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Popul Ecol (2017) 59:139–155 DOI 10.1007/s10144-017-0573-6

ORIGINAL ARTICLE

Early-life density-dependence effects on growth and survival in subantarctic fur seals

Nathan Pacoureau1 · Matthieu Authier2 · Karine Delord1,2 · Christophe Guinet1 · Christophe Barbraud1 

Received: 20 July 2016 / Accepted: 3 February 2017 / Published online: 21 March 2017 © The Society of Population Ecology and Springer Japan 2017

their diving abilities in order to withstand the extreme fast-ing periods that are characteristic of this fur seal popula-tion. This analysis provides significant insight of density-dependent processes on early-life demographic parameters of a long lived and top-predator species, and more spe-cifically on the pre-weaning stage with important conse-quences for our understanding of individual long-term fit-ness and population dynamics.

Keywords Arctocephalus tropicalis · Capture-mark-recapture · Growth model · Marine top predator · Population dynamics · State space model

Introduction

A fundamental endeavour in population ecology is to iden-tify the factors determining population abundance (May 1999). Among these, the role of density-dependence is still being debated. Its detection and the determination of its strength remain at the heart of current ecological and meth-odological issues (Berryman et  al. 2002; Berryman 2004; Lebreton 2009; Herrando-Pérez et  al. 2012). To better understand population dynamics, the effect of density on different age or stage classes should be quantified. Knowl-edge of density-dependence is also crucial to understand the impact of climate change on populations or in conser-vation biology (Hanski et al. 1996; Drake 2005). Density-dependence regulation of several large terrestrial mammal populations is well documented (Williams et al. 2013; and especially on large herbivores: see; Bonenfant et al. 2009). However, studies on density-dependence in marine mam-mals remain rather rare (Bonenfant et  al. 2009; Williams et al. 2013).

Abstract Understanding the regulation of natural popu-lations has been a long-standing research program in ecol-ogy. Current knowledge on marine mammals and seabirds is biased toward the adult component of populations and lacking are studies investigating the juvenile component. Our goal was to estimate demographic parameters on the pre-weaning stage of a subantarctic fur seal (Arctocepha-lus tropicalis) population on Amsterdam Island, suspected to be regulated by density-dependence. The influence of abundance on growth parameters (length and weight) and survival was assessed over a study period spanning 16 years. We evidenced a negative trend in population growth rate when density increased. Density-dependence models were favored for pup body size and mass growth. Abun-dance had a clear influence on body length at high popu-lation-density, pups grew slower and were smaller at wean-ing than pups born in years with low population density. Abundance partly explained pup body mass variation and a weak effect was detected on pre-weaning survival. The causal mechanisms may be increased competition for food resources between breeding females, leading to a reduction of maternal input to their pups. Our results suggested that pup favored survival over growth and the development of

Electronic supplementary material The online version of this article (doi:10.1007/s10144-017-0573-6) contains supplementary material, which is available to authorized users.

* Christophe Barbraud barbraud@cebc.cnrs.fr

1 Centre d’Études Biologiques de Chizé, UMR-CNRS 7372, 79360 Villiers-en-Bois, France

2 Observatoire PELAGIS, Université de la Rochelle, UMS-CNRS 3462, 4 allée de l’Océan, 17000 La Rochelle, France

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Marine mammals are top predators (sensu Sergio et al. 2014) widely accepted as keystone species because they can have disproportionate impacts on the structure and function of some marine ecosystems due to their large bio-mass and consumption of lower-trophic level preys (Bowen 1997; Sinclair 2003; Estes 2009; Estes et al. 2010). In addi-tion, they are considered as indicators of environmental change (Jessup et  al. 2004; Wells et  al. 2004; Boyd et  al. 2006; Moore 2008; Bossart 2011).

Pinnipeds are amongst the most visible marine mammals given their large size and their onshore phase during breed-ing (Hindell et al. 2003). Depending on species, individuals can congregate together to form huge and compact breed-ing colonies which allows to investigate density-dependent relationships. Nevertheless, the role and the intensity of density-dependence in pinnipeds population regulation remain poorly known.

Younger age classes of long-lived species constitute up to half of the total population and greatly contribute to the total reproductive value and demographic stochasticity (Sæther et al. 2013). Variations in vital rates of younger age classes could thus have long-term impacts on individual fitness and on the population dynamic and evolutionary processes (Gaillard et  al. 2000; Sæther et  al. 2013). Most demographic studies, particularly on marine mammals and seabirds, focused on life-history traits of the adult compo-nent of populations, but understanding early life demogra-phy is also required to obtain a panoptic view.

The aim of our study was therefore to estimate early-life history traits and to test density-dependence effects on the pre-weaning stage of a marine top predator, the subant-arctic fur seal (Arctocephalus tropicalis (Gray, 1872)) on Amsterdam Island, Indian Ocean. The fur seal population of Amsterdam Island has increased dramatically over the past decades (Guinet et al. 1994). Amsterdam Island is sur-rounded by subtropical relatively warm and low productiv-ity waters (Gregg and Rousseaux 2014). One might expect density-dependent processes to occur, either through space limitation on coastal breeding sites and/or by increased competition for food resources at sea. Therefore, our spe-cific objectives were to determine the influence of breeding population density on pre-weaning body-size and weight growth, and on pre-weaning survival. We tested for den-sity-dependence in pup abundance time series data taking into account observation error (Lebreton 2009). Then we tested the following predictions regarding growth rate and pup survival parameters:

1. A decrease in birth size and weight when population density increases. The main reason would be a dete-rioration of dams’ body condition when population increases due to an increased competition for food.

When competition increases the ability of a predator to forage is limited and food intake per capita decreases.

2. A decline in growth rates (snout-to-tail length and weight) of pups when population density increases. Due to high competition at sea, resources available for the dam may be limited and, by consequence, maternal inputs to pups before weaning. This constraint should be seen on pre-weaned pups because they are exclu-sively dependent of maternal input until weaning.

3. Finally, if pups are born smaller, lighter and have lower growth rates when density increases, their survival could be indirectly affected. We might also expect a decrease in pup survival due to trampling by adults as the population density increases on the breeding colo-nies.

Materials and methods

Study area and species

Subantarctic fur seals were studied on Amsterdam Island, Indian Ocean (37°552′S, 77°302′E). The island (approxi-mately 55 km²) is surrounded by subtropical, relatively warm (monthly average between 13 and 18 °C), and low productivity waters (Gregg and Rousseaux 2014).

The subantarctic fur seal is a long-lived and philopat-ric species. Females give birth to a single pup from late November to early January, with a mean parturition date in mid-December (Georges and Guinet 2000a). Dams alter-nate between foraging trips at sea, during which the pup fasts, and short lactation periods ashore. Lactating females undertake the longest recorded foraging trips (>30 days, > 1000 km from the colony) of any Otaridae (Beauplet et al. 2004). The pup rearing period lasts 10 months (Tollu 1974; Georges et al. 1999).

Data

Counts of newborn pups took place every year from 1994 to 2014 between 15 and 30 January on five distinct areas (areas 1, 2, 3, 31 and 32; Fig. 1) of the island. Three counts were carried out on each area the same day by three dif-ferent persons, and if counts differed by more than 10% a fourth count was conducted. In this study, only counts from areas 1 and 2 were used to estimate pup abundance, since their boundaries were clearly and permanently defined over the whole study period. Due to logistic constraints counts could not be carried out every year in all areas. We thus used log-linear models and the software TRIM v3.52 (Pan-nekoek and van Strien 2001) to estimate total abundance of pups in these areas.

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The number of pups in a given year is one component of population size and may depend on demographic fac-tors such as the proportion of breeding females or the age structure. Therefore, a relationship between pup life his-tory traits and the number of pups could be interpreted as density-dependence but could also be due to variations in demographic factors. However, given that no total popu-lation time series exist for this population and that female breeding probability, weaning probability and age structure were fairly constant during the study period in this popula-tion (Beauplet et  al. 2005, 2006; Authier et  al. 2011), we assumed that pup abundance depicted herein the total pop-ulation size.

During the study period, between 100 and 200 pups at the breeding colony of “La Mare aux Éléphants” on the north-east side of Amsterdam Island (Fig. 1, area 2) were temporarily identified within 12 h following their birth in December (Georges and Guinet 2000b)—except in 1998 when fieldwork did not begin before January (Chambellant et al. 2003). Pups were sexed, weighed (±0.1 kg) and meas-ured from snout to tail (±1 cm). At 1 month of age, marked pups were individually identified by permanent numbered plastic tags (Dalton Rototags, Dalton Supply, Nettlebed, UK) placed in connective tissue of the trailing edge of the fore flippers. Marked pups were longitudinally monitored until weaning (October) with two weighing and one size

measurement by month. Additional daily weighing was conducted in May and June on a sub-sample of 30 pups each year. This longitudinal monitoring allowed estimating growth rates and survival of individual pups.

Statistical analyses

Density-dependent effects were investigated in pup annual abundance and in three life-history traits: pup growth (snout-to-tail length and weight) and survival from birth to weaning. Since pup growth and survival vary according to sex (Georges and Guinet 2000a, 2001; Guinet and Georges 2000; Beauplet et al. 2005), males and females were ana-lysed separately. Some years (2002, 2004, 2008 and years before 1999) were removed from dataset used for analyses due to inadequate reliability and/or low sample sizes. Field protocols (counts, individual monitoring) could not be entirely fulfilled during those years due to logistical issues.

We used a Bayesian approach to model growth parame-ters and abundance. In absence of independent information to specify informative priors, weakly informative priors were used: Student or normal distributions (Gelman 2006). Sensitivity analyses were conducted to check results’ robustness: a range of different prior distributions were tested (not shown). Three Markov chains were run for each model with different initial values. Out of a total number of

Fig. 1 The 49 areas defined by Roux (1986) on Amsterdam Island to survey subantarctic fur seals. Study areas are 1, 2, 3, 31 and 32

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100,000 iterations, the first 30,000 were discarded (“warm-up”), and one in five in the remaining 70,000 were selected for posterior inference. Thus, parameter posterior distribu-tions were estimated from 42,000 values.

Convergence of each parameter was checked with the Gelman and Rubin diagnostic (1992). Plots of fitted value vs residuals were checked to visually assess goodness-of-fit.

Modeling population dynamics

Pup abundance time series from 1999 to 2014 were ana-lyzed using a discrete time stochastic Gompertz state-space model. This model allows to test density-dependence in time series and to estimate its intensity, whilst taking account of observation error (Lebreton and Gimenez 2013). Writing Nt for true abundance in year t and xt = ln(Nt) the model is defined through the state process equation:

where r is the logarithm of the multiplication rate (λ) when N = 1, DD is a constant parameter measuring the strength of density-dependence, and εxt is a normally dis-tributed process error with mean zero and process variance σN² (Lebreton and Gimenez 2013).

We linked the logarithm of the observed counts (Yt) with the logarithm of the true population size using the follow-ing equation:

where εYt is normally distributed observation error with mean zero and observation variance σY². We used uniform priors for εxt and εYt (∼unif(0, 5)), and for parameter DD we used Student-t prior distribution with mean 0, degrees-of-freedom parameter ν, and scale s (∼t distribution(0, ν = 7, s = 1/

√

0.001)), with ν and s chosen to provide minimal prior information (Gelman et al. 2008). Each chain was ini-tiated by assuming a prior distribution on the initial state centred around the first observation of abundance, x1 ∼ N(y1, 0.01). Several authors (Delean et al. 2013; Lebreton and Gimenez 2013) recommended the choice of a reason-able prior for r based on external comparative information. We used the comparative demographic approach (Niel and Lebreton 2005) to estimate priors for r for subantarctic fur seals with the following formula:

where s is the adult survival probability and α the mean age at first reproduction. Adult survival probabilities and age at first reproduction were taken from Beauplet et  al. (2006) and Dabin et  al. (2004), and were respectively between 0.9 and 0.95, and 5 and 8. The resulting prior dis-tribution for r was N(0.077, 0.01).

xt+1 = r + (1 − DD) × x

t+ �

xt,

Yt= x

t+ �

Yt,

r ≈ ln

�

(s × � − s + � + 1) +√

(s − s × � − � − 1)2 − 4 × s × �2

2 × �

�

,

Modelling growth parameters

We used a two-step methodology to study density-dependence on growth parameters. First, we fitted a density-independent growth model to length and weight measurements of pups by cohort. The second step con-sisted in adding density-dependent effects in different ways on these parameters and in selecting the most ade-quate model.

Step 1: growth models

Growth is continuous in pinnipeds, thus making asym-metric and non-linear functions more appropriate to model their growth (McLaren 1993). We chose the growth model developed by Jenss and Bayley (1937). It is a negatively accelerated exponential model with a linear asymptote. Growth is decomposed in two phases: an ini-tial and exponential phase that gives way to a linear phase later in life. This linear growth can admit an asymptotic growth or not, depending on the data.

Parameters were estimated from a mixed model (or hier-archical model). Our hierarchical model included a cohort effect (i) but no individual effect because some individuals had not sufficient growth data to permit including an indi-vidual effect. According to the Jenss-Bayley model, growth of a cohort i may be modelled with the following equation:

where the four parameters �ki are cohort specific growth

parameters, t is the age and �it is the residual error at age t

(stochastic growth variability, measurement error…). Each parameter �

ki can be decomposed: �

ki= �

0k+ �

1ki, where �0

k

are fixed effects common to all cohorts and �1ki are cohort-

specific deviations (random effects), for k = 1, …, 4. This model has a component for linear growth: �1i + �2i × t where �2i determines growth velocity. The other component is negative exponential: − exp(�3i + �4i × t) and models a progressive decrease of growth rate occurring quickly after birth.

The Jenss-Bayley model was inappropriate for model-ling weight of the extreme fasting behavior of pups (Ver-rier et al. 2011a). Therefore, we used an approach based on the difference in weight at a given age. Amsterdam Island fur seal pups reach their maximum weight in July around 230 days of age, and weight decreases beyond that date (Guinet and Georges 2000). A linear model was thus fitted over the period 30–230 days:

It represented the global linear growth rate of pups between their second month of life and the moment of

(1)lit= �1i + �2i × t − exp(�3i + �4i × t) + �

it,

(2)wit= �5i + �6i × t.

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their maximum weight. An early growth rate for the two first months of life of pup (0–60 days) was also estimated.

Step 2: abundance effect on growth parameters

Abundance effects on parameters of growth models were incorporated hierarchically. Each parameter was individu-ally linked to abundance by a linear function:

For length data modelled with the Jenss-Bayley model, we tested the effect of abundance (quantified by �

k),

obtained from the Gompertz state-space model, of the cur-rent year (N

t) and of abundance with a one year lag (N

t−1) on the length at birth parameters (�1i and �3i). Indeed, in pinnipeds, maternal characteristics, and hence environmen-tal conditions encountered during gestation, have a sig-nificant influence on length at birth (Georges and Guinet 2000a, b, 2001). For weight, the effect of abundance of the current year and with a 1 year lag was tested with linear functions in a similar fashion to Eq. 3. One year lag den-sity-dependent models tested the effect of density during gestation, which is the year before pup rearing.

We used the Deviance Information Criterion (DIC; Spiegelhalter et  al. 2002) for comparison between growth models, selecting the model with the lowest DIC. In prac-tice, a difference in DIC values between five and ten is regarded as sufficient to select the model with the lowest DIC (Spiegelhalter et  al. 2007). Analysis were performed using R Statistical Software v3.2.1 (R Core Team 2015) and via the interface from R (‘rjags’ package; Plummer 2015) to JAGS (‘Just Another Gibbs Sampler’; Plummer 2003). Estimates ± standard deviations are reported.

Modelling pre-weaning survival

We used capture–mark–recapture (CMR; Lebreton et  al. 1992) models to estimate survival probabilities. A monthly capture history was constructed for each indi-vidual from December to September. The few births (1% of individuals concerned) that occurred late November were shifted to December due to an insufficient num-ber of individuals. Since individuals were found freshly dead on the breeding colony, survival histories combined live encounters and dead recoveries and we used multi-state models (MSMR) (Pradel 2005) with two states: alive and dead. Capture histories were coded considering three events: 0 = “not observed”, 1 = “seen alive”, 2 = “seen freshly dead”. We started with model Φmonth.cohp-month.cohdcoh where probabilities of monthly survival Φ and capture p varied between months and cohorts (coh), and the monthly probability that a freshly dead individual was recovered d varied between cohorts. The parameter d

(3)�ki= �

0k+ �

k× N

i+ �

1ki.

was constrained to be constant across months because the relatively small number of dead recoveries by month was insufficient to estimate d for each month and each cohort.

Since the state freshly dead only appeared once in the capture histories, we could not use goodness-of-fit tests developed for multistate models (Pradel 2005). We thus assessed the fit of the Cormack–Jolly–Seber model using program U-CARE v.2.3.2 (Choquet et  al. 2009a). The global GOF test was built for males and females separately by adding each component of the GOF tests applied to each cohort separately. The CJS model fitted the data poorly (males: χ² = 190.75, df = 17, P < 0.001; females: χ² = 266.98, df = 15, P < 0.001). A closer inspec-tion indicated that the lack of fit was largely due to het-erogeneity in recapture probability (males: χ² = 179.07, df = 7, P < 0.001; females: χ² = 255.72, df = 7, P < 0.001). Individuals caught in month i were more likely to been caught in month i + 1 than individuals not caught in month i (trap-happiness). To account for trap-happiness, we considered two additional states: ‘trap-aware’ which follows any occasion where an individual is captured, and “trap-unaware” which follows any occasion where it is not captured (Pradel and Sanz-Aguilar 2012). Transition probabilities between states were modelled with a two-step procedure where survival and trap-dependence were considered as successive steps in transition matrices. The fit of this new model, which explicitly accounted for a trap-dependence effect, was satisfactory (see “Results”). From this initial constrained model, month and cohort effects were sequentially tested on each parameter start-ing with d, then p and finally on survival.

Model selection was performed with a modified version of the AIC corrected for small sample sizes (AICc; Akaike 1974). Two models we considered to differ when the AICc difference was greater than 2 (ΔAICc > 2; Burnham and Anderson 2002:70).

We then tested if variation in pup survival or capture could be best modelled with linear or quadratic (on a logit scale) trends by cohort or by month. Trends with varying slopes and intercepts by cohorts were tested. An ANODEV test (Skalski et  al. 1993) was used to detect these trends and the proportion of deviance taking into account (R²) was also calculated (Grosbois et  al. 2008). Once the best structure was selected for each parameter, corrected abun-dance obtained with the Gompertz state-space model was included as a covariate in interaction with survival of each cohort and the R² was calculated.

All estimates and AICc values were computed using program E-Surge v1.9.0 (Choquet et  al. 2009b). Because MSMR models are prone to local minima during the likeli-hood maximisation routine, we ran the same models with random initial values at least 10 times to ensure that they converged to the lowest deviance.

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Results

Population dynamics

Pup abundance increased between 1999 and 2014 (Fig. 2) from ≈1800 to ≈2600 individuals. This corresponded to a mean annual population growth rate of 1.025 (+2.5% per year).

Population growth rate (λ) tended to decrease between 1999 and 2014. The relationship between population growth rate and abundance suggested that, when the pup population exceeded 2400 individuals, growth rate fell below 1 (Fig. 3). However, the Gompertz state space model indicated that the posterior probability that density-depend-ence was constraining population growth (Pr (DD > 0)) was only 0.76 (95% credibility interval for parameterDD: −0.0156 to 0.0316). Although not definitive, this result was suggestive of density-dependence.

Body length

There was no significant trend in length at birth over the study period (Fig.  4). Growth model selection for length is shown in Table  1. Models with density-dependence were favoured for both sexes. The best models included an effect of abundance the current year or with a 1 year lag on growth parameters. Sensitivity analyses and examination of residuals suggested a good fit and robustness to prior choice (not shown).

Growth parameter estimates for body length of male and female pups based on a model with constant parameters are shown in Table  2. There was a significant sex differ-ence in parameter �0

1. This parameter was greater for males

(82.6 ± 0.9) than females (79.7 ± 0.8) (z = 2.406, P = 0.008). Others parameters did not differ significantly between sexes (all P’s > 0.359). Thus, males were longer at birth than females but grew at the same rate.

Density-dependence parameters are shown in Table 3 for the model with the lowest DIC for males and females. 95% Credibility intervals of parameter Ɵ1 and Ɵ3 didn’t include 0 in both sexes, which meant that parameters α1i and α3i were strongly influenced by abundance during the previous year. Parameter α2i appeared to be unrelated to abundance (95% credibility intervals of Ɵ2 included 0). Parameter α4i was influenced significantly by abundance of the previous year for both sexes, and by abundance of the current year for males (95% Credibility intervals of Ɵ4 didn’t include 0). Results nevertheless evidenced a negative effect of cur-rent year abundance on α4i for females (92% of values of Ɵ4 were smaller than 0).

Predicted growth curves for male and female pup length from the selected model [with density-dependence; see residuals in Fig. S1 in Electronic Supplementary Material (ESM)] showed no abundance effect on length at birth but a strong effect on growth (Fig. 5), suggesting that pup size at weaning was lower at high density than at low density.

Fig. 2 Observed (empty circle) and corrected (solid circle) abundance of pups on areas 1 and 2 from 1999 to 2014 obtained from a Gompertz state-space model. Error bars are standard errors

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Body weight

Over the study period, there was no trend in the maximum weight of male pups (Fig.  6), but female pups maximal weight decreased (slope estimate = 0.14, P = 0.04, R² = 0.28).

Males were heavier than females at birth (z > 5, P < 0.001), and grew faster than females during their first 2 months (z = 2.45, P = 0.007) (Table 4) and between 30 and 230 days (z > 5.22, P < 0.001) (Table  5). Model selection for growth during the two first months of life and between 30 and 230 days, indicated that density-dependent models

Fig. 3 Population growth rate (λ= Nt+1/Nt where Nt+1 is population size at time t + 1) of pups in relation to abundance at year t. Error bars are 95% confidence intervals

Fig. 4 Body size at birth for newborn females (solid circle) and males (empty square) sub-antarctic fur seal of “La Mare Aux Éléphants” from 1999 to 2014. Numbers are sample sizes for both sexes. Error bars are standard deviations

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were preferred for both sexes (Tables  6, 7, respectively). Sensitivity analyses and examination of residuals suggested a good fit and robustness to prior choice (not shown).

Density-dependence parameters are shown in Table  8 for models with the lowest DIC for males and females. α5i (weight at birth) of growth model between 0 and 60 days seemed to be unrelated to abundance for both sexes.

Growth rate of females between 30 and 230 days were strongly affected by abundance of the previous year (98% of values of Ɵ6 were smaller than 0), suggesting that females were lighter at 230 days at high density than at low density. The same trend was observed for males with 91% of values of Ɵ6 smaller than 0. In females, but not in males, growth rate from birth to weaning was strongly influenced by abundance of the previous year (90% of values of Ɵ6 were smaller than 0).

Pre-weaning survival

Goodness-of-fit tests of the MSMR model taking into account trap-dependence for males indicated a good fit (χ² = 11.68, df = 10, P = 0.31). Dead recovery probability var-ied according to cohorts. Capture probability increased for “trap-aware” individuals and decreased for others (Fig. 7a) in all cohorts. Survival increased quadratically by month and differently according to cohorts (Table 9; Fig. 7b).

For females, goodness-of-fit tests of the MSMR model taking into account trap-dependence indicated a good fit (χ² = 11.26, df = 8, P = 0.19). Dead recovery probability var-ied according to cohorts. Capture probability increased for “trap-aware” individuals and decreased for others (Fig. 8a) in all cohorts. Survival tended to increase quadratically by month and differently according to cohorts (Table  10; Fig. 8b).

Models with density-dependence were not selected with AICc compared to the models where survival varied quadratically by month and specifically by cohort, but had lower AICc values that models with the same monthly quadratic survival trend for all cohorts (Tables  9, 10). However, slope parameters for models where pup survival was a function of density were all statistically significant (Table  11), although the propor-tion of variance explained was low (Tables 9, 10). Slope

Table 1 Modelling the effect of abundance on body length from birth to weaning of male and female pup of subantarctic fur seals from Amster-dam Island

The number of individuals and observations are indicated in brackets for each sexNInd is the number of individualsNObs is the number of observations

Model DIC ΔDIC Penalty Mean deviance

♂NInd(623)NObs(4058)

DD model (linear effect of N − 1 on α1 and α3; N on α2 and α4) 22895.6 0.0 33.6 22,862DD model (linear effect of N − 1 on all αk) 22896.4 0.8 34.4 22,862DD model (linear effect of N on all αk) 22899.7 4.1 35.7 22,864Model without DD (fixed α for all years) 23041.8 146.2 4.8 23,037

♀NInd(800)NObs(5418)

DD model (linear effect of N − 1 on all αk) 30349.9 0.0 34.9 30,315DD model (linear effect of N − 1 on α1 and α3; N on α2 and α4) 30350.3 0.4 34.3 30,316DD model (linear effect of N on all αk) 30361.2 11.3 37.2 30,324Model without DD (fixed α for all years) 30794.8 444.9 4.8 30,790

Table 2 Growth parameter estimates for body length of male and female pups based on a model with constant parameters

Parameter Mean Standard deviation

Male Female Male Female

α1 82.60 79.70 0.93 0.77α2 0.0129 0.0113 0.0034 0.0028α3 2.85 2.84 0.05 0.04α4 −0.0162 −0.0162 0.0011 0.0011

Table 3 Percentage of negative values in the posterior distribution of density-dependence parameters (Ɵ) for body length

Values shown in bold indicate parameters for which 95% credible intervals do not include zero

Male Female

DD model (linear effect of N − 1 on α1 and α3; N on α2 and α4) Ɵ1 99.5 100.0 Ɵ2 26.4 15.6 Ɵ3 100.0 100.0 Ɵ4 97.3 91.7

DD model (linear effect of N − 1 on all α) Ɵ1 98.0 99.9 Ɵ2 12.3 43.4 Ɵ3 99.8 100.0 Ɵ4 96.3 96.5

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Fig. 5 Theoretical growth curve for male (black) and female (grey) at low density (1800 pups; solid lines) and at high density (2600 pups: dashed lines) based on density-depend-ent model (linear effect of N − 1 on all parameters α). The unit for age is days

Fig. 6 Maximum weight reached at 230 days (±15 days) for females (solid circle) and males (empty square) subant-arctic fur seal of “La Mare Aux Éléphants” from 1999 to 2014. Numbers are sample sizes for both sexes. Error bars are standard deviations

Table 4 Growth parameter estimates for weight of male and female pups from birth to 60 days based on a model with constant parameters

Parameter Mean Standard deviation

Male Female Male Female

α5 5.10 4.56 0.04 0.03α6 0.0429 0.0390 0.0012 0.0010

Table 5 Growth parameter estimates for weight of male and female pups from 30 to 230 days based on a model with constant parameters

Parameter Mean Standard deviation

Male Female Male Female

α5 6.11 5.50 0.08 0.06α6 0.0307 0.0272 0.0005 0.0004

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parameters suggested a negative effect of abundance on survival for both sexes.

Estimated pup’s annual survival between 1999 and 2014 are shown in Fig.  9. Males tended to have a lower survival probability (mean ± SE 0.53 ± 0.05) than females (mean ± SE 0.58 ± 0.04). For both sexes, exclud-ing the poor survival observed in 1999, there was a neg-ative trend for survival from 2000 to 2014.

Discussion

As population size increases in large mammals, density-dependent processes are enhanced and lead to a reduction in population growth rate (Sinclair 2003; Sibly et al. 2005;

Bonenfant et al. 2009). In subantarctic fur seals on Amster-dam Island, our analysis of pup abundance time series from 1999 to 2014 suggests that density-dependent pro-cesses occur in this population. We clearly showed a nega-tive influence of abundance on length and weight growth rates of pups. Pup survival between birth and weaning seem also related to abundance, but with a relatively weak influence. Additionally, our results support conclusions of several studies on subantarctic fur seals or other Otari-dae that males are heavier at birth than females (Trillmich 1986; Georges and Guinet 2000a; Chilvers et  al. 2007; Oosthuizen et al. 2015). However, we found a between-sex difference in weight growth rate, which was not detected previously in this population (Guinet and Georges 2000; Chambellant et al. 2003; but see; Luque et al. 2007; Oost-huizen et al. 2015).

Pup abundance

Previous studies on this subantarctic fur seal population suspected, but did not evidence, density-dependent pro-cesses to occur (Chambellant et  al. 2003; Dabin et  al. 2004; Beauplet 2005; Authier et al. 2011). The parameter DD quantifying density-dependence suggested that the population growth rate decreased when the population increased. Even if our modeling approach (state-space model) allowed to separate observation error and inherent stochastic noise in the time series (Lebreton 2009; Knape and De; Valpine 2012), count precision (estimated error of 12% by the Gompertz model) may not be sufficient to statistically detect a density-dependent effect. In addition,

Table 6 Modelling the effect of abundance on weight variation from birth to 60 days of male and female pup of subantarctic fur seals from Amsterdam Island

The number of individuals and observations are indicated in brackets for each sex

Models DIC ΔDIC Penalty Mean Deviance

♂NInd(618)NObs(2828)

DD model (linear effect of N on all αk) 9125.6 0.0 22.6 9103DD model (linear effect of N − 1 on all αk) 9125.7 0.2 22.7 9103Model without DD (fixed α for all years) 9220.0 94.4 3.0 9217

♀NInd(795)NObs(3691)

DD model (linear effect of N on all αk) 11355.4 0.0 23.4 11,332DD model (linear effect of N − 1 on all αk) 11355.4 0.0 23.4 11,332Model without DD (fixed α for all years) 11595.0 239.6 3.0 11,592

Table 7 Modelling the effect of abundance on weight variation from 30 to 230 days of male and female pup of subantarctic fur seals from Amsterdam Island

The number of individuals and observations are indicated in brackets for each sex

Models DIC ΔDIC Penalty Mean Deviance

♂NInd(477)NObs(11,506)

DD model (linear effect of N on all αk) 55256.5 0.0 24.5 55,232DD model (linear effect of N − 1 on all αk) 55256.7 0.2 24.7 55,232Model without DD (fixed α for all years) 56151.0 894.5 3.0 56,148

♀NInd(639)NObs(15,400)

DD model (linear effect of N − 1 on all αk) 69410.6 0.0 25.6 69,385DD model (linear effect of N on all αk) 69411.5 0.9 25.5 69,386Model without DD (fixed α for all years) 71462.0 2051.4 3.0 71,459

Table 8 Percentage of negative values in the posterior distribution of density-dependence parameters (Ɵ) for weight

A value shown in bold indicates a parameter for which 95% credible intervals does not include zero

Male Female

0–60 day 30–230 day 0–60 day 30–230 day

DD model (linear effect of N on all αk) Ɵ5 41.3 35.7 31.0 50.7 Ɵ6 14.5 63.3 90.0 76.6

DD model (linear effect of N-1 on all αk) Ɵ5 26.8 61.1 30.9 79.9 Ɵ6 78.3 90.7 90.1 97.8

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although we assumed that the number of pups depicted the total population size based on the relative temporal stability of female breeding probability and age structure (see “Materials and methods”), the number of pups make a relatively small percentage of the whole population on Amsterdam Island.

Pup growth

Contrary to our first prediction, no effect of abundance was found on birth length and weight. One hypothesis that

might explain this result is that subantarctic fur seal females in poor condition could delay or terminate their reproduc-tion instead of giving birth to a smaller pup. Indeed, pinni-peds may adjust the amount of energy allocated to the foe-tus (Bowen et al. 2002). Embryonic diapause occurs in fur seals (Bester 1995), during which embryo’s growth is sta-bilized for about 4 months in subantarctic fur seals. Dams must ensure simultaneously the growth of the embryo and the rearing of its pup from April to December. Prey avail-ability for dams is thus a major limiting factor for foetus growth and extended foraging trips of breeding females at Amsterdam Island (11–23 days in comparison of 1–12 days for other species: Boyd 1999; Georges and Guinet 2000b; Beauplet et al. 2004; Staniland et al. 2010) suggest that per capita prey availability is relatively low (Beau-plet et  al. 2004). It was shown in a fur seal species with an analogous lactation period that females in poor body condition were less likely to give birth the following year (Guinet et  al. 1998). These authors reported higher abor-tion rates and lower implantation rates when dam body condition was poor. Another non-exclusive hypothesis could be that during the last 3 months of gestation, when most of prenatal pups’ growth is taking place, no or little density-dependence occurs on the foraging areas. During this period after their pup is weaned and 3 month prior to parturition, females are able to extend their foraging range over large areas resulting in an intrasexual competition between females which may be reduced as individuals are spread over a much larger foraging area compared to the pup rearing period. Females can also reside in high prey density areas, without having to commute back and forth to their breeding location.

We found that body growth rate of pups was influenced by pup abundance of the previous and the current year, verifying our second prediction. In pinnipeds, especially in fur seals, pup growth rate during rearing reflects the level of maternal input because pups are entirely depend-ent of their mothers for nutrition (Trillmich 1996; Guinet and Georges 2000; Guinet et al. 2000; Bowen et al. 2002; Verrier et al. 2011a; Gentry and Kooyman 2014). Thus, we suspect that when population size increased, intraspecific and specifically intrasexual competition between lactating adult females also increased in this oceanographic context of impoverished prey availability (Gregg and Rousseaux 2014), leading to reduced maternal input to pups and thus limiting pup growth. In this case density, expressed as the number of females per km² of foraging habitat, would affect foraging performances of breeding females and con-sequently pup growth.

Alternatively, but not exclusively, the reduction in pup growth could be due to negative effects of density onshore. For example, high numbers of females and pups per m² on the breeding colony may facilitate dispersion of diseases

a

b

Fig. 7 a Capture probability variation for “trap-aware” individuals (empty circle) and “trap-unaware” individuals (solid circle) for males pups. b Survival probability variation for males pups in 2013. Error bars are 95% confidence intervals

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and more aggressive behavior of other breeding females or males towards conspecific or pups, thereby leading to non-lethal infection or mother–pup separations (Harcourt 1992; Cassini 1999; Chilvers et  al. 2005). The effect of abun-dance of the previous year on pup growth rates could be also due to carry-over effects of density during gestation. However, we were not able to unravel delayed and direct effects in our study.

The deterioration of growth performance due to density-dependent processes, combined with the extreme repeated fasting durations that pups have to face, result in the low-est growth rate from birth to weaning ever observed among Otaridae (see Chambellant et  al. 2003; Beauplet 2005). Growth rates at Amsterdam Island seemed most likely to be the lowest growth rates among Otaridae, even lower than at Marion island or Gough island (Oosthuizen et al. 2015).

We could not fit the Jenss-Bayley growth curve models to pup weight data. Linear models accounting for an effect

of abundance were favoured. Weight growth rate param-eters from 30 to 230 days were influenced by abundance with a stronger effect on female pups than male. Hence, if we assume that, as for body length growth, density-depend-ent effects translate into lower maternal input during years with high density, the same impact might appear on weight growth rate. This effect of abundance on pup weight growth was also apparent, although not as strong, for growth rates from birth to 60 days growth.

Pup survival

Our results suggest a weak negative effect of abundance on pre-weaning pup survival for both sexes. We suggest two non-exclusive alternative hypotheses to explain this weak effect of abundance on pre-weaning survival. First, as sug-gested by Georges and Guinet (2000a), the topology of “La Mare aux Éléphants” (large boulders and blocks of rock)

Table 9 Modelling capture (p) and survival (Φ) probabilities for young males between birth and weaning

Trends were tested with an analysis of deviance (ANODEV). ANODEV is the F-statistic (F(df1,df2)), R² is the proportion of variance taking into account by the trend. Selected models are indicated in boldAICc Akaike’s information criterion corrected for small sample size, ΔAICc AICc difference between the model and the best model, k number of parameters estimated, Dev Deviance

Model Hypothesis tested AICc ΔAICc k Dev ANODEV P R²

Modelling capture probabilities Φmonth*coh […]dcoh

 pmonth+coh Monthly variation by cohort (additive effect) 3425.81 0.00 172 3066.54 pcoh_linear Linear trend between cohorts 3427.01 1.20 158 3098.16 0.62(27,14) 0.861 pmonth*coh_quadratic Cohort specific monthly quadratic trend 3428.09 2.28 208 2989.57 1.90(77,156) <0.001 0.48 pcoh_quadratic Quadratic trend between cohorts 3429.22 3.41 160 3096.03 0.56(29,12) 0.901 pmonth*coh_linear Cohort specific monthly linear trend 3445.43 19.60 182 3064.29 1.10(51,182) 0.319 pcoh Varying by cohort 3460.55 34.70 156 3136.03 pmonth Varying by month 3537.66 111.85 148 3230.41 pmonth_linear Monthly linear trend 3543.04 117.23 134 3265.84 6.70(3,14) 0.005 0.59 pmonth_quadratic Monthly quadratic trend 3545.60 119.79 136 3264.12 3.70(5,12) 0.029 0.61 p Constant 3589.63 163.82 132 3316.70 pmonth*coh Varying by cohort and by month 3635.66 209.85 364 2831.68

Modelling survival probabilities […]pmonth_lineardcoh

 Φmonth*coh_ quadratic Cohort specific monthly quadratic trend 3522.24 96.43 56 3408.65 4.70(38,78) <0.001 0.70  Φmonth*coh_linear Cohort specific monthly linear trend 3668.34 242.53 43 3581.40 1.80(25,91) 0.023 0.46 Φmonth+coh Monthly variation by cohort (additive effect) 3685.62 259.81 38 3608.88 Φcoh_quadratic Quadratic trend between cohorts 3734.75 308.94 32 3670.23 0.47(14,16) 0.919 Φcoh_ linear Linear trend between cohorts 3759.31 333.50 31 3696.82 0.25(13,7) 0.985 Φmonth Varying by month 3762.10 336.29 26 3709.76 Φcoh Varying by cohort 3797.71 371.90 30 3737.25 Φmonth_ quadratic Monthly quadratic trend 3807.80 381.99 20 3767.59 4.20(2,6) 0.072 Φmonth_ linear Monthly linear trend 3826.55 400.74 19 3788.37 5.30(1,7) 0.055 0.43 Φ Constant 3884.27 458.46 18 3848.10

Modelling density-dependence on survival […]pcoh*month_quadraticdcoh

 Φmonth*coh_ quadratic.N.N² Quadratic density-dependence 3744.74 318.93 26 3692.39 0.21 Φmonth*coh_ quadratic.N Linear density-dependence 3793.79 367.98 23 3747.51 0.06

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offers many hiding places where pups can avoid a density-dependent mortality due to trampling by adult males (Har-court 1992). Therefore, such an effect of density, expressed as the number of females per m² in the breeding colony, seems unlikely.

Second, pre-weaning survival may be favoured at the expense of body and weight growth when abundance increases. There is a strong trade-off between growth and survival in pinnipeds (Trillmich 1996), and the extreme fasting endured by pups may exacerbate this trade-off. During the rearing, pups must both manage their fat reserves and develop their swimming and diving abilities

(Beauplet et  al. 2003; Guinet et  al. 2005; Verrier et  al. 2011b). Amsterdam Island pups seem to favor energy sparing, in order to survive to the increasing fasting dura-tion during lactation, over swimming abilities (Beauplet et  al. 2003; Verrier 2007), making density-dependent effect more visible for growth than for survival. Indeed, young of the year do not spend much time in water devel-oping their abilities but rest on land (Arnould et al. 2003; Guinet et  al. 2005; Verrier 2007; Verrier et  al. 2009, 2011b).

Nevertheless, this trade-off potentially makes pups vulnerable to environmental conditions once they become independent and leave the colony. In many mammal spe-cies including fur seals, large size and heavy weight at weaning are positively related to post-weaning survival (Festa-Bianchet et al. 1997; Beauplet et al. 2005; Gaste-bois et  al. 2011; Verrier et  al. 2011a). In fur seals, this relationship is probably linked to foraging capacities, since Guinet et  al. (2005) found changes in diving per-formance related only to pup size and not to its age. Since density-dependence reduces pup growth and weaning condition, increasing abundance is expected to have a strong negative effect on post-weaning juvenile survival. Bonenfant et  al. (2009) showed that density-dependent effects are generally not found on survival from birth to weaning in large vertebrate herbivores giving birth at one offspring annually, compared to species with several off-spring (that have a higher energy expenditure per breed-ing attempt), or post-weaning survival (e.g., Clutton-Brock et al. 1987).

Possible joint density-independence influence

Environmental factors such as oceanographic conditions on the foraging areas were not taken into account herein due to a lack of accurate knowledge on at-sea population distribution and thus on oceanographic factors that could potentially affect foraging efficiency. Although our study investigated and evidenced density-dependence processes in early-life demographic traits, extrinsic factors, poten-tially interacting with density-dependent effects, may contribute to population dynamics. The negative trend in yearly pre-weaning survival of pups could be due to trends in environmental factors such as oceanic produc-tivity, competition with other meso-predators at sea, or direct predation on subantarctic fur seals at sea.

Conclusion

Compared to terrestrial mammals (Bonenfant et al. 2009; Williams et al. 2013), relatively few studies investigated

a

b

Fig. 8 a Capture probability variation for “trap-aware” individu-als (empty circle) and “trap-unaware” individuals (solid circle) for females pups. b Survival probability variation for females pups. Error bars are 95% confidence intervals

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the effects of density-dependence in marine mammals (Eberhardt 1977, 2002; Rotella et al. 2009; Ferrari et al. 2013; Williams et  al. 2013). Pinnipeds are good model species to investigate density-dependence in large marine

mammals and long-lived species. Results obtained here are consistent with the existing literature on large ter-restrial mammals. We found that early-life demographic traits were related to breeding population abundance. We clearly evidenced a deterioration in pup growth and body condition at weaning when breeding population increased. A strong intraspecific competition between lactating adult females, exacerbated by low productivity of foraging habitat, was suspected to occur when popula-tion size increased and lowered maternal input to pups, thus limited their growth. Body condition is generally connected with survival and it appeared herein a strong trade-off in favour of survival. Pup pre-weaning condition may be more sensitive to stressful conditions than pre-weaning survival, and may respond to increasing density before pre-weaning survival.

Given how female body length is a critical determinant of reproductive success under selection (Beauplet and

Table 10 Modelling capture (p) and survival (Φ) probabilities for young females between birth and weaning

Trends were tested with an analysis of deviance (ANODEV). ANODEV is the F-statistic (F(df1,df2)), R² is the proportion of variance taking into account by the trend. Selected models are indicated in boldAICc Akaike’s information criterion corrected for small sample size, ΔAICc AICc difference between the model and the best model, k number of parameters estimated, Dev Deviance

Model Hypothesis tested AICc ΔAICc k Dev ANODEV P R²

Modelling capture probabilities Φmonth*coh […]dcoh

 pmonth+coh Monthly variation by cohort (additive effect) 4141.25 0.00 172 3786.21 pmonth*coh_linear Cohort specific monthly linear trend 4158.09 16.84 182 3781.71 1.46(51,182) 0.037 0.29 pcoh_quadratic Quadratic trend between cohorts 4158.30 17.05 160 3828.77 0.49(29,12) 0.943 pcoh_linear Linear trend between cohorts 4162.57 21.32 158 3837.28 0.42(27,14) 0.974 pmonth*coh_quadratic Cohort specific monthly quadratic trend 4166.15 24.90 208 3729.71 1.62(77,156) 0.006 0.45 pcoh Varying by cohort 4199.87 58.62 156 3878.81 pmonth_quadratic Monthly quadratic trend 4269.65 128.40 136 3990.79 7.16(5,12) 0.003 0.75 pmonth_linear Monthly linear trend 4272.61 131.36 134 3997.95 9.30(3,14) 0.001 0.67 pmonth Varying by month 4273.48 132.23 148 3969.33

pmonth*coh Varying by cohort and by month 4323.02 181.77 364 3543.92 p Constant 4325.45 184.20 132 4054.99

Modelling survival probabilities […]pmonth_ quadraticdcoh

 Φmonth*coh_quadratic Cohort specific monthly quadratic trend 4357.35 216.10 58 4240.11 3.10(38,78) <0.001 0.60 Φmonth+coh Monthly variation by cohort (additive effect) 4470.27 329.02 40 4389.67 Φmonth*coh_linear Cohort specific monthly linear trend 4523.98 382.73 45 4433.23 1.52(25,91) 0.078 0.29 Φmonth Varying by month 4556.90 415.65 28 4500.61 Φcoh_quadratic Quadratic trend between cohorts 4579.07 437.82 34 4510.64 0.37(14,6) 0.941 Φcoh_linear Linear trend between cohorts 4583.27 442.02 33 4516.87 0.42(13,7) 0.916 Φmonth_quadratic Monthly quadratic trend 4626.06 484.81 22 4581.88 5.20(2,6) 0.049 0.64 Φmonth_linear Monthly linear trend 4632.00 490.75 21 4589.84 11.01(1,7) 0.013 0.60 Φcoh Varying by cohort 4680.29 539.04 32 4615.90 Φ Constant 4763.24 621.99 20 4723.09

Modelling density-dependence on survival […]pmonth_ quadraticdcoh

 Φmonth*coh_quadratic.N Linear density-dependence 4613.38 472.13 25 4563.15 0.06 Φmonth*coh_quadratic.N.N² Quadratic density-dependence 4614.66 473.41 28 4558.37 0.07

Table 11 Values of beta parameter for density-dependent parameter slope in the model with quadratic density-dependence in survival for males and linear density-dependence in survival for females. Mean estimate (95% confidence intervals) are reported

Interaction with linear parameter of survival

Interaction with quadratic parameter of survival

Quadratic density-dependent model for male βN 28.7 (20.0; 37.4) −35.7 (−45.7; −25.8) βN² −27.5 (−36.2; −18.8) 34.3 (24.5; 44.2)

Linear density-dependent model for female βN 1.1 (0.5; 1.8) −1.2 (−2.0; −0.4)

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Guinet 2007; Authier et al. 2011), subantarctic fur seals on Amsterdam Island offer promising grounds for investigat-ing how much density-dependence processes during early-life shape future fitness (post-weaning-survival, reproduc-tive performance…).

Acknowledgements We thank the field workers involved in mis-sions on Amsterdam Island for collecting the data. The long-term demographic study was supported by the French Polar Institute IPEV (program No 109, resp. H. Weimerskirch), Terres Australes et Antarctiques Françaises and Zone Atelier Antarctique et Subantarc-tique (CNRS-INEE) Handling and manipulation of all animals were approved by the IPEV ethics committee. All animals in this study were cared for in accordance with its guidelines. We thank D. Bes-son for the data management. We thank N.G. Yoccoz for constructive comments on earlier drafts.

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