For

females in states F or E, we ignored age and breeding experience

whenmodelling/ and p (each rate was constrained to be the same for

all active mothers within a year), but we allowed w to differ by state

(but not age). For females in state S, we ignored age and breeding

experience. When modelling w, our primary interest was in estimat-

ing breeding probabilities for females that survived from year t to

t + 1, i.e. given a female’s breeding state in year t, we were interested

in her probability of being in a pup-producing state (F or E) in year

t + 1 given that she survived to year t + 1. Thus, we used parame-

terizations that estimated the following transitions directly: (i)

wPage classFt (probability that a pre-breeder of a given age class in year t

will have her first pup in year t + 1; varies by year and age classes

within P), (iii) wFEt (probability that a female that had her first pup in

year t will have another pup in year t + 1; varies by year), (iii) wEEt

(probability that a female that produced a pup in year t and at least

once before will have another pup in year t + 1; varies by year) and

(iv) wSEt (probability that a female that had a pup prior to year t but

not in year t will produce a pup in year t + 1; varies by year). From

any state, only two transitions were possible (e.g. for females in state

P, wPF and wPP were possible but wPE and wPS were not), so the two

impossible transitions were assigned probability zero in analyses [see

Appendix S1 (Supporting information) for further details of

capture–recapture analyses].

HIERARCHICAL MODELL ING OF MARK–RECAPTURE

ESTIMATES

Having selected a multi-state model from a set of candidate models

and having evaluated its fit by the data and found it satisfactory, we

proceeded with inference conditional on this model. Such inference is

often limited to what can be learned by interval estimation, either of

model parameters or of functions of model parameters, and is based

on the assumption that the sampling distribution of the maximum

likelihood estimator is multivariate normal with variance matrix R

given by the inverse of the estimated information matrix. Writing b

for the vector of parameters describing the selected model and b for

the maximum likelihood estimates (MLE), this asymptotic sampling

distribution is designated as ½bjb� ¼ Nkðb;RÞ, where k is the dimen-

sion of b.

The assumption of asymptotic normality of the MLE can be used

for more than interval estimation: we used it for Bayesian analysis of

a hierarchical extension of the multi-state model. We first describe a

hierarchical model for parameters of the multi-state model using

probability distributions [b|X], where X is a vector of hyperparame-

ters. Combining the specified sampling distribution, the hierarchical

structure and a prior [X], Bayesian analysis is based on the posterior

distribution

½b;Xjb� / ½bjb�½bjX�½X�:

Thus, given the sampling distribution assumption ½bjb� ¼ Nkðb;RÞ,wecan investigate the hierarchical structure [b|X] using theMLE b as data.

164 J. J. Rotella et al.

� 2011 TheAuthors. Journal ofAnimal Ecology� 2011British Ecological Society, Journal of Animal Ecology, 81, 162–173

We describe the hierarchical model considered subsequently, not-

ing for now that it involvedmeans, precisions and correlation param-

eters; these were assigned diffuse normal, diffuse gamma and

uniform priors, respectively.

We approximated the posterior distribution for the parameters of

interest using Markov Chain Monte Carlo (MCMC) simulations in

OpenBugs (Lunn et al. 2009) with four chains of length 125 000; each

was startedwith different initial values, and values were stored after a

burn-in of length 500.We calculated the Gelman–Rubin convergence

statistic, as modified by Brooks & Gelman (1998) after 20 000 steps

were completed for each chain. No thinning was performed.

We evaluated Monte Carlo error by calculating the standard devi-

ation of mean values for each parameter among four independent

chains, which was then used to calculate the precision of the MCMC

sampling (1:96 sd=ffiffiffi4p

). We summarized attributes of the posterior

samples using the base packages in program r version 2.11.0 (R

Development Core Team 2010).

Hierarchical modelling not only allows the evaluation of process

variances and covariances, but also yields improved estimation of the

multi-state model parameters via shrinkage. We measured gains in

precision as GP = 100% (1 ) Posterior variance ⁄ Squared standard

error). For example, if GP = 25%, the posterior variance is 25%

smaller than the sampling variance of the MLE (squared standard

error).

The top-ranked multi-state model had additive effects of year and

factor level on the logit scale for survival rates / and transition prob-

abilities w. We designate the parameters estimated in program

MARKby a vector b, and theirMLEs are b.

Our hierarchical model for b begins with a latent vector

h ¼ ðe/1979; . . . ; e/

2007; ew1979; . . . ; ew

2007; a/1 ; . . . ; a/

5 ; aw1 ; . . . ; aw

11Þ0

in which e/yrand ew

yr are 29 potential year effects on survival

and transition probabilities, respectively. We note that few

marked animals early in the study combined with a minimum

age of first reproduction of 4 years of age prevented us from

obtaining MLEs of survival until 1980 and of transition proba-

bilities until 1984. The a/1 ; . . . ; a/

5 are factor-level effects on sur-

vival, and aw1 ; . . . ; aw

11 are factor-level effects on transition

probabilities. The five factor levels for survival were baseline sur-

vival for pups, yearlings, pre-breeders ‡2 years old, active moth-

ers and skip breeders. The 11 factor levels for transitions were

baseline probabilities of first reproduction for 8 age classes of

pre-breeders (ages 4, 5, …, 10 and ‡11 years old) and baseline

breeding probabilities for females in states F, E and S. We write

h � N74(074, R) and modelled it as a 74-dimension mean-zero

multivariate normal random variable with covariance matrix

R ¼r2

/I29 r/rwC29�29 029�16r/rwC

029�29 r2

wI29 029�16016�29 016�29 1000I16

24

3574�74

;

where bold zeros indicate matrices of zeros of specified dimension,

bold Is denote identitymatrices of specified dimensions and

C ¼

0 q 0 � � � 0

0 0 q . .. ..

.

0 0 0 . ..

0... ..

. ... . .

.q

0 0 0 � � � 0

26666664

3777777529�29

:

Parameter q on the superdiagonal of C is the correlation between

year effects on survival from year t to t + 1 and breeding probabili-

ties in year t + 1.We expected that this correlation might be positive

for the following reasons. Female Weddell seals depend heavily on a

capital breeding strategy and incur reproductive costs (Hadley,

Rotella & Garrott 2007). Further, evidence suggests that maternal

parturition mass varies with environmental conditions and is related

to offspring survival (Wheatley et al. 2006; Proffitt et al. 2007a, b;

Proffitt, Garrott & Rotella 2008). Thus, as has been shown in other

capital-breeding seals (Boyd 2000), decisions about whether or not to

produce a pup in a given year ought to be condition dependent and

vary annually. Embryos are implanted in the summer (Stirling 1969),

and gestation occurs throughout the winter, which might be a chal-

lenging period for survival as well as maintaining pregnancy. Thus,

as discussed by Coulson, Gaillard & Festa-Bianchet (2005), survival

and fertility might be elevated or depressed depending on conditions.

ForWeddell seals, environmental conditions during Antarctic winter

months between pupping seasons t and t + 1 might have similar

effects on survival probability and the subsequent rate of pup pro-

duction.

Survival and transition probabilities for the selected multi-state

model can all be calculated from h. For example, the 1980 survival

rate for factor level one (pups) is/1980,1, which satisfies

logitð/1980;1Þ ¼ e/1980 þ a/

1 :

For consistency with theMLE, we rewrite this as

logitð/1980;1Þ ¼ B/1980 þ A/

1 ;

where A/1 ¼ a/

1 þ e/1992and B/

1980 ¼ e/1980 � e/

1992: This reparameter-

ization is necessitated by the imposition of identifiability constraints

in maximum likelihood estimation: in program MARK, we set 1992

as the baseline year for survival. Similarly, we used 2007 as a baseline

year for transition probabilities and defined parameters

Awf ¼ aw

f þ ew2007 and Bw

yr ¼ ewyr � ew

2007. Survival estimation began in

1980 because data limitations prevented us from estimating pup sur-

vival rates for the initial cohort of pups tagged in 1979. Because of

delayed maturity until at least 4 years of age, the actual transition

probabilities presented here begin with estimates forwrs1984:

The parameter vector b ¼ ðB/1980; . . . ;B/

1991;B/1993; . . . ;B/

2006;

Bw1984; . . . ;Bw

2006;A/1 ; . . . ;A/

5 ;Aw1 ; . . .Aw

11Þ0, is obtained as a linear

transformation of the latent vector h, namely b = Qh, where

Q ¼

I12 �112 0 0 0 0 0 00 �114 I14 0 0 0 0 00 0 0 0 I23 �123 0 00 15 0 0 0 0 I5 00 0 0 0 0 111 0 I11

266664

37777565�74

:

Thus, b � N65(065, QRQ¢). It should be noted that the Is in Q are

identity matrices, 1s are vectors and 0s are vectors or matrices of

zeros of required dimensions, consistent with nonzero elements of

block columns. Block column four consists of r · 7matrices of zeros,

corresponding to seven latent variables not needed for the calculation

of b (these are e/2007; e

/2008;e

w1979; . . . ; ew

1983Þ:OpenBUGS code (available

from the authors upon request) analyses bjb ¼ N65ðb;VÞ; for a

knownmatrixV, and b � N65(065, QRQ¢).We used our estimates of the hyperparameters underlying / and w

to make predictions of probabilities / and w for females in different

Demographic buffering inWeddell seals 165

� 2011 TheAuthors. Journal ofAnimal Ecology� 2011 British Ecological Society, Journal of Animal Ecology, 81, 162–173

breeding states and age classes for the sampled years (/ for 1980–

2006 and w for 1984–2007, which yield breeding probabilities for

1985–2008) and for an as-yet-unsampled year, which are useful as

values for a typical year.

EVALUATING EFFECTS OF VITAL RATE CHANGES ON

POPULATION GROWTH RATE

We constructed an age- and breeding-state-based, post-breeding

matrix model (Caswell 2001) for female seals in which age of

recruitment and subsequent breeding schedules were flexible, seals

could live up to 30 years of age (the maximum ever recorded in

40 years of data collection), litter size was 1 pup and sex ratio

for newborn pups was 50 : 50 (Fig. S1, Supporting information).

We parameterized the model with mean vital rate values esti-

mated for an as-yet-unsampled year. Prior to using these in

matrix calculations, we used methods described in Hadley et al.

(2006) to adjust estimates of / for tag loss, which is known to

occur at low rates in our population, and to bias estimates low

if not accounted for (Arnason & Mills 1981; Nichols et al. 1992;

Bradshaw, Barker & Davis 2000). The adjustment method was

based on animal age (Pistorius et al. 2000), and the probability

of losing both tags given estimated probabilities of losing one

tag; the method treated the probability of losing each tag as an

independent event. We recognize that it has been shown for

some species of pinnipeds that marker-loss rates for different tags

on the same animal might not be independent (Bradshaw, Barker

& Davis 2000; McMahon & White 2009). However, for the years

of study reported on here, overall tag retention has been esti-

mated to average 0Æ99 (range = 0Æ95–0Æ999, Cameron & Siniff

2004) such that dependencies, if present, should have resulted in

little bias in our estimates and little or no effect on our estimates

of process variation. The high rates of tag retention in our data

relate to improvements in tag types prior to 1980 as well as the

fact that we implement daily efforts during each field season to

re-tag any animal with any missing or broken tags. Also, the ani-

mals are highly detectable and approachable for re-tagging.

Finally, we suspect that Weddell seals might have higher rates of

tag retention than that found in some other pinnipeds, because

they haul out on ice and snow rather than rocky beaches. Thus,

their tags are less likely to be abraded or to tangle on plants that

can occur at greater abundance at lower latitudes (Bradshaw,

Barker & Davis 2000). For example, Beauplet et al. (2005) esti-

mated tag loss rates of 21% for animals crossing beaches with

volcanic rocks, and Boyd et al. (1995) reported rates of 8Æ7% in

an area with rocky beaches and abundant plants in associated

shallow waters.

Using a projection interval of 1 year, we calculated asymp-

totic growth rate (k1) and k1’s sensitivity (S) to changes in vital

rate means (hi) using chain-rule differentiation (ð@k1=@hiÞ,Caswell 1978). Similar to Gaillard & Yoccoz (2003), we

neglected stochasticity when calculating sensitivity because the

life history being investigated is slow, survival rates are high,

fertilities are low, coefficients of variation are low for process

variation in vital rates (mean = 0Æ25) and population growth

rates are <2. For such a scenario, stochasticity is not expected

to have strong effects on mean k1 or sensitivities (Benton,

Grant & Clutton-Brock 1995); empirical support for this expec-

tation was recently provided by Altwegg, Schaub & Roulin

(2007). We calculated variance-stabilized sensitivity (VSS) of k1to each vital rate with the arcsine square-root formula provided

by Link & Doherty (2002), i.e.

VSS ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffihið1� hiÞ

pk1

!@k1@hi

:

When comparing demographic probabilities, VSS provides a bet-

ter measure of the effect on k of changes in vital rates than does

unscaled sensitivity because VSS operates on a scale where changes

in rates are functionally independent of the magnitude of the rates

(Link & Doherty 2002). The issue of scaling is important to consider

as it can complicate comparisons of sensitivities. Proper scaling

(more precisely, parameter transformation) allows changes in differ-

ent parameters to be comparable. In some scenarios, transformations

might be needed to facilitate comparisons between potential changes

to survival rates (bounded between 0 and 1) and fertilities (taking on

positive values that can be large). This was not the case in the work

presented here as all parameters in question are rates of survival or

transition. However, as explained by Link & Doherty (2002: 3301),

transformations can also be important when comparing changes in

different rates because ‘an increase of 10% (proportional or absolute)

is one thing for a survival rate of 50%, quite a different thing for a

survival rate of 90%, and an impossibility for a survival rate of 95%’.

Elasticities certainly present an appealing alternative to sensitivities

for evaluating the importance of changes in demographic parameters

as they regard proportional changes and are unitless (Caswell 2001).

However, elasticities (E) can be affected by the details of parameteri-

zation. In particular, elasticities for survival and for mortality (or 1-

survival) will differ unless the survival rate equals 0Æ5 (Link &Doher-

ty 2002). In the work presented here, all rates are parameterized as

either the probability of surviving or of breeding, and so elasticities

could have been used. We chose to use VSS so as to avoid possible

problems of comparison with other studies that can be performed

using different parameterizations (e.g. mortality instead of survival

or probability of skipping reproduction instead of probability of

reproducing).

EVALUATION OF DEMOGRAPHIC BUFFERING

HYPOTHESIS

To understand howwe tested the buffering hypothesis, it is important

to consider several aspects of the development of various tests that

can be used. Noting the occurrence of the product

ð�1=k2 � VarðhÞSðhÞ2Þin Tuljapurkar’s (1982) asymptotic expan-

sion for stochastic k, Pfister (1998) suggested the negative association

between squared sensitivity and variance. The demographic hypothe-

sis is then that the correlation Var(h) and S(h) is negative. Becauseð�1=k2 � VarðhÞSðhÞ2 ¼ �1� CVðhÞ2EðhÞ2Þ (see Morris & Doak

2004 for details), one might equivalently express the hypothesis as a

negative correlation between squared values of elasticity and coeffi-

cients of variation. In the work presented here on Weddell seals, all

vital rates are probabilities measured on the unit scale. For such

rates, Morris & Doak (2004) reported that a spurious correlation

exists between sensitivities and vital rates because of a functional

relation between the mean and the variance for such rates.

Accordingly, they recommended that future investigations of demo-

graphic buffering be based on relativized variances (RV), which

measure a vital rate’s level of variability relative to its maximum pos-

sible value. We followed their recommendation and calculated

RVhi ¼ r2hi=ðhi � ð1� hiÞÞ. Noting that VarðhÞSðhÞ2 ¼ RVðVSSÞ2

(for rate parameters), we used the correlation between RV and VSS

as the primary basis of our evaluation of the demographic buffering

hypothesis as this approach maintains a strong connection to

166 J. J. Rotella et al.

� 2011 TheAuthors. Journal ofAnimal Ecology� 2011British Ecological Society, Journal of Animal Ecology, 81, 162–173

Pfister’s (1998) motivation for the demographic buffering hypothesis.

To allow comparisons of results from different approaches to evalu-

ating the buffering hypothesis, we also calculated Spearman’s rank

correlations between (i) sensitivity and variance, as in the seminal

work by Pfister (1998) and (ii) sensitivity and RV, as in Morris &

Doak (2004). For each pairing, we predicted a negative correlation

after considering estimates of process covariance between vital rates

(Doak et al. 2005). We also compared our estimates of process varia-

tion in hyperparameters for survival and breeding probability and

assessed how well that difference corresponded with sensitivity

results for survival and breeding probabilities.

Results

MARK–RECAPTURE MODEL-SELECTION RESULTS

Capture–mark–recapture data were available from 5558

females tagged as pups between 1979 and 2007 and moni-

tored through 2008, by which time 917 had been resighted

with a pup at least once. These 917 females produced 2679

pups and provided 1090 observations of skip breeders. Esti-

mated over-dispersion was slight for these data (c = 1Æ06).In the most-supported mark–recapture model, patterns

of annual variation (on the logit scale) in / and w were

shared (additive structure) for pre-breeders and recruited

females (effects for / and w were separated from one

another), and p for pre-breeders and skip breeders varied

among years. A model in which patterns of annual varia-

tion were allowed to differ between pre-breeders and

recruited females for / and w was also well supported

(DAICc = 0Æ80; Table S1, Supporting information). The

two top-ranked models produced similar estimates

(between-model differences in estimates: average for differ-

ences in / = 0Æ002, SD of differences <0Æ01; average for

w = 0Æ004, SD = 0Æ05) and had 95% confidence intervals

that overlapped for all estimates. Accordingly, we used

estimates from the best-supported model (Table S2, Sup-

porting information) for variance decomposition and

matrix modelling.

HIERARCHICAL MODELL ING OF MARK–RECAPTURE

ESTIMATES

The Gelman–Rubin convergence statistic clearly indicated

that our hierarchical model had reached convergence within

a few hundred iterations. Our MCMC simulations were of

sufficient length to ensure with 95% confidence that the

posterior means reported were, on average, within 0Æ0005(SD = 0Æ0003) of the true values. We summarize findings

about hyperparameters by features (mean, standard devia-

tion, etc.) of their posterior distributions.

Our analysis provides evidence that logit(w) wasmore vari-

able than logit(/). The average difference between rw

(mean = 0Æ57, SD = 0Æ10) and r/ (mean = 0Æ37,SD = 0Æ07) was 0Æ20 (SD = 0Æ11); rw was the larger of the

two quantities with probability 0Æ97. The posterior mean of qthe correlation between logit(/t)and logit(wt), was 0Æ34

(SD = 0Æ21); the posterior probability for q > 0 was 0Æ94.Because /t is the survival rate from the pupping season in

year t to the pupping season in year t + 1, andwt is the prob-

ability of producing a pup in year t + 1 given the breeding

state in year t, the positive correlation indicates that years

with higher survival rates tended to be immediately followed

by pupping seasons in which the probability of producing a

pupwas also high.

Posterior means of /ryear and wrb

year were typically similar

to corresponding MLE, but, as expected, Bayesian esti-

mates of year effects were shrunk towards the mean value.

Accordingly, the Bayesian hierarchical analysis provided

gains in precision (mean GP = 22%, SD = 19%,

Table S3, Supporting information). For the 65 estimated

parameters, 30 of the top 32 GP values were for parame-

ters having to do with /ryear (26 were for year effects, four

were for state-specific offsets). GP was >50% for five

parameters and 30–50% for another 12 parameters. In

addition to improving precision, the hierarchical modelling

approach also allowed us to produce parameter estimates

for more years (Figs S2 and S3, Supporting information).

For example, the hierarchical structure allowed us to esti-

mate /S1980 based on survival of seals in other states in that

year and the dependencies estimated for survival rates

among seals in different states.

Posterior distributions of all vital rates for an as-yet-

unsampled year (Tables 1 and S3, Fig. S4, Supporting infor-

mation) reveal that/ for pups and yearlings is lower than it is

for older seals. Forw, the posterior distribution indicates thatrecruitment probability, which is estimated to be only 0Æ04 atage 5, climbs to 0Æ41 by age 8 and then remains at a similar

level for pre-breeders >8 years old. Subsequent-year breed-

ing probability was lower for first-time mothers (0Æ46) thanfor experienced mothers or skip breeders, for which the rate

was 0Æ66.

EVALUATING EFFECTS OF VITAL RATE CHANGES ON

POPULATION GROWTH RATE

We estimated k1 as 0Æ98 when the mean predicted value of

each vital rate in an as-yet-unsampled year (Table 1) was

used to parameterize our matrix model. Based on estimates

of k1 obtained using each set of vital rates in the posterior dis-tribution for an as-yet-unsampled year, it was clear that

estimated process variation in vital rates can change popula-

tion growth from strongly declining to rapidly increasing

(mean = 0Æ99; SD = 0Æ06; 0Æ025, 0Æ5 and 0Æ975; quan-

tiles = 0Æ87, 0Æ99, and 1Æ08, respectively). Despite such varia-

tion, the geometric mean of k1 was only 0Æ002 lower than the

arithmetic mean.

Our estimates of vital-rate variation, RV, sensitivities, and

VSS are useful for evaluating the demographic buffering

hypothesis because each varied substantially across the vital

rates (Table 1). For example, vital-rate-specific values for

RV ranged from 0Æ012 to 0Æ81, and those for VSS ranged

from<0Æ001 to 0Æ120. Because correlations between all pairs

Demographic buffering inWeddell seals 167

� 2011 TheAuthors. Journal ofAnimal Ecology� 2011 British Ecological Society, Journal of Animal Ecology, 81, 162–173

of vital rates were positive and because each vital rate repre-

sented either the probability of survival or of producing a

pup, process variance in any vital rate is expected to have

negative effects on k1.Regardless of whether we used sensitivity or VSS to evalu-

ate effects of changes in vital rates on population growth,

changes in / were always predicted to have greater effects

than changes in w. However, the details of rankings for sensi-

tivity to changes in / for different classes of females did vary

among sensitivity metrics and scalings (Table 1). Variance-

stabilized metrics consistently ranked /pup and /yearling

higher than did unscaled sensitivity, kept /mother as one of

the two most important vital rates and lessened the impor-

tance of /pre�breederð2þÞ and /skip. Among breeding probabili-

ties, changes in wEE and wSE are expected to have the largest

impact on fitness.

EVALUATION OF DEMOGRAPHIC BUFFERING

HYPOTHESIS

In support of the buffering hypothesis, we found, as reported

earlier, greater temporal variation in breeding probability

(mean rw = 0Æ57, SD = 0Æ10) than in survival rate (mean

r/ = 0Æ37, SD = 0Æ07), whereas k1 was more sensitive to

changes in survival rates than to changes in breeding proba-

bilities. Results of correlation analyses were also in keeping

with the prediction that vital rate variation would be lower

for those vital rates that had the greatest effects on fitness.

We found evidence of a strong negative correlation between

(i) sensitivity and variance (Spearman’s q = )0Æ82,P < 0Æ001, one-tailed test of no negative correlation), (ii)

sensitivity and RV (Spearman’s q = )0Æ89, P < 0Æ001, one-tailed test of no negative correlation) and (iii) RV and VSS

(Spearman’s q = )0Æ78, P < 0Æ001, one-tailed test of no

negative correlation).

Discussion

Our evaluation of multi-state model structures for pre-breed-

ers and recruited females advanced previous work by Hadley

et al. (2006), Hadley, Rotella & Garrott (2007), which

explored variation in vital rates for either pre-breeders or

recruits but not both simultaneously. The top-ranked model

indicated that females of different ages and breeding states

shared similar patterns of annual variation in/ (additive year

effects on the logit scale) and also in w (a separate set of addi-

tive year effects on the logit scale independent from those for

/). Subsequent hierarchical modelling of mark–recapture

estimates indicated that survival and breeding probabilities

were positively correlated across years such that there was a

tendency for a given year to be good or bad for all vital rates.

This is an interesting result because young pre-breeders are

thought to emigrate temporarily from breeding colonies until

they are near the typical ages of first reproduction (age 7–8),

whereas females that have recruited to the breeding popula-

tion are likely to be present in the breeding colonies even in

years when they skip pup production (Testa & Siniff 1987;

Hadley, Rotella & Garrott 2007; Rotella et al. 2009). Thus,

despite the fact that females of different ages and breeding

states appear to occupy different locations, at least during the

breeding season, their vital rates tend to follow similar

patterns. This could be interpreted as evidence that environ-

mental conditions at broader, rather than finer, spatial scales

in the Ross Sea are important drivers of population dynamics

for the study population. However, knowledge of the region’s

food web and its connections with broad-scale drivers such

as the SouthernOscillation and features such as sea-ice extent

is incomplete (Smith, Ainley & Cattaneo-Vietti 2007) and

must be improved to allow an understanding of what under-

lies the observed patterns in seal vital rates.

Regardless of the ultimate drivers of environmental condi-

tions, changes in food conditions seem a possible proximate

cause of annual variation in demographic performance for

Weddell seals. Weddell seals are capital breeders that rely

heavily on stored reserves during lactation. For animals in

our study population, average parturition mass of mothers

and weaning masses of pups vary strongly among years and

are related to broad-scale oceanographic variables (Proffitt

et al. 2007a, b). Further, weaning mass is positively related to

maternal parturition mass (Wheatley et al. 2006) and to the

probability of surviving to age three (Proffitt, Garrott & Ro-

tella 2008). However, it is not yet known whether an adult

female’s body mass is also related to her survival rate and

subsequent breeding probability in Weddell seals. In the few

Table 1. Features of posterior distribution for Weddell seal vital

rates in an as-yet-unsampled year (based on data from 1979 to 2008

from Erebus Bay, Antarctica) along with the relativized variance

(RV) of each rate, k1’s sensitivity to each of the individual vital rates,

and variance-stabilized sensitivity (VSS)

Vital rate Mean (SD) RV Sensitivity VSS

/Ppup 0Æ60 (0Æ10) 0Æ041 0Æ105 0Æ052/Pyearling 0Æ51 (0Æ10) 0Æ040 0Æ123 0Æ063/Page�2 0Æ95 (0Æ03) 0Æ014 0Æ382 0Æ088/F or E 0Æ89 (0Æ04) 0Æ018 0Æ368 0Æ120/S 0Æ95 (0Æ03) 0Æ012 0Æ175 0Æ040wPFage 5 0Æ04 (0Æ03) 0Æ017 0Æ009 0Æ002

wPFage 6 0Æ19 (0Æ09) 0Æ052 0Æ007 0Æ003

wPFage 7 0Æ32 (0Æ12) 0Æ068 0Æ005 0Æ003

wPFage 8 0Æ41 (0Æ13) 0Æ074 0Æ004 0Æ002

wPFage 9 0Æ41 (0Æ14) 0Æ076 0Æ002 0Æ001

wPFage 10 0Æ48 (0Æ14) 0Æ081 0Æ001 0Æ001

wPFage<10 0Æ39 (0Æ14) 0Æ079 0Æ002 0Æ001

wFE 0Æ46 (0Æ14) 0Æ075 0Æ004 0Æ002wEE 0Æ66 (0Æ12) 0Æ069 0Æ033 0Æ016wSE 0Æ66 (0Æ13) 0Æ070 0Æ019 0Æ009

Breeding states are the following: pre-breeder (P), first-timemother

(F), experiencedmother (E) and skip breeder (S). Estimates of appar-

ent survival probability (/) were corrected for tag loss and are pre-sented by age class for pre-breeders (pups, yearlings and ‡2 years

old) but not for females that have recruited to the breeding popula-

tion (states F, E or S). Estimates ofwrs represent the probability of

transitioning from breeding state r in year t to a pup-producing state

(s = F orE) in year t + 1. For females in stateP in year t, transition

rates varied by age class in year t (5, 6, …, 10, ‡11 years old); age was

ignored for females in states F,E and S in year t.

168 J. J. Rotella et al.

� 2011 TheAuthors. Journal ofAnimal Ecology� 2011British Ecological Society, Journal of Animal Ecology, 81, 162–173

studies of large mammals that investigated such questions for

adults, the results are mixed (Festa-Bianchet, Gaillard & Jor-

genson 1998; Gaillard et al. 2000) such that further work is

needed to understand what underlies positive correlations.

Positive correlations in annual vital rates at the popula-

tion level have been reported for many species and are

more common than negative correlations (Clutton-Brock

1988). For example, Jenkins, Watson & Miller (1963)

reported that years with good breeding success for red

grouse (Lagopus lagopus scoticus Lath) also tended to be

years with higher adult survival. Similarly, Nur & Syd-

eman (1999) reported that survival and breeding probabil-

ity were positively correlated in Brandt’s cormorants

(Phalacrocorax penicillatus Brandt). Positive correlations

between survival and breeding strengthen selection on life

histories (Orzack & Tuljapurkar 1989; Benton & Grant

1996, 1999), increase variability in annual population

growth rates and eliminate any buffering against environ-

mental variability that would occur with negative correla-

tions between rates (Jongejans et al. 2010). Given the

importance of correlations in vital rates (van Tienderen

2000; Coulson, Gaillard & Festa-Bianchet 2005; Doak

et al. 2005), it is important to estimate them for a greater

variety of species using appropriate methods that account

for sampling variance (Link & Nichols 1994).

In the work reported here, we estimated process variation

and covariation in survival and breeding probabilities with a

hierarchical model. For our species’ life history, wherein litter

size is fixed at one pup, the results of our hierarchical model-

ling provided insights into all vital rates simultaneously.

Until recently, it was difficult to estimate process variation

and covariation in vital rates; accordingly, most past reports

of correlations must be considered with caution until re-anal-

ysis employing recent developments in hierarchical models

can be performed.

In this study, we used a two-phase analysis in whichwe first

produced standard mark–recapture estimates of vital rates

and then analysed those results with a Bayesian hierarchical

analysis. One might ask what is gained (or lost) by such hier-

archical analysis ofMLE relative to analysis based on poster-

ior distributions from the original data X. Given that the

maximum likelihood estimate is unique, it is a function of a

sufficient statistic. Thus, it can be shown that, given the sam-

pling distribution ½bjb� is multivariate normal (an asymptotic

result typically taken for granted), the posterior distribution

½b;wjb� is the same as the posterior distribution [b, w|X].Hierarchical analysis based on MLE can be performed even

if the original data are not available, might sometimes result

in computational efficiencies and provides a means of esti-

mating process variation from existing data for diverse

species.

As has been shown in a number of other long-lived species

(Brault & Caswell 1993; Caswell, Fujiwara & Brault 1999;

Sæther & Bakke 2000; Gaillard & Yoccoz 2003; Oli &

Dobson 2003), k1 was most sensitive to changes in survival of

prime-age animals. Population growth rate was less sensitive

to changes in breeding probabilities, which is also in keeping

with findings for other long-lived species with flexible breed-

ing schedules (Jenouvrier et al. 2005; Forcada, Trathan &

Murphy 2008). We found strong evidence of buffering in

Weddell seal vital rates. In accordance with the demographic

buffering hypothesis, our estimates of process variation in

vital rates were inversely related to sensitivity. Specifically,

variation was greatest in breeding probabilities, intermediate

for survival rates of young animals and lowest for survival

rates of older animals. These results expand on work per-

formed by Forcada, Trathan & Murphy (2008) that used

published estimates of vital rates for the Erebus BayWeddell

seal population and showed evidence of buffering but that

was not able to incorporate estimates of process variance and

covariance.

Our results suggest that adult survival rate is canalized

to buffer fitness from environmental variation (Gaillard &

Yoccoz 2003). However, female Weddell seals do incur

reproductive costs to survival rate (Hadley, Rotella &

Garrott 2007). We estimated that survival rate for mothers

averaged 0Æ89, whereas the mean for skip breeders and

older pre-breeders was 0Æ98. Thus, Weddell seals are not

able to buffer their mean survival rate from being lower

when they produce a pup. It seems likely that they are

unable to avoid such costs because of their heavy reliance

on a capital breeding strategy whereby they undergo

extreme reductions in body mass during pup rearing

(Wheatley et al. 2006). However, it does appear that they

use a flexible breeding tactic to minimize variation in sur-

vival rate and thereby achieve some buffering. Wheatley

et al. (2006) also found that females adjust their maternal

expenditure during lactation in a manner consistent with

demographic buffering. Thus, it appears that female

Weddell seals can use reproductive flexibility at different

stages in the reproductive cycle that are in keeping with

the buffering hypothesis.

Although we found evidence for demographic buffering,

several aspects of the work merit discussion as there is room

for improvement in future analyses. First, our models

assumed that several vital rates were constant across a vari-

ety of ages (e.g. /pre�breederð2þÞt , /ForE

t , wEEt , wSE

t ). Our age

classes were those identified by Hadley et al. (2006), Hadley,

Rotella & Garrott (2007) in investigations that considered

models with more complex age structure and that allowed

for possible senescent declines in each of the vital rates.

However, modelling of Weddell seal vital rates performed to

date has not considered individual heterogeneity in individ-

ual fitness components that might reasonably be expected to

occur in life-history traits (Vaupel, Manton & Stallard 1979)

and that, if present, could mask senescence in vital rates

(Cam et al. 2002). When senescence is not properly

accounted for, estimates of demographic responses to per-

turbations can be biased (Festa-Bianchet, Gaillard & Cote

2003). Recent advances in mark–recapture analyses now

make it possible to evaluate individual heterogeneity in vital

rates (e.g. King et al. 2009; Schofield, Barker & MacKenzie

2009; Gimenez & Choquet 2010; Link & Barker 2010).

Further, it seems possible that senescence can occur in

Demographic buffering inWeddell seals 169

� 2011 TheAuthors. Journal ofAnimal Ecology� 2011 British Ecological Society, Journal of Animal Ecology, 81, 162–173

Weddell seal vital rates given the widespread evidence for

actuarial senescence (increase in mortality with age)

reported across diverse vertebrate species (Ricklefs 2010),

and a recent report of physiological senescence in muscles of

Weddell seals 17 years of age and older that could impair

survival and ⁄or reproduction (Hindle et al. 2009). Accord-

ingly, we intend to use hierarchical models that include indi-

vidual random effects to re-evaluate possible senescence in

vital rates in future analyses. If senescence occurs in the vital

rates, we suspect that our current analyses might overesti-

mate temporal process variance in rates for prime-age

females that were estimated based on pooled data from

prime-age females and older females, i.e. females that might

be less able to resist harsh environmental conditions. If true,

our results regarding demographic buffering might be con-

servative, and actual buffering of the rates for prime-age

females might be even stronger than reported here.

An additional issue worthy of investigation is possible

serial autocorrelations in Weddell seal vital rates. If environ-

mental conditions are auto-correlated, between-year correla-

tions in vital rates can have sizeable effects on population

growth rates (Tuljapurkar & Haridas 2006), which could

influence the optimal life-history tactics in a stochastic envi-

ronment. Further, the effects of between-year correlations in

vital rates can have positive or negative effects on stochastic

growth rate depending on circumstances (Tuljapurkar, Gail-

lard & Coulson 2009). Temporal correlations in vital rates

can come from lagged responses, and it is certainly possible

to envision how lagged responses in reproductive costs might

occur in a capital breeder (Tuljapurkar, Gaillard & Coulson

2009). In future analyses, we plan to investigate possible

serial correlations in vital rates and to incorporate findings

on between-year correlations in further analyses of demo-

graphic buffering.

As exemplified by a number of recent papers on stochastic

demography (e.g. Boyce et al. 2006, Engen et al. 2009;

Barbraud et al. 2011; Sim et al. 2011), an improved under-

standing of demographic responses to environmental varia-

tion is important for both basic and applied reasons.

Knowledge of vital rate distributions across a range of envi-

ronmental conditions for species of interest provide valuable

information on how species have coped with environmental

variation in the past andmight respond to possible future sce-

narios regardless of whether that variation is directional (e.g.

global warming), periodic (e.g. El Nino Southern Oscillation)

or non-periodic and non-directional (Berteaux & Stenseth

2006). However, it is difficult at present to reach broad con-

clusions about demographic buffering in animal populations

because of the dearth of detailed studies and because of ana-

lytical issues inmany existing studies.

Among published analyses, a variety of approaches have

been used for estimating process variance and covariance

and for scaling variances and sensitivities, and the approach

used can influence results (Link & Doherty 2002; Doherty

et al. 2004; Morris & Doak 2004; Doak et al. 2005). In many

instances, process variation has been ignored or strong sim-

plifying assumptions have beenmade, and scaling issues have

not been considered. In other cases, despite having a long-

term study with careful work on covariation based on

detailed data, it has still not been possible to estimate process

covariation for all vital rates (Reid et al. 2004). To allow for

more detailed analyses to be conducted in the future, Morris

&Doak (2004) made a plea for biologists to publish vital rate

estimates. It would also be useful to publish details of the

underlying estimates of model parameters (e.g. logit-scale

coefficients), including estimates of variances and covari-

ances, as we have shown here how these can be used in hierar-

chical modelling of process variation. If that happens, new

versions of previous meta-analyses of demographic buffering

(e.g. Gaillard, Festa-Bianchet & Yoccoz 1998; Pfister 1998;

Sæther & Bakke 2000; Gaillard & Yoccoz 2003) can be

performed that incorporate new developments in analysis

methods.

Despite the continued need for more studies across a

greater diversity of taxa and life histories (Koons et al. 2009;

van de Pol et al. 2010), there is growing, though not univer-

sal, support for the demographic buffering hypothesis. A

number of recent studies with careful analyses of excellent

demographic data report that the vital rates to which popula-

tion growth rate was most sensitive also tended to be those

with lower variation (e.g. Reid et al. 2004; Jenouvrier et al.

2005; Forcada, Trathan & Murphy 2008; van de Pol et al.

2010). For a long-lived seabird, however, results were

equivocal (Doherty et al. 2004). Further, for the Antarctic

fur seal (Arctocephalus gazella Peters), buffering was in evi-

dence during the earliest decade of the study but lost in recent

years when the population was in decline (Forcada, Trathan

& Murphy 2008). This last result emphasizes the importance

of considering population status and ecological context when

interpreting the results of studies of demographic buffering.

The data reported on here for Weddell seals were collected

in a marine ecosystem during a period when its top- and mid-

dle-trophic levels were not substantially impacted by human

activity (Smith, Ainley & Cattaneo-Vietti 2007) and when the

population of seals was stable (Rotella et al. 2009). Accord-

ingly, the vital rate estimates reported here provide useful

baselines that can be compared with what is found under

contrasting circumstances for Weddell seals or other closely

related species in the Southern Ocean. Estimates of adult sur-

vival rates and breeding probabilities for Weddell seals in

eastern Antarctica are available for 26 recent years (Lake

et al. 2008). Similar to what we report here, Lake et al.

(2008) found that breeding females had consistently high

annual survival rates but variable breeding probabilities and

used a flexible breeding strategy to avoid reproductive costs

to survival. Results from studies of other pinnipeds in the

Southern Ocean indicate that there might be some interspe-

cific consistency in this pattern.

Studies of subantarctic fur seals (Arctocephalus tropicalis

Gray) in the southern Indian Ocean found that the propor-

tion of pups surviving from birth to their first return to their

birth island ranged widely among cohorts (27–75%),

whereas survival rates for adult females were high and con-

sistent among years (Beauplet et al. 2005, 2006). Relevant

170 J. J. Rotella et al.

� 2011 TheAuthors. Journal ofAnimal Ecology� 2011British Ecological Society, Journal of Animal Ecology, 81, 162–173

results for Antarctic fur seals also show evidence that demo-

graphic buffering can occur (Forcada, Trathan & Murphy

2008). Southern elephant seals (Mirounga leonina Linnaeus)

have been studied in several locations with different popula-

tion trajectories, food resources and predator communities.

As in Weddell seals, elephant seals had high temporal varia-

tion in fertility (Bradshaw et al. 2002) and survival through

the first year of life (McMahon & Burton 2005). Within a

location, survival rate was lowest in the first year of life and

then higher and relatively stable across ages later in life

(Pistorius, Bester & Kirkman 1999). Further, juvenile

survival rate and age at primiparity varied by location,

whereas survival rates for older animals were more consis-

tent (McMahon, Burton & Bester 2003). Similar to what we

report here for Weddell seals, population growth rate for

elephant seals was more sensitive to changes in survival rates

than to changes in fertility, and survival rates for immature

seals were important to growth rate and variable among

years (McMahon et al. 2005). It appears that in both spe-

cies, future research such as that performed by de Little

et al. (2007) on extrinsic and intrinsic drivers of survival of

young seals will be provide useful insights into stochastic

demography in these species. Although not all of studies of

Southern Ocean pinnipeds provide all of the elements neces-

sary for a full evaluation of demographic buffering, they do

provide compelling examples of how studies of vital rates

can play a crucial role in understanding how populations

will respond to future environmental change. They also play

an important role in developing hypotheses that can be eval-

uated with fuller analyses.

Acknowledgements

We thank the many individuals who have worked on projects associated with

the Erebus Bay Weddell seal population since the 1960s. We thank J. D. Nic-

hols for helpful suggestions during analysis, and we thank D. B. Siniff for dis-

cussions that improved this manuscript. We are grateful to J.-M. Gaillard, J.

D. Nichols and two anonymous reviewers for their useful comments on earlier

drafts of the manuscript. The project was supported by the National Science

Foundation, Division of Polar Programs (grant no. DEB-0635739 to R. A.

Garrott, J. J. Rotella, and D. B. Siniff) and prior NSF grants to R. A. Garrott,

J. J. Rotella, D. B. Siniff and J. W. Testa. Logistical support for fieldwork in

Antarctica was provided by Raytheon Polar Services Company, Antarctic

Support Associates, the United States Navy and Air Force, and Petroleum

Helicopters Incorporated. Animal handling protocol was approved by Mon-

tana State University’s Animal Care andUse Committee (Protocol #41-05).

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Handling Editor: Corey Bradshaw

Supporting Information

Additional Supporting Information may be found in the online

version of this article.

Fig. S1. Life cycle graph for the age- and breeding-state-based,

post-breeding matrix model of female Weddell seals in Erebus Bay,

Antarctica.

Fig. S2.Annual estimates of apparent survival rate for animals in dif-

ferent breeding states and age classes (pups, yearlings, pre-breeders

‡2 years old, mothers, and skip breeders) for 1980–2006 produced by

maximum likelihood (MLE, gray points with 95% confidence inter-

vals as gray error bars) or Bayesian hierarchical modelling (MCMC,

black points with 2.5% and 97.5% quantiles of posterior distribution

as black error bars).

Fig. S3. Estimated breeding probabilities for female Weddell seals

‡5 years old during 1985–2008 that were produced bymaximum like-

lihood (MLE, gray points with 95% confidence intervals as gray

error bars) or Bayesian hierarchical modelling (MCMC, black points

with 2.5% and 97.5% quantiles of posterior distribution as black

error bars).

Fig. S4. Posterior densities of apparent survival rates and breed-

ing probabilities for an-as-yet unsampled year for female

Weddell seals in different combinations of age class and breed-

ing state based on data from 1979 to 2008 from Erebus Bay,

Antarctica.

Table S1. Model-selection results for competing multi-state mark–

recapture models for state- and year-dependent apparent survival

rates (/), breeding probabilities (w), and detection rates (p) for female

Weddell seals in Erebus Bay, Antarctica, 1979–2008. AICc, DAICc

(difference inAICc value between the topmodel and each subsequent

model),wi (weight of evidence in favor of each model i), k (number of

estimated parameters), and deviance are shown for each of the mod-

els evaluated.

Table S2. Coefficients estimated with modelling mark–recapture

modelling of age-class-, state- and year-dependent apparent survival

rates (/), breeding probabilities (w), and detection rates (p) for female

Weddell seals in Erebus Bay, Antarctica, 1979–2008.

Table S3. Posterior means and standard deviations from Bayesian

hierarchical modelling of coefficients relating apparent survival and

transition probabilities to pup-producing breeding state for female

Weddell seals by age and breeding state in 1980–2008.

Table S4. Features of the posterior distribution of apparent survival

rates (/) and breeding probabilities ðwrsageclassÞ in an as-yet-unsampled

year for female Weddell seals in different age classes and breeding

states.

Appendix S1. Details of modelling capture-recapture analyses of

apparent survival rate and breeding probabilities for Weddell seals in

Erebus Bay, Antarctica using data from 1979 to 2008.

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re-organized for online delivery, but are not copy-edited or typeset.

Technical support issues arising from supporting information (other

thanmissing files) should be addressed to the authors.

Demographic buffering inWeddell seals 173

� 2011 TheAuthors. Journal ofAnimal Ecology� 2011 British Ecological Society, Journal of Animal Ecology, 81, 162–173