An evolutionary perspective on reproductive individual heterogeneity in a marine vertebrate

Authors


Summary

  1. Although the quantification of individual heterogeneity in wild populations' vital rates has recently attracted growing interest among ecologists, the investigation of its evolutionary consequences remains limited, mainly because of the difficulties in assessing fitness and heritability from field studies on free-ranging animals. In the presence of individual variability, evaluation of fitness consequences can notably be complicated by the existence of trade-offs among different vital rates.
  2. In this study, to further assess the evolutionary significance of previously quantified levels of individual heterogeneity in female Weddell seal (Leptonychotes weddellii Lesson) reproductive rates (Chambert et al. 2013), we investigated how several life-history characteristics of female offspring were related to their mother's reproductive rate, as well as to other maternal traits (age and experience) and environmental conditions at birth.
  3. The probability and age of first reproduction (recruitment) of female offspring was not related to their mother's reproductive rate, suggesting the absence of a maternal trade-off between the number and quality of offspring a female produces. Evidence of a positive, but relatively weak, relationship between the reproductive rates of a mother and her female offspring was found, suggesting some degree of heritability in this trait.
  4. Using a simulation approach based on these statistical findings, we showed that substantial differences in the number of grandchildren, produced through female progeny, can be expected among females with different reproductive rates.
  5. Despite the presence of substantial stochastic variability, due to environmental fluctuations and other unidentified mechanisms, and in the light of the fact that the metrics obtained do not provide a full measure of real fitness, our results do suggest that the individual reproductive variability found in female Weddell seals could potentially have important fitness consequences.

Introduction

The investigation of among-individual differences in phenotypic quality, survival and reproduction in wild populations is gathering more and more attention in the ecology literature (e.g. Cam & Monnat 2000; Cam et al. 2002, 2012; Bergeron et al. 2008, 2011; Steiner, Tuljapurkar & Orzack 2010; Aubry et al. 2011). At first, ecologists were mainly interested in controlling for latent individual heterogeneity in population studies because it can hamper the detection of individual life-history trade-offs, such as reproductive costs or senescence (Service 2000; Cam et al. 2002; Weladji et al. 2008). More recently, there has been a growing interest in the evolutionary significance of individual variability in wild populations (Wilson & Nussey 2010; Bergeron et al. 2011). Investigating how individual heterogeneity relates to fitness and assessing whether it has heritable bases are important steps to better understand the extent to which this variability can be under selective pressure. Fisher's fundamental theory of natural selection postulates that the rate of change in fitness in a population is equal to the additive genetic variance in fitness (Fisher 1958). From this theory, it is predicted that traits strongly associated with fitness, such as life-history traits, will exhibit low additive genetic variance and therefore low heritability (Charlesworth 1987; Mousseau & Roff 1987). Therefore, the potential for current action of natural selection in wild populations is generally expected to be low as a result of past selective filtering (Kruuk et al. 2000), and some empirical studies have provided direct support to this prediction (Gustafsson 1986; Mousseau & Roff 1987; Roff & Mousseau 1987). On the other hand, some mechanisms, such as environment fluctuation or frequency-dependent selection, can be responsible for the maintenance of substantial levels of genetic variance in traits closely linked to fitness (Charlesworth 1987). The existence of such patterns has been found in some field studies (e.g. Van Noordwijk, van Balen & Scharloo 1980) and is supported by empirical evidence for the existence of natural selection bouts, often attributed to environmental variation, in the wild (Siepielski, DiBattista & Carlson 2009). Further investigation involving different taxa and various environmental and historical contexts are therefore needed to strengthen our empirical knowledge of the prevalence and dynamics of natural selection in nature (Mousseau & Roff 1987; Kruuk et al. 2000; Siepielski, DiBattista & Carlson 2009).

Here, we investigate several aspects of the potential evolutionary consequences of individual reproductive heterogeneity in a population of Weddell seals (Leptonychotes weddellii). In a previous study, Chambert et al. (2013) were able to quantify the amount of latent individual variation in female reproductive rates; based on their results, they suggested that females of high quality (here, defined by the magnitude of an individually varying effect pertaining to reproductive rates) could be expected to have a lifetime reproductive output twice as large as that of low-quality females. This finding suggests that the among-female variability in reproductive rates quantified in this population could yield important fitness differences. However, a female's fitness does not simply depend on the number of offspring she produces, but also on the reproductive success of her offspring, which will ultimately determine her genetic contribution to the population through her number of grandchildren (Hunt et al. 2004). Therefore, a thorough assessment of the fitness consequences of the quantified level of individual heterogeneity must also consider how a female's reproductive rate may be related to her offsprings' lifetime reproductive success. First of all, one must consider potential trade-offs between offspring quantity and quality, which are expected to occur at the individual level (Lack 1947; Stearns 1992). If there is more variation in resource allocation than acquisition, a negative relationship between reproductive rates and offspring quality will be expressed at the among-individual level (Van Noordwijk & De Jong 1986). Females producing more offspring than average will do so at the cost of lower offspring quality, such that they will not necessarily have larger fitness. On the other hand, if among-individual variance primarily concern resource acquisition (Van Noordwijk & De Jong 1986), a positive relationship is expected between offspring quantity and quality (Reznick, Nunney & Tessier 2000), and a female's fitness should be positively related to her reproductive rates.

The relationship between a female's reproductive performance and the success of her offspring can also be affected by other maternal factors (Mousseau & Fox 1998), both environmental and genetic. First, environmental conditions early in life can be an important determinant of survival and future reproductive success (Lindström 1999; Lummaa & Clutton-Brock 2002). Therefore, in fluctuating environments, females can directly influence their offspring's fate through the choice of which years they reproduce in. This type of flexible strategy is more prevalent in iteroparous species where investment in any reproductive event is highly costly (Erikstad et al. 1998), but also requires the environment to be sufficiently predictable. Fitness will be maximized for individuals who are able to spread their reproductive effort across years with the most favourable conditions. In the study population of Weddell seals, large annual fluctuations in cohort size (i.e. number of pups born each year) have been observed (Garrott et al. 2012), varying from 169 to 603 pups within the last 10 years. This pattern suggests females use a flexible reproductive strategy, varying both age at recruitment (Hadley et al. 2006) and frequency of subsequent reproduction to cope with important annual variations in environmental conditions (Hadley, Rotella & Garrott 2007b; Rotella et al. 2009; Chambert, Rotella & Garrott 2012; Garrott et al. 2012). Secondly, offspring quality can be positively influenced by maternal quality through the effects of heritable factors, either genetic or epigenetic. In such a case, individual variation in female reproductive rates will produce similar variation in fitness, and because there is heritability, traits involved should be under natural selection. But because heritability of reproductive frequency is expected to be very low (Charlesworth 1987), such a scenario seems very unlikely.

In this study, we addressed the evolutionary consequences of individual reproductive heterogeneity in female Weddell seals through three successive analyses. First, we investigated the relationship between female reproductive rates and several life-history characteristics of their female offspring. In this first analysis, we also assessed the influence of other maternal traits (age, breeding experience) and environment at birth on offspring reproductive success. Next, using a mother–daughter regression approach, we quantified the degree of heritability in female reproductive rates. Finally, using a simulation approach based on the results of the first two analyses, we calculated the expected number of grandchildren (proxy of fitness) produced by females with different reproductive rates. Because we do not have information on male reproduction, our inferences on fitness were limited to the contribution of female progeny. We acknowledge and discuss the fact that in a polygynous species such as the Weddell seal (Stirling 1969), maternal resource allocation could potentially be biased towards male progeny (Trivers & Willard 1973; Hewison & Gaillard 1999), a mechanism potentially having important fitness consequences. Despite this limitation, our endeavour at further investigating cross-generational influences of individual reproductive heterogeneity in females provides important insights regarding the evolutionary consequence of individual reproductive heterogeneity in wild animal populations.

Materials and methods

Study population and data collection

The study population forms colonies in Erebus Bay [Ross Sea, Antarctica (77·62°–77·87°S, 166·3°–167·0°E)], and each reproductive female births a single pup during October–November. Females typically start breeding at age 7 or 8 and reproduce in 65% of years thereafter, but substantial disparities in reproductive frequency have been shown (Chambert et al. 2013). This population has been monitored through a mark–recapture programme for more than four decades (Siniff et al., 1977). Each year, colonies are frequently visited during the pupping season to tag pups and unmarked adults, and five to eight population surveys are conducted. During surveys, all tagged and untagged seals encountered are recorded, along with their sex and reproductive status. Since 1982, virtually every pup born in the study population has been tagged and, currently, virtually all resident females and more than 85% of adults hauling out in the area each year are marked. Each female with a pup is detected (Hadley et al. 2006), and non-reproductive females attending the study area are also highly detectable (Rotella et al. 2009). Males are also detected on the ice, but information about their reproductive contribution cannot be directly obtained from field observations. Thanks to the intensive monitoring of the population and the strong female philopatry of this species (Cameron et al. 2007; Hadley, Rotella & Garrott 2007a), we are able to precisely track the reproductive history of locally born females and their offspring (Garrott et al. 2012; Rotella et al. 2012; Chambert et al. 2013).

Statistical modelling

First, we investigated the potential effects of several maternal covariates and cohort size (as a surrogate of annual environmental conditions) on female offspring's probability of recruitment and age at first reproduction. As defined in this study (see below), probability of recruitment, that is, first reproductive event, is a combination of (i) survivorship from birth to age at reproductive maturity and (ii) probability of first reproduction by age 10 conditional on having survived the juvenile period. Secondly, we quantified the relationship between a mother's and daughter's individual reproductive effects. These variables, denoted ‘MomIRE’ for mothers and ‘OffspIRE’ for adult female offspring, corresponded to individually varying parameters pertaining to reproductive rates from Chambert et al. (2013). To incorporate the uncertainty associated with these parameters, we used a subset of 2,000 values picked at regular intervals from the collection of Markov chain Monte Carlo (MCMC) draws used to approximate their posterior distributions.

We used a Bayesian approach for inferences, based on both parameter posterior distributions and model comparison. All models were implemented in program OpenBUGS (Lunn et al. 2009), using a Gibbs sampling algorithm and MCMC to sample the posterior distribution of parameters. To perform model comparison, we incorporated binary inclusion variables wk (Link & Barker 2006; Royle & Dorazio 2008), used as multipliers on each of the k parameters. With this approach, competing models can be defined by the combination of values (0 or 1) for each wk, given that the kth parameter is present in the model only when wk = 1. Because vague priors were used on all regression coefficients, total prior uncertainty was maintained constant across competing models by properly scaling the variance of priors as explained by Link and Barker (2006). A uniform U(0,100) distribution was specified for total prior variance V, and all regression coefficients were assigned a normal prior with mean 0 and scaled variance equal to V/Km, where Km is the number of parameters in model m. We assumed no prior knowledge and thus specified equal prior probability for all competing models, which resulted in a prior probability of 0·5 for each inclusion variable wk. The posterior probabilities of competing models provided a measure of model support and allowed derivation of the posterior probabilities of each wk. The support of a covariate was assessed from the extent to which the posterior probability of the associated inclusion parameter wk was larger than its prior probability of 0·5. For each analysis, we ran 2 parallel chains from different sets of initial values, had a burn-in period of 5000 iterations and used the subsequent 1 000 000 iterations for inference. Adequate convergence was checked using visual examination of sample path plots. We also checked that all competing models were visited during the MCMC procedure (see Table 1).

Table 1. Model selection results from the first step of analyses of offspring probability of recruitment and age at first reproduction. The top part of the table shows the posterior probability of each competing model, while the bottom part shows the posterior probability of inclusion of each covariate. Note that non-informative priors were assumed, such that each covariate had a prior probability of inclusion of 0·5 and the prior model probabilities were equal among all competing models (0·125). The covariates considered were cohort size (CohSize), mother age (MomAge) and mother experience (MomExp) at the time of offspring birth
ModelProbability of recruitmentAge at first reproduction
Model posterior probabilityMCMC sample size*Model posterior probabilityMCMC sample size*
Constant0·009183 360·8271 653 290
CohSize0·5551 109 8490·068136 878
MomExp0·0005130·086171 494
MomAge0·00355740·00815 163
CohSize + MomExp0·03263 2060·00815 667
CohSize + MomAge0·354707 8460·0023815
MomExp + MomAge0·0005950·0012902
CohSize + MomExp + MomAge0·04794 0810·000791
CovariatePosterior probability of covariate inclusion
Probability of recruitmentAge at first reproduction
  1. MCMC, Markov chain Monte Carlo.

Mother age0·4040·011
Cohort size0·9880·079
Mother experience0·0790·095

Probability of recruitment and age at first reproduction

For the analysis on probability of recruitment, the binary response variable of interest (Y) was the occurrence (Y = 1) or not (Y = 0) of a first reproductive event, by age 10, of a female offspring. This variable Y was modelled as a Bernoulli trial, with a probability π of recruiting by age 10. We used age 10 as a threshold age for recruitment as did Garrott et al. (2012) because more than 96% of females that ever recruited have done so by age 10. This threshold allowed us to include as many cohorts as possible while minimizing errors due to ignoring females that recruited later than the threshold. The data set of interest consisted of 1154 females born before 2003, 283 of which had recruited by age 10 at the end of the study (2012). Age at first reproduction was considered for the sample of 283 individuals born before 2003 and recruited by age 10. As a discrete positive variable, age at first reproduction was modelled with a Poisson distribution with theoretical mean and variance λ. We rescaled the response variable by subtracting the minimum age of recruitment (age 5) from the actual age of recruitment of an individual. This discrete variable appeared adequately characterized by a Poisson random variable (min = 0, mean = 2·63, var = 1·98, Poisson dispersion test: χ2 = 213, d.f. = 282, = 0·99, dispersion estimate = 0·76).

The same set of covariates representing maternal and environmental effects was considered in both analyses. To account for environmental conditions at birth, we used the size of the cohort in which an offspring was born. This covariate (CohSize) was defined as the standardized value of the total number of pups born that year and was believed to represent a good proxy of environmental conditions, as more pups are expected to be produced when environmental conditions are favourable (Garrott et al. 2012). For maternal traits, we considered the age (MomAge) and experience (MomExp) of the mother at offspring's birth. The covariate MomAge was defined as the standardized value of true age, and its effect was modelled as quadratic, which was chosen to capture more variability than a linear trend and because it represents several alternative biologically relevant age trends (e.g. senescence effects, terminal investment). Although the experience of a female can be defined as the number of pups she produced, this variable is intimately connected with age. Therefore, we defined a new variable MomExp corresponding to the standardized value of experience for each specific age. The values of this metric can be defined and biologically interpreted as the relative deviation of a female's experience from the population average experience across all females still alive at a given age. A potential relationship among covariates was checked graphically (Fig. S1, Supporting information), and the absence of any apparent pattern indicated that independence could be assumed.

We first assessed the support for each of these covariates and then investigated the support for MomIRE, the covariate of primary interest. This approach allowed making inference on MomIRE conditional on a model including only relevant covariates. To check whether such a sequential approach affected our results, we also performed an analysis based on a single model including all the covariates at once and found no notable differences in parameter estimates. In the sequential approach presented here, the relative support for each covariate was assessed from the posterior probability of the associated inclusion parameter wk. We also used the posterior distributions, both conditional on specific models and averaged across models (unconditional), of the regression parameters βk associated with each covariate k to assess their support. Interaction effects of cohort size and maternal covariates on offspring vital rates have never been evidenced in this population (Hadley, Rotella & Garrott 2007b), and given the time delay between birth and recruitment, we did not expect any such interaction on offspring recruitment. Therefore, for the ease of interpretation and because they were not of primary interest here, covariate interactions were not considered. Probability of recruitment (by age 10) π was thus modelled as follows:

display math

Similarly, for age at first reproduction, the parameter λ of the Poisson distribution was modelled as follows:

display math

The support of MomIRE was conditional on the best model identified in the previous analysis step and based on the mean posterior distribution of an inclusion variable wIRE and the posterior distribution of a regression parameter βIRE. The models were defined as follows:

display math

where θπ and θλ represent the intercept (μπ or μλ), relevant parameters βk and covariates k of the most supported model identified in the previous step, for each analysis, respectively.

Relationship between mother and offspring reproductive individual effect

From a sample of 264 offspring–mother pairs, we investigated the relationship between individual reproductive effects of offspring (OffspIRE) and their mother (MomIRE), while incorporating uncertainty associated with both these variables through use of their posterior distributions, instead of single point estimates, in the analysis. For comparison, we also performed analyses using only the mean of the posterior distribution as point estimates. The relationship between the two variables was investigated by a linear regression, where OffspIRE was the response variable and MomIRE the explanatory variable:

display math

As in previous models, parameters wIRE and βIRE correspond, respectively, to an inclusion and a regression slope parameters. The mean value of OffspIRE is represented by β0, and ε is an error term with residual standard error σε.

Expected reproductive contribution from different types of females

Simulations were used to predict the expected reproductive contribution, measured as (i) number of offspring and (ii) number of grandchildren, of females having low, average and high reproductive rates (thereafter, ‘quality’). Low- and high-quality females were defined by a posterior mean MomIRE value of 2 SD below and above average, respectively. These values were chosen to highlight differences among females of notably different qualities while still representing a reasonable proportion of the population (about 5% of all females). Average-quality females were defined by a posterior mean MomIRE value equal to the average value in the population. We performed 20 000 simulations for each type of female, and each simulation consisted of four steps. First, the number of offspring produced over the expected post-recruitment life span of 9 years was simulated using individual-specific annual reproductive rates. In addition to the effect of MomIRE, reproductive rates varied by year and as a function of an individual's reproductive state the previous year and age (quadratic trend), as described in Chambert et al. (2013), and the values of associated parameters we used here corresponded to the posterior means obtained in the same study. Given that the mean age at recruitment is 7·62 years, recruitment was assumed to occur at age 8 for all females. With a post-recruitment life span of 9 years, the last reproductive occasion was at age 17 and each female could thus produce between a minimum of one (because all females considered here were recruited to the breeding population) and a maximum of ten offspring. These features were representative of the study population, as in our data about 75% of females had been recruited by age 8, 97% were not seen alive after age 17 and 93% produced a total of 10 or fewer pups. In a second step, among the total number of offspring produced, we calculated the expected number of females using a pup sex ratio of 0·50 estimated from the data (SE = 0·01). This sex ratio was assumed constant in the simulations because we did not find any evidence of variation among cohorts or mothers, based on their age, experience or reproductive rate. In a third step, we simulated the number of female offspring expected to recruit. Sources of variation and parameter values pertaining to recruitment probability were based on the findings of the present study (see 'Results'; Tables 1 and 2). Finally, the expected number of grandchildren produced by these recruited female offspring was calculated using individual-specific reproductive rates similar to those used in the first step, varying as a function of reproductive state, age and individual reproductive value (estimated OffspIRE; see 'Results') but averaged across year conditions. Reproductive occasions were assumed to occur within the same age span (8–17) as the one used in the first step for mother's reproduction. Cumulative probabilities and distribution summary statistics, calculated from the 20 000 simulations, were used to compare the expected values of reproductive contribution among the three types of female considered.

Table 2. Summary of parameter posterior distributions from the analyses of offspring recruitment probability and age at first reproduction. The mean, lower (2·5% quantile) and upper (97·5% quantile) limits of a 95% credible interval (LCI and UCI, respectively) are shown. Parameters are regression coefficients associated with the covariates considered in the models: cohort size (βcoh), mother experience (βexp) and a first- (βage1) and second-order (βage2) mother age effects. Posterior summaries presented here are averaged across competing models (see Table 1) and therefore incorporate model uncertainty. We note that for all parameters, model-conditional posterior distributions (see Tables S1 and S2, Supporting information) were similar to the model-averaged ones
ParameterProbability of recruitmentAge at first reproduction
MeanLCIUCIMeanLCIUCI
βcoh0·260·130·400·06−0·010·14
βexp0·05−0·080·17−0·07−0·140·00
βage10·00−0·540·470·14−0·060·32
βage2−0·31−0·730·080·05−0·130·21

Results

Probability and age at recruitment

Results of model selection from the first step of the analysis (Table 1) indicate that CohSize was the only covariate to receive strong support (posterior probability of inclusion = 0·988) in the analysis of probability of recruitment. The estimated relationship between CohSize and probability of recruitment was found to be positive (Table 2; βcoh: model-averaged posterior mean = 0·26, 95% CI = [0·13; 0·40]; see also Table S1, Supporting information, for model-conditional posteriors), suggesting that pups from larger cohorts had greater chances of recruiting by age 10. The effect of CohSize is in fact quite large (Fig. 1) given that, over the range of cohort sizes that occurred between 1983 and 2003, values of recruitment probabilities are expected to vary from 0·19 [0·16, 0·23] to 0·34 [0·30, 0·39]. None of the other considered covariates had any substantial effect on either recruitment probability or age at first reproduction (Table 1). MomAge seemed to receive marginal support in the recruitment probability analysis, but we note that (i) the posterior probability of inclusion of this covariate (0·404) was actually lower than its prior probability (0·5), and (ii) posterior distributions of both MomAge effects (βage1 and βage2) largely overlapped zero (Table 2; Table S1, Supporting information). Based on these results, the only covariate included in the second step of the recruitment probability analysis was thus CohSize. Concerning age at first reproduction, as no covariate had any apparent substantial effect (Tables 1 and 2; Table S2, Supporting information), the second step of the analysis was based on the constant model, which clearly received the most support (model posterior probability = 0·827).

Figure 1.

Observed and estimated relationship between birth cohort size and probability of recruitment by age 10. The size of a cohort is defined as the total number of pups born in that particular year. From the estimated trend (βcoh: model-averaged posterior mean = 0·26, 95% CI = [0·13; 0·40]), values of recruitment probabilities are expected to vary from 0·19 [0·16, 0·23] to 0·34 [0·30, 0·39] across the range of cohort sizes observed between 1982 and 2003 (represented on the graph). The points represent the observed proportion of seals from each cohort that recruited by age 10. We note that the outlier value (proportion = 0·0; open circle) is due to a small sample size effect (n = 2) and do not represent the true recruitment proportion of the corresponding cohort (1983). The black solid line represents the estimated mean trend, while the grey dotted lines represent the 95% credible interval (2·5% and 97·5% quantiles).

We found no support for a relationship between MomIRE and either probability of recruitment (posterior of wIRE = 0·21) or age at first reproduction (posterior of wIRE = 0·03). Prior odds of 1 : 1 were converted to posterior odds of (i) 3·75 : 1 in favour of the simple model, including only covariate CohSize, in the analysis of recruitment probability and (ii) 29·35 : 1 in favour of the constant model for age at recruitment. Moreover, the posterior distributions of the slope βIRE associated with MomIRE clearly overlapped zero (Probability of recruitment: βIRE = 0·22 [−0·12, 0·56]; Age at first reproduction: βIRE = 0·01 [−0·13, 0·15], respectively). These results suggest that the females with different reproductive rates produced pups with similar recruitment characteristics (overall probability and age of primiparity).

Relationship between individual reproductive effects of mother and offspring

We found suggestive support for a positive relationship between MomIRE and OffspIRE, as the posterior probability of inclusion of MomIRE (wIRE = 0·65) was larger than its prior probability of 0·5. The estimated regression slope βIRE was relatively weak (mean = 0·05), but the estimated 95% credible interval (0·04; 0·06) included only positive values, providing evidence for a positive relationship. We also emphasize that the uncertainty in MomIRE and OffspIRE values was fully taken into account here, resulting in conservative estimates of the relationship. Indeed, a regression analysis based on the posterior means of MomIRE and OffspIRE (i.e. with no uncertainty associated; Fig. 2a) provides a larger estimate of the regression slope (0·12 [0·03, 0·21]) and good support for the effect of MomIRE (= 0·008). We also note the estimated correlation (standardized regression slope; Fig. 2b) between the two variables is 0·16 [0·04, 0·28]. Furthermore, a closer look at OffspIRE values or offspring from the same mothers (represented by vertical lines in Fig. 2) reveals that mothers with a high MomIRE tend to consistently produce pups with a high OffspIRE. This pattern is, however, not very strong, given that many vertical lines cross the averaged regression line, further supporting the idea of a low, but non-null, heritability of reproductive rates.

Figure 2.

Relationship between mother and offspring estimated individual effects pertaining to reproductive rates. (a) Plot of the posterior means of OffspIRE against MomIRE, with the estimated regression slope (inline image = 0·12) represented by the black line. (b) Plot of the standardized posterior means of OffspIRE against MomIRE, with the estimated correlation slope (0·16) represented by the black line. Points pertaining to a same mother are linked by a vertical line. Most vertical lines cross the regression line, suggesting independence between mother and offspring, but several mothers with a high MomIRE seem to consistently produce pups with a high OffspIRE. This intermediate pattern of independence/non-independence is in accordance with the low heritability estimated. We also note that the variance in relative reproductive rate values among mothers is larger than the variance among offspring, which probably simply results from the fact that longer time series are available for the subsample of mothers, allowing for more variability to be captured.

Expected reproductive contribution from different types of females

In the simulations, we included only the covariate effects found to be relevant in the statistical analyses described above. Therefore, offspring age at recruitment was assumed to be constant among females and cohorts given that none of the covariate we considered received any support. For recruitment probability, the estimated effect of cohort size (βcoh = 0·26) was included (Table 2). To depict realistic annual variability, standardized values of cohort size, and corresponding reproductive year effect, were randomly drawn from the observed distribution. Finally, because we found support for a weak correlation between OffspIRE and MomIRE, offspring individual effects were calculated from the mother's value MomIRE using the posterior means of regression coefficients (β0 = −0·02; βIRE = 0·05) and were applied to offspring reproductive rates.

Substantial differences in expected number of descendants among females of different quality were found (Tables 3 and 4). In relative terms, we found that a female with a high reproductive rate is expected to produce 2·0 times as many recruited females and 2·1 times as many grandchildren as a female with a low reproductive rate. Indeed, although stochastic variation is quite large (Table 3), the average number of grandchildren, in absolute terms, expected to be produced through the female progeny is 3·6, 5·8 and 7·5 for females with low, average and high reproductive rates, respectively. We note that the distribution of number of grandchildren (Fig. S2, Supporting information) appears to be zero-inflated and multimodal because it corresponds to a mixture of distributions for each possible realized value for the number of recruited female offspring (0, 1, 2, 3 …) produced by the grandparent female. The quantiles of the distribution of absolute number of grandchildren (Table 3) and upper tail probabilities (Table 4, Fig. 3) also provide support for substantial differences among females. In particular, the probability of having no grandchildren is 76% higher for a low-quality female (0·58) relative to that for a high-quality female (0·33). Further, the chances of having a large number of grandchildren are much greater for a high-quality female (Table 4, Fig. 3). For instance, the probability of having ≥10 grandchildren is about three times larger for a female of high quality (0·29) than for one of low quality (0·10), and for the probability of having ≥20 grandchildren, this relative difference in odds reaches 7 : 1 (0·07 vs. 0·01). Overall, these simulation results suggest that observed levels of individual heterogeneity in reproductive rates translate into substantial differences in terms of number of grandchildren expected to be produced through the female progeny.

Table 3. Summary statistics of simulation results. The expected number of offspring (top) and grandchildren (bottom) were simulated for three types of parent females defined by their rate of reproduction and denoted as low (2SD below average), average and high (2 SD above average) quality (see 'Materials and methods' for details). The expected number of grandchildren concerns only offspring produced through the female progeny of the grandparent female. The distribution summaries shown are the mean, standard deviation (SD) and the 2·5% and 97·5% quantiles (Quant.)
Distribution summariesLow qualityAverageHigh quality
Expected number of offspring
Mean4·46·98·8
SD1·31·31·0
Quant. 2·5%247
Quant. 97·5%7910
Expected number of grandchildren (from female progeny)
Mean3·65·87·5
SD5·06·37·2
Quant. 2·5%000
Quant. 97·5%162124
Table 4. Upper tail probabilities of the expected number of grandchildren for each type of female. Three types of grandparent female are defined based on their rate of reproduction, respectively, denoted as low (2 SD below average), average and high (2 SD above average) quality (see 'Materials and methods' for details). The relative difference is calculated as the proportional change in probability for the high-quality (HQ) female relative to the low-quality (LQ) female (Relative difference = (PHQPLQ)/PLQ). All the metrics shown were obtained from simulation results
Number of grandchildrenLow-quality femaleAverage-quality femaleHigh-quality femaleRelative difference (PHQPLQ)/PLQ (%)
None0·580·420·33−43
≥10·420·580·6758
≥50·410·570·6661
≥100·100·210·29192
≥150·040·110·17305
≥200·010·040·07638
Figure 3.

Upper tail probabilities of increasing expected number of grandchildren [Pr(x ≥ N)], for each type of female and relative difference in these probabilities between high- and low-quality females. Tail probabilities are displayed as smoothed curves over the range of possible number of grandchildren (x-axis). The three types of female considered vary in terms of reproductive rates and are denoted as high quality (HQ), average quality (AQ) and low quality (LQ). The relative difference is defined as the proportional change in probability for the high-quality female relative to the low-quality female ([PHQPLQ]/PLQ). These results were obtained from simulations.

Discussion

Environmental and maternal influences on offspring recruitment

Offspring recruitment was more influenced by cohort size than any of the maternal traits considered (age, experience and reproductive rate). Although birth cohort conditions did not appear to affect age at recruitment, it was positively related to recruitment probability. Interestingly, cohort effects on recruitment rates have been suggested to be mainly linked to environmental conditions prevailing during in utero foetal development rather than after birth (Garrott et al. 2012). It is likely these early-life conditions influence recruitment rates primarily by affecting survival at very young ages, when seals are the most vulnerable and mortality is the highest (Rotella et al. 2012), although cohort effects on pre-recruitment survival appear to persist for c. 6 years after birth (Stauffer, Rotella & Garrott 2013). We did not find any influence of maternal age and breeding experience on offspring's recruitment probability and recruitment age. Evidence of a negative influence of mother's age on the probability of offspring recruitment conditional on survival was reported previously (Hadley, Rotella & Garrott 2007b). However, the same study also found that pre-recruitment survival was affected by maternal age in the opposite direction and therefore tended to be higher in offspring born to older females. Because in our analysis, the recruitment variable was unconditional on survival, it is probable that these two opposite maternal effects cancelled each other out yielding no difference in overall recruitment chances. Regarding the lack of influence of maternal experience, our findings are in accordance with previous studies on this population (Hadley, Rotella & Garrott 2007b). The novelty of our approach was to standardize the values of reproductive experience by age to eliminate the correlation between these two covariates. Despite this effort of standardization, we still did not detect any effect, which strengthens previous conclusions (Hadley, Rotella & Garrott 2007b).

Overall, cohort effects seemed to have a larger influence on recruitment than maternal age and experience. Studies directly comparing the effect of environment at birth vs. maternal traits on offspring recruitment are scarce, but a similar pattern to what we report here has been found in other large mammals (e.g. bighorn sheep Ovis canadensis: Jorgenson et al. 1993; moose Alces: Sæther & Heim 1993). In birds and mammals, persistent influences of early-life environment on offspring survival and future reproduction are often mediated by parental conditions (Lindström 1999). Therefore, environmentally driven maternal traits, as well as maternal care and behaviour, could still have important effects on offspring success (Maestripieri & Mateo 2009).

Offspring recruitment also appeared independent of maternal reproductive rates. Individual trade-offs between offspring number and quality are theoretically predicted (Smith & Fretwell 1974; Stearns 1992) and have been demonstrated in a broad range of taxa (Schroderus et al. 2012), including several primates and also humans (Gillespie, Russell & Lummaa 2008; Walker et al. 2008). Our result does not necessarily indicate the absence of such a trade-off at the individual level in Weddell seals, but rather suggests among-female variation in resource acquisition (Van Noordwijk & De Jong 1986). Larger variation in reproductive frequency vs. offspring quality implies that females engage in reproduction only with sufficient resources to successfully rear their pup. A similar conservative maternal care strategy exists in ungulates (Albon, Mitchell & Staines 1983; Sand 1996) and is likely a common feature of species with low potential fecundity and high maternal investment (Erikstad et al. 1998).

Relationship between mother and offspring reproductive rates

We found evidence for a positive, but weak correlation between reproductive rates of mothers and their female offspring. This result suggests weak heritability of this fitness-related trait and is in accordance with theoretical predictions (Fisher 1958; Charlesworth 1987), as well as previous empirical evidence in Drosophila (Roff & Mousseau 1987), collared flycatchers Ficedula albicollis (Gustafsson 1986) and 75 other wild populations of vertebrates and invertebrates (Mousseau & Roff 1987). The low heritability in female reproductive rates could also be linked to the fact that it is a complex trait determined by a multitude of phenotypic characteristics not necessarily heritable and heavily influenced by the environment, as shown in red deer Cervus elaphus (Kruuk et al. 2000). When considering that only about 24% of all female seals ever born survive the pre-recruitment period, it is noteworthy that we still detected some heritability in this subset of ‘good quality’ individuals which already went through a strong selective filter (pre-recruitment survival). Based on our results, it is not possible to know what proportion of such heritability is due to genetic factors vs. non-genetic maternal effects, two possible mechanisms that are particularly hard to disentangle in a species like Weddell seals in which females rely heavily on stored capital during the lactation period (Wheatley et al. 2008). We, however, note that it is unlikely that our findings simply result from spatial variation in resource availability. First, although different colonies (i.e. temporary aggregation sites) are formed every year within Erebus Bay, there is no strong natal philopatry associated with them. Moreover, the acquisition of the majority of food resources important to reproductive success mainly occurs far from colonies and at a different time of year. There is therefore no direct association between the place of birth of a mother and her pup, nor between colonies and resource acquisition.

Evidence for such heritability in reproductive rates naturally raises the question of whether the population average for this trait has been changing over time, as a potential result of directional selection. Interannual fluctuations are observed, but over the last 30 years, the population has been very stable, and no trend has been manifested in this trait or any other vital rate (Rotella et al. 2009; Chambert, Rotella & Garrott 2012). The low heritability value we found might thus lie within the expectations of a neutral model of demographic variation (i.e. no genetic basis; Steiner & Tuljapurkar 2012), especially considering the high annual variability in offspring numbers. Future investigations will be needed to (i) test whether the amounts of fitness variation and heritability are greater than what would be expected under a purely neutral model and (ii) identify phenotypic traits underlying such heritable variation.

Evolutionary perspective of heterogeneity in reproductive rates

Despite substantial stochastic variability, simulations reveal important differences in the expected number of grandchildren, produced via female progeny, among females with contrasting reproductive rates. Higher numbers of grandchildren can logically be expected from females with higher reproductive rates, but here we emphasize that it also results from the low heritability and the lack of negative trade-off with offspring recruitment that would counter such simple relationships. Together, our results indicate that maternal fitness is more influenced by the number than the quality of offspring produced. Similar patterns have been found in other mammal species with expanded maternal care. For instance, in Eurasian red squirrels (Sciurus vulgaris), a mother's fitness is mainly explained by the number of litters she produces and is directly linked to her access to food resources (Wauters & Dhondt 1995). In pre-industrial humans (Gillespie, Russell & Lummaa 2008), maternal fitness was shown to be positively related to fecundity in resource-rich families but not in resource-poor families, indicating that producing more children was a good strategy only for mothers having access to sufficient resources. The capacity for higher frequency of reproduction in female Weddell seals is also likely linked to their ability to access resources, presumably prey (Hadley, Rotella & Garrott 2007b). Varied resource acquisition is also expected to affect offspring quality (Smith & Fretwell 1974) and might similarly influence pup provisioning among mothers and therefore pup's condition at weaning (Wheatley et al. 2006). The lack of offspring recruitment variation among mothers could partly result from the stochasticity of post-weaning offspring's survival (Stauffer, Rotella & Garrott 2013) mitigating maternal investment differences.

Regarding the heritability of reproductive rates, it is interesting to note the negative value (−0·02) of the estimated intercept of the mother–offspring regression, which might indicate that an offspring's reproductive rate value tends to be lower than that of its mother. This result strengthens our conclusion that this trait is not presently under directional selection. This pattern can also be directly seen in Fig. 2, as a relatively high density of data points lies just below the expected means. A similar pattern has been found for birth mass in St Kilda's Soay sheep, for which offspring tend to be born at a body mass that is closer to the population average than to their mother's birth mass (Coulson & Tuljapurkar 2008). This transmission bias was identified as the main mechanism countering the positive selection pressure for increased birth mass and is therefore responsible for the stasis observed in this trait (Ozgul et al. 2009). Such a transmission bias on female reproductive rates seems to exist in the Weddell seal population, and it could explain the lack of trend in pup production over the last 30 years. It is also interesting to note that despite the existence of substantial annual fluctuations in reproductive success, total population size has been very stable over time.

The scope of inference of our results regarding fitness and heritability is somewhat limited by the fact that only the reproductive contribution of females is currently available for this population. In polygynous species like Weddell seals, the reproductive contribution of males can greatly vary, such that the quality of male offspring produced by a female can strongly affect her fitness. Maternal investment of high-quality mothers is thus generally expected to be higher in sons (Trivers & Willard 1973). However, because Weddell seals display low sexual dimorphism and relatively low variation in male reproductive contribution for a polygynous species (Harcourt et al. 2007), the fitness differences among sexes and therefore the potential bias in maternal investment are probably small (Hewison & Gaillard 1999). Regarding heritability, we know that the approach based on parent–offspring regression that we used presents several limitations (Kruuk 2004; Coulson & Tuljapurkar 2008), mainly due to potential confounding of genetic and environmental factors. The use of the full pedigree of animals, including the paternal component, would provide better information. Despite these limitations, our findings regarding heritability and cross-generational effects of female reproductive rates represent a first important step in better understanding the fitness consequences and more broadly the evolutionary significance of individual reproductive heterogeneity. To pursue this effort, future studies will need to investigate proximate mechanisms responsible for fitness variation and decipher the role of differential maternal investment between male and female progeny, male reproductive contribution and potential heterogeneity in survival.

Acknowledgements

The authors thank M.D. Higgs and J.D. Nichols, as well as two anonymous reviewers, for helpful comments that helped improving the manuscript. We are also very grateful to the many individuals who have worked on the projects associated with the Erebus Bay Weddell seal population since the 1960s. The project was supported by the National Science Foundation, Division of Polar Programs (Grant No ANT-1141326 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 Lockheed Martin, Raytheon Polar Services Company, Antarctic Support Associates, the United States Navy and Air Force, and Petroleum Helicopters Incorporated. Animal handling protocol was approved by Montana State University's Animal Care and Use Committee (Protocol #2011-38).

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