**Marking and resighting**

Capture-mark-recapture (CMR) datasets were collected from the elephant seal populations breeding on the northern isthmus of Macquarie Island (54°30' S, 158°50' E) over two periods of different population density: (1) the high-density era between 1951 and 1965 when the number of breeding females (*n*_{f}) breeding there was approximately 5000 and (2) the low-density era between 1993 and 1999 when *n*_{f }was ca. 2500 to 3000 [22,30,31,67]. During both periods of investigation, newly weaned pups were hot-iron branded after weaning in November [for details see [30,68-70]]. During the high-density era, 6506 seals were branded from thirteen cohorts: 1951 to 1965 (excluding 1956 and 1958), with a mean of 500 seals branded each year. During the low-density era, 10721 pups were branded from five cohorts (1993 to 1997, with a mean of 2144 pups marked each year). We have determined previously that branding in this manner has had no long-term effects on the condition or survival of the seals [69,71], and that branding is an appropriate conservation tool [71]. This study was approved by the Antarctic Animal Care and Ionising Radiation Usage Ethics Committee (Department of the Environment, Commonwealth of Australia), and the Tasmanian Parks and Wildlife Service.

Systematic re-sighting searches were made of all the isthmus beaches where most of the marked seals return [30,68]. There was high variation in the frequency and intensity of the searches during the high-density era [26]; the low-density study had a more rigorous re-sighting strategy [22]. On both occasions, reports of marked seals found away from Macquarie Island were rare [22,26,72]. The years with poor search effort from 1961–1985 (see Fig. 1A) (i.e., when recapture rates were consistently low and inestimable in the CMR models described below) were excluded from the analysis.

**Phenomenological evidence for density dependence**

We compiled survey data on the relative abundance of breeding elephant seals at Macquarie Island over time for the two periods of investigation (high- and low-density eras) (see [67], [73] and [22] for data and full methods) (Fig 1A). The survey data consisted of complete counts of the entire adult female population done on a single day each year (15 October). This is the standard method to estimate relative population size for southern elephant seals [74].

To determine the strength of evidence for density dependence using phenomenological (abundance) data, we applied the technique of Brook and Bradshaw [24] to each abundance time series. We adopted a multiple-working hypotheses approach based on information-theoretic model selection and multi-model inference [75]. We first defined an *a priori *model set of five population dynamical models [17] used to describe phenomenological time-series data based on variants of the generalized *θ*-logistic population growth model:

where *N*_{t }= population size at time *t*, *r *= realized population growth rate, *r*_{m }= maximal intrinsic population growth rate, *K *= carrying capacity, *θ *permits a nonlinear relationship between rate of increase and abundance. The term *ε*_{t }has a mean of zero and a variance (*σ*^{2}) that reflects environmental variability in *r*. For each high-density and low-density time series we used maximum-likelihood estimation to fit model parameters (via linear regression for the density-independent random walk [RW] and exponential [EX] models, and for the density-dependent Ricker-logistic [RL] and Gompertz-logistic [GL] models; non-linear regression based on Newton optimization was used to fit the density-dependent full *θ*-logistic [TL] model – [76]). An index of Kullback-Leibler information loss, Akaike's Information Criterion corrected for small sample sizes (AIC_{c}) weights, was used to assign relative strengths of evidence to each model [75]. The relative support for density dependence is simply the summed weights of the three density-dependent models (RL, GL and TL). More details are given in Brook and Bradshaw [24].

**Capture-mark-recapture analysis**

Capture history matrices were constructed from the re-sighting histories of individual seals, with multiple re-sights within a year treated as a single sighting. Capture matrices were analyzed using the capture-mark-recapture (CMR) program MARK [77] which provides maximum-likelihood estimates of apparent survival and re-sight probability based on the Cormack-Jolly-Seber (CJS) time-variant model structure and several models appearing as special cases of this general model [11]. The two fundamental parameters estimated in these models are , the apparent survival probability (true survival confounded with permanent emigration – the latter is considered to be low given the high return rate of seals to the relatively isolated Macquarie Island) of individuals between the *n*^{th }and (*n *+ 1)^{th }year (*n *= 1,..., *k *- 1), and *p*, the re-sight probability for all individuals in the *n*^{th }year (*n *= 1,..., *k*) [77].

We tested whether the CJS-model assumptions were met with parametric goodness-of-fit (GOF) tests implemented by the simulation procedures available in MARK [11]. Here, encounter histories are simulated that exactly meet the CJS assumptions by a bootstrap procedure, and then the simulated data are compared to the observed data to test for goodness-of-fit [77]. The variance inflation (over-dispersion) factor, *ĉ*, was calculated from this procedure and used to correct AIC_{c }values [11]. Different models combining the main parameters and their hypothesized effects (see below) were compared using AIC_{c }[75,78]. We accounted for some of the potential over-dispersion by using the second-order approximation AIC_{c}, denoted QAIC_{c }[75]. Models containing covariates were compared to the general model (time- and age-variant survival) using the information-theoretic evidence ratio (*ER*) [75]. The evidence ratio is calculated as the QAIC_{c }weight of any one model divided by a simpler comparison model QAIC_{c }weight. The *ER *therefore estimates how many more times likely the model in question is over the model(s) to which it is being compared [75].

**Sex and age effects**

We examined if there were any differences in survival probability between the sexes; there was little evidence for a difference (see Results), so the sexes were pooled. First-year survival is a good indicator of potential recruitment given that naïve elephant seals have the highest risks of dying compared to other age classes [22]. Therefore, we split the datasets into two age classes: first-year (1 year) and "adult" (> 1 year). This allowed for a direct comparison of the effects of the covariates on first-year survival and subsequent population recruitment.

**Environmental conditions**

We used annual averages of the Southern Oscillation Index (SOI) [79] to examine the hypothesis that environmental stochasticity affects annual survival probability [22]. The SOI is a measure of El Niño-Southern Oscillation (ENSO), and it reflects the patterns of variability in the weather and sea surface temperatures of the Southern Ocean [80]. We standardized the mean January-October SOI values by subtracting the mean SOI for January to October from a 50-year mean (1950–2000). This period (Jan-Oct) corresponds to the seals' annual winter foraging trips to sea [33,34]. It has been shown that both the average SOI during the newly weaned seals' first foraging trip and the conditions prevailing during the mother's pre-partum foraging (as inferred from weaning mass) both affect first-year survival [22,38,49]. As such, we included measures of the SOI anomaly during both periods as covariates in our *a priori *model sets to examine their relative support (weaning mass data for the entire dataset were unavailable). Two separate CJS model sets were constructed using these two expressions of the SOI conditions: (1) the first set employed the SOI values relating to the first-year seals' first foraging trip (e.g., seals branded in 1993 foraged for the first time in late-1993 and throughout 1994); (2) the second set used the SOI corresponding to the environmental conditions prevailing during the mother's pre-partum foraging (e.g., mothers of seals born in 1993 were foraging over-winter in 1993).

**Population density**

Published counts of female seals on the isthmus during the breeding season were used to measure the effect of population density on survival [73]. Both the density of breeding females from the current year, and the density of the breeding females from the previous year were included in the models considered as density covariates. This approach allowed us to examine the possibility of a lag effect of density on survival. The density covariates were standardized by calculating the minimum value in the covariate vector and subtracting this from all other values. The maximum value was calculated for this new vector, and the new vector was then divided by the maximum. The density covariates were incorporated into models with and without the SOI covariates. MARK includes covariates in the CJS model by expressing the natural logarithm of the probability of survival as a logistic function of the covariates:

where logit() is the logit-transformed survival estimate of a seal with the covariate *x*, *β *is the logit function calculated in MARK for *x *and SD is the standard deviation of *x*. This function is fixed in the log-likelihood for survival as in a logistic regression. This model assumes that there is an optimal value of the covariate and that there are some selective penalties associated with extreme values [77].

**Authors' contributions**

SCD took the lead in writing the manuscript and did the analyses. CJAB, MAH and CRM initiated the study, and CJAB contributed to data analyses. All authors assisted in writing the manuscript and approved the final version.

**Acknowledgements**

We thank all who participated in the field study at Macquarie Island. Funding was provided by the Department of the Environment and Heritage, Commonwealth of Australia. We thank two anonymous reviewers for helpful comments to improve the manuscript.