Phenomenological evidence for density dependence
For the high-density time series (1951–1965), there was good evidence for density-dependent population growth, with the summed Akaike's Information Criterion corrected for small samples size (AICc) weights for the three density-dependent models = 77.4 % (Fig. 2A, Table 1). There was also strong evidence for density-dependent population growth for the low-density time series (1993–1999), where the summed AICc weight for the density-dependent models was 89.3 % (Fig. 2B, Table 1).
Capture-mark-recapture
The parametric goodness-of-fit bootstrap results for both the high- and low-density eras showed evidence for lack of fit to the Cormack-Jolly-Seber (CJS) model assumptions (P [48].
To account for over-dispersion, the inflation factor, c, was used to correct the AIC values in all remaining analyses. For the high-density dataset, ĉ was calculated for each model set using the observed and simulated deviance and deviance degrees of freedom. For the low-density dataset, the values of ĉ calculated for each model set were considered too high (> 3) to be incorporated directly into the correction of AIC, so the model sets were compared with values of ĉ ranging from 1 to 10 to look for major discrepancies in first-year survival estimates and model weighting [see Additional file 1, tables 1 to 3].
During the low-density era and for the model set examining the effect of age, the model-averaged parameter estimates for first-year survival varied by a maximum of ± 2 % with ĉ ranging from 1 to 10 [see Additional file 1, table 1]. Likewise, model rankings only changed relative to the recapture probability p [see Additional file 1, table 1]. In the sex-effect model set, model-averaged parameter estimates for first-year survival varied by only 0.1 % with changes to ĉ, and the general model 
(age*time)p(time) had > 83 % of the model weight for all values of ĉ [see Additional file 1, table 1]. Varying ĉ within the SOI-covariate models [see Additional file 1, table 2A] and the density models [see Additional file 1, table 2B] also indicated little change to the model ranking with respect to survival probability, although there was some bias in the estimates of survival probability (see below). Models examining the effects of population density and SOI together demonstrated little bias (2 %) in parameter estimates with varying ĉ, although model rankings varied substantially [see Additional file 1, tables 3]. It should be noted, however, that the presence of excessive over-dispersion provides important information regarding the population structure in its own right. Previous work has determined that capture heterogeneity and survival vary as a function of weaning mass [49], so a certain degree of over-dispersion is expected.
Sex and age effects
For the high-density era, the model that incorporated time- and age-based survival had over 99.9 % of the model weight (Table 2). Neither first-year or adult survival varied with gender (the general model, (age*time) p(time) was allocated > 99.9 % of the model weight; Table 3); therefore, male and females were pooled for all subsequent analyses. The most parsimonious model for the low-density era was one that incorporated time and age effects on survival (Table 2). There was no evidence that first-year survival varied with gender (the model ignoring the effect of gender accounted for > 99 % of the wQAICc; Table 3), so males and females were again pooled for all subsequent analyses.
Environmental conditions and density considered separately
For the high-density era, there was strong evidence that the probability of both first-year and adult survival varied with the standardized SOI (information-theoretic evidence ratio [ER] = 5881; Table 4). The most parsimonious model contained the SOI covariate representing the environmental conditions during the time naïve seals were foraging (ER = 4732, Table 4). For the low-density era and over all values of ĉ, > 74 % of the model weight was allocated to models with first-year survival varying with SOI measured during the pregnant mother's pre-partum foraging trip (Table 4; Fig. 3A). However, the model-averaged estimates of first-year survival varied by 63 % over the range of ĉ examined. Despite this variation in first-year survival, this model set clearly shows that environmental conditions (expressed as SOI) during the year of the mother's pre-partum foraging trip describe an important component of the variation in first-year survival (ER > 3.5).
When the density covariate was considered alone, there was evidence that first-year survival varied with annual density in the high-density era (ER = 8.5; Table 5; Fig. 3B). For the low-density era, model weightings varied substantially over the range of ĉ; however, estimates of first-year survival varied by only 2 %. There was weak evidence for a density effect on first-year survival during this era (Table 5; Fig. 3B).
Combining intrinsic and extrinsic factors
During the high-density era, the model including the SOI values measured during the mother's pre-partum foraging trip had > 99 % of the model weight (Table 6, Fig. 3A), but there was no evidence that density explained additional variance in first-year survival (ER 6). When population density was low, the high degree of variation in model weighting with changes to ĉ made determining the combined effects of these two covariates on first-year survival suspect (i.e., the variance among survival estimates was 175 %) [see Additional file 1, table 3]. Nonetheless, we assumed the same ĉ value from the high-density era to contrast models; this revealed that the models with the most support (combined QAIC weights > 99 %) incorporated the mother's foraging trip SOI, and there was little evidence for a density or pup-year SOI anomaly effect (Table 3).
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