Although senescence in reproductive success has been observed in a number of wild animal populations, longitudinal analyses determining the actual processes responsible for population-level patterns of ageing, and in particular, the relative contributions of within-individual senescence vs. selective mortality, are rare. Furthermore, many studies also only consider single traits in isolation, despite evidence that different aspects of physiology and fitness may show varying patterns of senescence.
We used data from an unmanaged population of Soay sheep on the islands of St Kilda, NW Scotland to analyse age-related change in four aspects of female reproductive performance: annual fecundity, twinning rate and the maternally influenced offspring traits of lamb birth weight and early survival. We present the results of three analytical techniques, which attempt to disentangle the contributions of within-individual ageing, selective mortality and terminal effects to the observed population-level patterns of age-specific change.
All four traits showed considerable age-related change, but population-level trajectories varied markedly across them. Population-level patterns were underpinned by considerable within-individual senescence including within-individual terminal declines in performance occurring only in the final year of life. However, at the population level, these processes were also masked to some extent by selective disappearance (mortality) of poor breeders.
The contributions of individual-level ageing and selective mortality to population-level ageing patterns varied considerably between traits, as did the nature of individual-level senescence. We did not observe detectable significant late-life declines in all four traits: in particular, there was no evidence of senescence in twinning rate. The results indicate that senescence may not be ubiquitous across all aspects of reproductive performance within a population.
Across multiple taxa, age-related change in phenotypic traits is typically characterized by early-life improvement, followed by a late-life decline or senescence, which may be defined as a decline in physiological function with age. Senescence manifests itself as a deterioration in body condition and demographic parameters such as reproductive performance and survival probability (Monaghan et al. 2008). Age-related declines in a variety of traits have now been reported in numerous natural populations, including survival probability (e.g. Beauplet et al. 2006; Descamps et al. 2008), reproductive performance (e.g. Bouwhuis et al. 2009; Sharp & Clutton-Brock 2010; Martin & Festa-Bianchet 2011), body mass (Nussey et al. 2011) and immune function (Palacios et al. 2007). It is however becoming increasingly clear that age-related changes in the population mean of a trait may be driven by processes other than within-individual senescence, such as correlations between average performance and longevity (Curio 1983; van Noordwijk & de Jong 1986), although as yet we have little idea of the relative contributions of different processes to overall population-level patterns. In this study, we examine the contributions of individual senescence and selective mortality to population-level patterns of age-related change in four female reproductive traits in a naturally regulated population of Soay sheep (Ovis aries).
Despite the prediction of evolutionary theories of senescence that reproductive performance should decline from reproductive maturity (Williams 1957; Hamilton 1966), most reproductive traits studied in wild vertebrates have demonstrated an initial increase following maturity, followed by a subsequent, later decline after a period of ‘prime’ performance. The initial increase in performance may be explained by increasing body size or weight (Sparkman, Arnold & Bronikowski 2007), increased parental competence (Balbontin et al. 2007) or selective mortality of poor parents at an early age (Reid et al. 2003). The subsequent decline is often interpreted as senescence, which often takes the form of a gradual decline (e.g. Bouwhuis et al. 2009; Sharp & Clutton-Brock 2010). However, some traits show extremely rapid declines at the very end of life, and such ‘terminal effects’ have been observed both independently of chronological age (e.g. Nussey et al. 2011) and in conjunction with gradual ageing-related declines (Martin & Festa-Bianchet 2011). As well as fecundity, traits which are associated with maternal effects may also decline, such as the decline in egg volume, which underpins a decline in chick size in blue-footed boobies (Sula nebouxii) with maternal age (Beamonte-Barrientos et al. 2010). This suggests that senescence affects not only female reproductive physiology, but also their capacity to provision offspring to ensure rapid growth and high survival. To date, the majority of studies of senescence in wild animal populations have analysed single traits in isolation, but it is becoming increasingly clear that the nature of senescence may vary across traits (Nussey et al. 2009; Lecomte et al. 2010; Massot et al. 2011). It is also unclear how the available empirical evidence of variation fits with the expectation of a general decline across all physiological systems predicted by evolutionary theory (Williams 1957). This highlights the need to consider multiple traits and to examine differences in the manner of age-related change across traits to understand population- and individual-level senescence.
Population-level changes in trait means with age are underpinned by both individual-level processes such as development or senescence, and changes in population composition due to selective mortality (van de Pol & Verhulst 2006; Rebke et al. 2010). A key issue is that survival probability may be correlated with reproductive performance, and therefore, whilst changes in population-level mean performance may be the result of the improvement and subsequent decline of individual performance (individual-level effects), they may also be due to selective mortality of individuals with either high or low average performance (population-level effects; van de Pol & Verhulst 2006). Such ‘selective disappearance’ can either mask or overestimate the variation in traits due to individual-level processes. However, far from being a statistical nuisance, selective disappearance may be a biologically interesting phenomenon and determining how it contributes to population-level ageing patterns may aid our understanding of the consequences of ageing in natural populations.
In this study, we investigate population-level age-related changes in four female reproductive traits: annual fecundity (AF), litter size, offspring birth weight (OWT) and offspring survival (OS) to independence in a longitudinally monitored feral population of Soay sheep in the St Kilda archipelago, NW Scotland. Detailed phenotypic data on this population have been collected for over 25 years (Clutton-Brock & Pemberton 2004) enabling study of a variety of female reproductive traits. Previous studies have shown that senescence in a measure of parasite resistance is dependent on experience of prior environmental conditions (Hayward et al. 2009) and that senescence in body weight is rapid, occurring only in the final year of life (Nussey et al. 2011). Senescence in a measure of individual annual fitness has also been reported (Jones et al. 2008), and some of the variation in senescence in this measure has been attributed to genetic variation (Wilson et al. 2007). However, despite evidence for population-level age-specific variation in reproductive success (Clutton-Brock et al. 1996; Robinson et al. 2006), no detailed analyses of within-individual changes in such traits have been performed. We describe population-level patterns of ageing, and test for differences between the four traits in their ageing trajectories. We then aim to disentangle the contributions of within-individual ageing, selective disappearance and terminal effects using three analytical methods.
Materials and methods
Since 1985, the unmanaged population of Soay sheep on the island of Hirta (638 ha) in the St Kilda archipelago, NW Scotland has been the subject of an individual-based study (Clutton-Brock & Pemberton 2004). The Village Bay area, encompassing a third of the total area of the island and approximately a third of its sheep population, is the focus of the study. Field work is carried out in three two-month periods per year (March/April; July/August; October/November), during each of which 10 censuses take place, recording the survival and location of known individuals. The vast majority of mortality occurs over winter, which may be marked by low food availability, high population density, poor weather and high gastrointestinal parasite prevalence (Coulson et al. 2001). Lambing occurs in April, with intensive daily monitoring of the study area recording the exact birth date of over 99% of lambs. Over 95% of lambs are captured within a week of birth, tagged, weighed and blood sampled. Females may produce a lamb in the year after they are born, and the proportion of females doing so depends strongly on population density (Clutton-Brock et al. 1991). The proportion of females producing twins is 2–23% (Clutton-Brock et al. 1992) and is higher in heavier females (Clutton-Brock et al. 1997) and in years of low population density (Clutton-Brock et al. 2004). Twinning is associated with higher annual fitness than producing singletons unless environmental conditions are exceptionally harsh (Wilson et al. 2009). A negative genetic correlation between litter size and birth weight contributes to the lower birth weights of twins (Wilson et al. 2005), which are less likely to survive to August (Jones et al. 2005) than singletons. Survival of lambs past their first winter, when 22–98% die, is strongly associated with birthweight and summer weight (Clutton-Brock et al. 1992; Milner, Elston & Albon 1999). Maternal provisioning is therefore a critical determinant of OS and hence female fitness. Summer weight is measured by capturing around 60% of the Village Bay population during the August field season. Reproductive success declines in old age at the population level in both sexes (Robinson et al. 2006), but no detailed analysis of within-individual changes in such traits has been performed.
We analysed age-related variation in four female reproductive traits: two related to female fecundity (‘fecundity traits’), and two which are strongly determined by the effect of a female on her offspring's performance (‘maternal effects’).
Annual fecundity (AF) was scored as 0 if a female was alive in April, but was not observed to have given birth to a live lamb; it was scored as 1 if a female was observed to be caring for at least one lamb. Note that we included only live births and excluded cases of stillbirth (which are typically recorded), as well as pre-term abortion (which are not recorded). If AF was scored as 1, twinning (TW) was scored as 0 if one lamb was present and as 1 if the female produced twins.
Since growth between a lamb's birth and its first capture is rapid, offspring birth weight (OWT) was calculated as the residuals of a regression of weight at capture on capture age. If a lamb was observed in any population census following the August after birth, offspring survival to independence (OS) (c. 4 months of age) was scored as 1; if a lamb was found dead before August or never seen in subsequent censuses, OS was scored as 0. Less than 1·5% of lambs are tagged and then never sighted again and are assumed to have died because lambs not seen with their mother in the August following birth have no chance of survival.
We wished to investigate the age-related changes of the four traits across the life span and during late life, and to investigate contributions of individual-level senescence and selective disappearance to population-level age-related change using longitudinal data. To describe differences in ageing patterns between the traits, we fitted nonparametric smoothing functions using generalized additive models (GAMs). We then attempted to determine the contributions of individual-level senescence and selective disappearance to the overall ageing pattern using two methods. First, we used a linear mixed-effects model approach (van de Pol & Verhulst 2006), the results of which we used to investigate differences in ageing trajectories of the traits. Second, we used a decomposition of population-level age-related change into within-individual improvement and senescence, and changes due to the alterations in composition of the population with age (Rebke et al. 2010).
We analysed ageing-related changes in reproductive performance using generalized linear mixed-effects models (GLMMs), in r version 2.13.0, using the package ‘lme4’ (Bates, Maechler & Bolker 2011). This method determines the contribution of within-individual change vs. changes in population composition to overall age-related variation by including the following variables:
Selective disappearance: We accounted for the effects of selective mortality on estimates of ageing by including longevity (range 1–13 years) as a linear and quadratic covariate to model selective disappearance (van de Pol & Verhulst 2006). An effect of longevity would indicate an association between mean individual performance and longevity, generating population-level changes in mean performance with age. Longevity was retained in all models, even if not statistically significant, to account for all of the variation in the trait accounted for by life span. An effect of age having accounted for longevity indicates that a portion of change in performance is due to within-individual ageing (van de Pol & Verhulst 2006).
Ageing: Female age (range, 1–12 years) was included as a covariate with linear and quadratic terms where indicated.
Terminal effects: To investigate the possibility of sudden decreases (terminal decline) or increases (terminal investment) in reproductive performance at the very end of life, we included a factor to indicate whether it was a female's last year of life (1) or not (0).
Previous studies on this population have shown evidence for senescence in a measure of parasite resistance (Hayward et al. 2009) and in body weight (Nussey et al. 2011). Therefore, changes in reproductive traits could be underpinned by senescence in these traits. In the current analysis, we wished to describe overall ageing patterns in reproductive traits, but we also repeated all analyses also accounting for both female body weight and parasite burden (see Appendix S1, Supporting information). These analyses revealed that, in line with previous research (Clutton-Brock et al. 1996, 1997), body weight was positively associated with all four reproductive traits, but including body weight and parasite burden did not influence the ageing patterns we observed.
We also accounted for effects of environmental variables, namely population density (Clutton-Brock et al. 1996) and climatic conditions (Forchhammer et al. 2001), on reproduction by including population density in the August prior to reproduction (PPD), and the North Atlantic Oscillation (NAO) for the previous winter (Stenseth et al. 2003) in all models. Natal litter size and lamb sex are both associated with lamb birth weight and survival (Clutton-Brock et al. 1992) and were therefore included in the analysis of these traits. Lamb sex and litter size were also included as fixed effects in analyses of lamb birth weight and survival. All models included random effects of female identity, to account for individual differences in reproductive success and year of sampling, to account for variance in reproductive success between years.
AF, TW and OS were scored as binary response variables and analysed using a binomial error distribution and logit link function. OWT followed a Gaussian distribution, so we used linear mixed-effects models. We sequentially removed fixed effects in the order of least significance, as assessed by Wald z statistics in the case of binomial traits and chi-square statistics in the case of OWT. Significance of random effects was tested using a likelihood ratio test. Sample sizes for each response variable are shown in Tables 1–4.
Table 1. Parameter estimates for variables included in the final model for annual fecundity (AF)
The final whole-life mixed-effects model, describing variables statistically associated with AF. Presented is the result of the final GLMM with binomial errors, with data on 3535 female life years from 894 females across 23 years.
Table 2. Parameter estimates for variables included in the final model for twinning (TW)
The final model describing variables statistically associated with probability of TW across the whole range of ages. Results shown are from a GLMM with binomial errors on 2260 reproductive attempts by 548 females across 23 years.
Table 3. Parameter estimates for variables included in the final model for offspring birth weight (OWT)
NAO, North Atlantic Oscillation.
Final model showing variables statistically associated with OWT across the full range of female ages. Results are from a GLMM with normal errors performed on data from 2134 lambs born to 495 females across 23 years.
Lamb sex (female)
Lamb sex (male)
Table 4. Parameter estimates for variables included in the final model for offspring survival
NAO, North Atlantic Oscillation.
Final whole-life model showing variables statistically associated with offspring survival (OS). Results are from a binomial GLMM used to analyse survival of 2549 lambs born to 541 individual females across 23 years.
Lamb sex (female)
Lamb sex (male)
Whole-life mixed-effects models
We first fitted mixed-effects models across ages 1–12, for all four traits. To assess the factors contributing to age-specific variation, we included linear and quadratic terms for longevity and age, and a two-level factor for terminal effects.
Late-life mixed-effects models
All four traits showed an initial improvement with age, followed by a peak in middle age and subsequent decline. To determine whether this late-life decline was statistically significant and to quantify the contribution of selective disappearance, we next restricted the analyses to data from individuals aged 6 years and older for each trait, with age as a linear covariate only. We chose the age of six as the boundary because none of the traits were markedly improving or declining at this time, and six has been used as the boundary between early and late life in previous studies of this population (e.g. Clutton-Brock et al. 1996; Coulson et al. 2001). We also repeated these analyses with the boundary defined by the age at which each trait was predicted to peak in the whole-life GLMMs, but this did not qualitatively affect the results and so we do not present these additional results here. We tested the contribution of selective disappearance to ageing by comparing the significance and magnitude of the parameter estimate for age in the final models for each trait with and without longevity included. Late-life sample sizes are shown in Table 5.
Table 5. Parameter estimates for longevity and age in late-life mixed-effects across all traits
The influence of selective disappearance on each of the four reproductive traits analysed in females aged 6 and older. The third and fourth columns show parameter estimates for longevity from the late-life model described in the text; the fifth column shows the parameter estimate for age from the same model. The sixth column shows the parameter estimates for age from the model with both longevity terms omitted; % change gives the % change between the two parameter estimates for age.
Significance of each parameter estimate is denoted thus: ***P < 0·001; **0·001 ≤ P < 0·01; *0·01 ≤ P ≤ 0·05. N(IDs) shows the sample size for each trait followed by the number of individual females in parentheses.
To test for differences in the ageing trajectories of the four traits across life and in late life, we used GAMs in the r package ‘mgcv’ (Wood 2006). GAMs fit nonparametric smoothing functions to a continuous covariate (age), which are not restricted to follow a specific polynomial form; hence, comparison of ageing patterns of the four traits could be made without assuming the traits followed a quadratic pattern. We fitted GAMs through standardized age-specific means for each trait, corrected for other effects already shown to be important in the above models. To generate the standardized age-specific means, we repeated the whole-life mixed-effects models for each trait with age fitted as a fixed factor with 12 levels (1–12 years) rather than as a continuous covariate. We removed statistically nonsignificant terms as in the whole-life models described above; longevity was retained in all models. We then took the 12 age-specific predictions from the final model for each trait and standardized these values by subtracting the mean of the model predictions and dividing by their standard deviation for each trait, giving all traits a mean of 0 and standard deviation of 1. We then compared GAMs that fitted different nonparametric smoothing functions to different groups of traits to determine whether all traits followed the same age-specific pattern or whether their age-specific patterns varied. For instance, we compared patterns in fertility traits (AF and TW) vs. offspring traits (OWT and OS).
We then investigated late-life changes in the traits, by repeating the GAMs on the predictions from the age of six onwards, centring predictions from mixed-effects models on the value at age six, then dividing by the range of values of the traits from 6 to 12. As the age-specific predictions from GLMMs contained varying degrees of error (higher error at later ages because of lower sample size), GLMM estimates were weighted by 1/SE in the GAM analyses. Results from GAMs without these weights were very similar; we present results from weighted models. The model with the lowest Akaike Information Criterion value was selected.
Decomposition of age-specific change
We used the method of Rebke et al. (2010) as an alternative to mixed-effects models to describe age-related changes in reproductive traits. The method can provide an exact decomposition of population-level age-related change in the average of a phenotypic trait (P) into within-individual change (I) and change due to selective disappearance (D). Following Rebke et al. (2010), the population-level change is the difference between the average of a trait at one age and the average at the previous age measured in all individuals in the population. Ix, the change due to within-individual development or senescence between age x and age x + 1, is the difference between the mean value at age x and the mean value age x + 1, estimated only in individuals that were measured at both ages or the mean of the differences of individual trait values at consecutive ages:
where ij,x is the individual change in phenotype i for individual j measured at both age x and age x + 1 (and so Ix = ∑j(ij,x)/n). For each age, we then defined the cumulative effects of within-individual change as the sum of average changes up to each age ().
The change due to selective disappearance is the difference between the trait mean at age x for individuals that survived and the trait mean for the whole population at age x. This can alternatively be calculated as the covariance between the trait and relative survival (individual survival divided by mean survival; Rebke et al. 2010), that is, the mean across all individuals present at x of:
where sj,x is survival of individual j from age x to age x +1 scored as a binary trait, μ(traitx) is the mean trait value for all individuals measured at age x and μ(sx) is the mean survival of individuals of age x to age x + 1 (and so Dx = ∑(dj,x)/n). For each age, we then also defined the cumulative effects of selective disappearance as the sums of effects at each age ().
We examined the contribution of individual development and selective disappearance to observed population-level changes, first by assessing the pattern of each of these across ages and second by calculating the total contribution of these effects across the life span. We calculated the absolute total change in each trait by summing the absolute change due to both individual development and selective disappearance; dividing the total absolute change due to selective disappearance by this amount then provides an estimate of the proportion of total absolute change due to selective mortality:
where PD is the proportion of absolute phenotypic change due to selective disappearance, Dabs = ∑(|Dx|) across all ages, or the total absolute change in the trait across all ages due selective disappearance, and Iabs = ∑(|Ix|), or the total absolute change due to within-individual change summed across all ages. We also calculated the proportion due to within-individual change, PI (=1−PD). We then calculated these proportions across early life (during improvement) and the later part of life (during trait decline). A number of issues can arise from this analysis when not all live individuals can be recaptured at all ages, which must be appreciated when interpreting results (see Appendix S2, Supporting information).
There was considerable population-level age-related variation in all four traits, but substantial differences across traits in the nature of this variation (Fig. 1). In the analyses presented below, we first describe how these patterns differed between traits and then determine the contributions of within-individual change, terminal effects and selective disappearance to these patterns.
Whole-Life Analysis (Mixed-Effects Models)
Analysis of age-related changes using mixed-effects models demonstrated marked individual-level changes in all four reproductive traits across ages. For brevity, we do not discuss the effects of the environmental effects population density and NAO. Parameter estimates for these (when statistically significant) are reported in the tables of full whole-life models for each trait.
There was marked age-related change in AF, which increased from age 1 to a peak at age 7 (parameter estimates, Table 1) and subsequently declined. This individual-level effect was statistically significant after accounting for selective disappearance (longevity). There was also a strong terminal decline, such that females were less likely to reproduce in their final year of life.
Twinning was associated with a quadratic effect of age, suggesting an increase in the probability of producing twins until age 8, followed by a subsequent levelling-off (Table 2). This was statistically significant after accounting for longevity. Females that had at least one lamb were no less likely to produce twins in their last year of life than they were in any other year (terminal effect = 0·1809 ± 0·2504, z = 0·72, P = 0·470).
The final whole-life model for OWT again suggested an early-life increase followed by a late-life decline, with a predicted peak at age 7 (Table 3). This was after accounting for selective disappearance, and there was a trend for a terminal effect (−0·1167 ± 0·0646, χ2 = 3·25, d.f. = 1, P = 0·071).
Offspring birth weight was associated with a quadratic effect of age suggesting an increase in the probability of OS with maternal age, until a peak at age 6 and a subsequent decline (Table 4). There was also a terminal decline, with lambs less likely to survive to weaning if their mother was in the final year of life.
Late-Life Analysis (Mixed-Effects Models)
We next analysed age-specific changes in each trait from age 6 onwards, testing for declines consistent with senescence, and for the contribution of selective disappearance. We focus on the effects of individual age and the contribution of selective disappearance (Table 5).
There was a strong negative association between AF and age, suggesting a within-individual decline in late life after accounting for the positive association with longevity. The strong influence of selective disappearance on the population-level pattern is further demonstrated by the large change in the parameter estimate for age on removing longevity from the model (Table 5). This suggests that selective mortality of individuals of low fecundity could mask senescence and that within-individual senescence is more pronounced than it appears from the population-level pattern.
The association between TW probability and age was negligible and not statistically significant in late life, and the effect of longevity was negative but again not statistically significant.
There was a negative association between OWT and maternal age, and a positive association with longevity. This suggested that there was an individual-level decline in OWT, which was masked to some extent by selective disappearance of individuals with a tendency to produce light lambs. When longevity was removed from the model, there was a moderate decrease in the parameter estimate for age, suggesting that as for AF, selective disappearance masks senescence.
Finally, there was a strong negative association between age and OS, and a positive association with longevity. However, there was little change in the age estimate when longevity was excluded from the model, suggesting that population-level change in OS with age is due largely to within-individual effects.
Comparison of Ageing Patterns Across Traits: GAMs
We first fitted GAMs to age-specific estimates of reproductive traits from GLMMs across all ages, having controlled for longevity and additional fixed effects. We compared five models, which grouped the traits in different ways to test for differences between traits in their patterns of ageing-related change (Table 6, ‘Whole-life’). The predictions from the model which received the highest support (Fig. 2a) suggested that AF changed little between the ages of 4 and 9, before declining very sharply from nine onwards. Litter size showed no decline, improving from the earliest ages until age 8 before levelling off. Finally, the maternal effects traits (OWT and survival) showed a gradual decline from the age of 4. These results reveal explicit differences in the age-related trajectories and in the timing and manner of senescence between traits. We next compared the late-life trajectories of the four traits from age 6 onwards using GAMs fitted to age-specific predictions from GLMMs of reproductive performance from this age onwards, comparing models 1–5 as above. In this instance, model 3, which fitted separate smoothing functions to litter size vs. the other three traits, received the best support (Table 6, ‘Late life’). Litter size was not predicted to decline from age 6, and even increased slightly (Fig. 2b), while the other traits were predicted to show an accelerating decline.
Table 6. A statistical comparison of generalized additive models (GAMs) investigating patterns of ageing in female reproductive traits
Comparison of GAMs fitted to standardized age-specific estimates of reproductive traits across the life span and during late life (from the age of 6 onwards). Different nonparametric smooths were fitted to different sets of traits as indicated by the groupings, where traits in the same group are separated with a comma, and the groups are separated with a colon. The traits are as follows: annual fecundity (AF); probability of twinning (TW); offspring birth weight (OWT); and offspring survival (OS). The AIC value of all models is shown, with the model with the lowest AIC selected as the best fit; the ΔAIC values are shown in relation to the best model, which is shown in italics.
(AF, LS, OWT, OS)
(AF, LS) : (OWT, OS)
(LS) : (AF, OWT, OS)
(AF) : (LS) : (OWT, OS)
(AF) : (LS) : (OWT) : (OS)
Decomposition of Age-Specific Change
We next used an approach developed to decompose population-level change into contributions from within-individual improvement and senescence, and contributions from selective mortality. The results largely agreed with those of the mixed-effects models and the GAMs, but with subtle differences that emphasize the strengths and weaknesses of the different analytical approaches.
Annual fecundity showed profound age-related change, with contributions from both within-individual effects and selective disappearance. The population-level decline from age 5 was underpinned by a considerable decline due to individual senescence and a positive effect of selective disappearance of individuals with low fecundity (Fig. 3a). Of the total absolute change across all ages, 42·04% was due to selective disappearance; across early life (up to and including age 6), 60·03% was due to selective disappearance; across late life, 31·40% was due to selective disappearance, with the remaining change in each case attributed to within-individual change. This suggests a considerable influence of selective disappearance during both early and late life.
Twinning also showed considerable age-related change, but followed a markedly different pattern. The population-level pattern suggested increasing likelihood of TW up to age 6, followed by a plateau (Fig. 3b). The individual-level pattern supported the conclusions of the mixed-effects model analysis, which provided no evidence for senescence in TW. The effects of selective disappearance were generally low or negative during early and late life, suggesting selective death of individuals that produced twins. Across all ages, selective disappearance accounted for 18·19% of the absolute change in probability of TW; selective disappearance exerted a small influence in early life, accounting for 8·05% of absolute change, but had a greater influence in late life, where it accounted for 25·18% of age-specific change.
Offspring birth weight showed an inverse U-shaped population-level pattern (Fig. 3c). As with AF, there was a strong within-individual decline at later ages, and although the positive effect of selective disappearance was not as strong, it increased with age. This was reflected in the fact that selective disappearance accounted for 21·31% of the absolute change across all ages; this was only 5·95% in early life, but accounted for 38·31% of the absolute change in later life.
The population-level change in OS showed a decline from age 8 onwards. A gradual individual-level decline began around age 4; the influence of selective disappearance was weakly positive but increased with age (Fig. 3d). Overall, selective disappearance accounted for 27·57% of absolute change in OS with age; in early life, it accounted for only 16·38%, but in late life, it accounted for 37·09%, showing a pattern similar to that for OWT.
In this study, we investigated age-specific changes in four female reproductive traits in a naturally regulated population of Soay sheep. We tested for differences in ageing patterns of the four traits using GAMs and for declines in reproductive performance in old age as an indicator of senescence. We determined the importance of within-individual change vs. selective disappearance in shaping overall age-specific patterns, using mixed-effects models and a phenotypic decomposition approach. Below, we discuss the results on a trait-by-trait basis, enabling comparison of the results of the different methods for the same trait, before evaluating the analytical methods.
The whole-life mixed-effects models showed evidence of a terminal decline in AF, as has been shown previously in this population for body weight (Nussey et al. 2011). This could suggest a final loss of physiological function in females, culminating in failure to reproduce caused by oocyte exhaustion (Armstrong 2001) and subsequent death.
The late-life patterns predicted by the different analytical methods were largely in agreement. The whole-life mixed-effects models supported a quadratic association with age, with a predicted peak in performance at age 7, while the GAMs and the decomposition approach both predicted a population-level plateau from age 4 to 9 and a subsequent decline. The decomposition approach revealed that this was underpinned by a decline in individual performance from around age 5 and an increase in selective disappearance. The late-life mixed-effects model also supported a strong influence of selective disappearance on the late-life decline in AF, with high mortality of poor breeders potentially masking senescence. The results from GAMs (Fig. 2) more closely matched the predictions for the population-level pattern from the decomposition analysis (Fig. 3a). As GAMs are not restricted to follow a specific functional form, they may more accurately describe the population-level pattern than the mixed-effects models, which assume that age-related change follows a quadratic trajectory. Overall, the results suggest strong influences of both individual ageing and selective disappearance, with a within-individual decline from middle age counteracted by an increasingly strong influence of selective disappearance.
Probability of TWINNING
A surprising result was the lack of any indication of senescence in litter size or twinning probability (TW). Recent work has suggested that senescence is widespread in natural populations (Nussey et al. 2008), so a lack of senescence in this key reproductive trait is intriguing, although not unprecedented. Cross-sectional studies of immune phenotype in tree swallows Tachycineta bicolour (Palacios et al. 2007) and wandering albatrosses Diomedea exulans (Lecomte et al. 2010) have revealed that not all traits show detectable senescence in other systems. However, these may be regarded as traits less closely linked to fitness than TW, which is a key component of fitness and under relatively strong selection (Wilson et al. 2009); indeed, the albatross study did find evidence of senescence in the ability of both sexes to successfully rear a chick (Lecomte et al. 2010). Dizygotic TW rates in humans are often observed to increase with age (Bulmer 1970; Hoekstra et al. 2008), with a peak in the late 30s ascribed to increasing follicle stimulating hormone (FSH) levels with age (Beemsterboer et al. 2006). However, in human studies where data from females aged over 40 are treated separately, a decline in TW rate in the oldest individuals has been observed (Parazzini et al. 1991; Tandberg et al. 2007), which has been attributed to declining quality of ova (Broekmans, Soules & Fauser 2009). However, in our study, late-life GAMs predicted an increase rather than a decrease in TW at later ages (Fig. 2b).
Twinning was also the only trait that showed a negative effect of selective disappearance in the late-life models and in the decomposition analysis, suggesting that individuals who were more likely to produce twins died earlier. This suggests a fecundity-longevity trade-off and is consistent with the high survival cost of TW to young mothers in this population (Clutton-Brock et al. 1996; Tavecchia et al. 2005). Such a negative association between longevity and reproductive performance has been shown to create a false impression of senescence in a study of red-billed choughs (Pyrrhocorax pyrrhocorax), where age-related variation was due largely to early mortality of females that raised more offspring (Reid et al. 2010), but was clearly not sufficient here to generate a population-level appearance of late-life decline.
Offspring Birth Weight
Generalized additive models predicted that OWT increased rapidly at early ages, followed by a gradual decline from around age 4. Body weight in female Soay sheep only declines in the final year of life (Nussey et al. 2011), suggesting a gradual decline in body condition may not underlie declining OWT in older females. These results do not support the prediction from life-history theory that females should make a terminal investment in reproduction in their final year of life, when residual reproductive value is at its lowest (Clutton-Brock 1984). Instead, it seems that females invest less in reproduction, as shown by a decline in offspring weight with increasing age. Previous studies of wild ungulates have also found that offspring growth rates and weight decrease gradually with maternal age (Weladji et al. 2010; Martin & Festa-Bianchet 2011), indicating a higher cost of reproduction for older mothers (Martin & Festa-Bianchet 2010) and making terminal investment unlikely.
There was a marked effect of selective disappearance on OWT in the late-life models: mothers who produced smaller lambs had shorter lives. This was echoed by the decomposition analysis, which showed that selective disappearance contributed little to the population-level ageing pattern of OWT, until around age 8. Overall, the ageing pattern for OWT was similar to that for AF, with an early life increase followed by a decline. However, the analysis suggests that the decline in OWT began earlier and was more gradual and that selective disappearance was less important.
Overall, OS showed a similar pattern to OWT. The within-individual pattern predicted by the decomposition analysis suggested that both traits declined gradually from around age 6 before rapidly declining thereafter. The contribution of selective disappearance to age-specific changes in the decomposition analysis of OS increased at later ages, and the whole-life mixed-effects models also suggested that longevity was not associated with either OWT or OS. These two traits therefore appear to follow a similar pattern, with a relatively modest contribution of selective disappearance and an accelerating within-individual decline; this was confirmed by GAMs which fitted the same smoothing function to both traits, both across life and during the late-life decline. Senescence will be expected in traits which are underpinned by traits that themselves show senescence: for instance, the fact that older mothers have lighter lambs will likely contribute to declining lamb survival in old age. A study of great tits (Parus major) was able to show that senescence in brood size and more rapid senescence in fledgling number contributed to senescence in offspring recruited to the breeding population, which was most rapid of all (Bouwhuis et al. 2009). The GAMs appear to show that this is the case at the population level in Soay sheep, but the decomposition analysis suggests that this is not the case at the individual level.
A Comparison of Methods
We have analysed age-specific patterns in four reproductive traits in a natural population of Soay sheep, using three analytical methods. Implementing these methods side-by-side highlights their relative merits and that using a variety of analytical frameworks with different attributes may strengthen confidence in the observed patterns. Accounting for selective disappearance using mixed-effects models (van de Pol & Verhulst 2006) allows causes of variation in ageing trajectories to be investigated by addition of interaction terms to model formulae and also provides a quantitative description of the magnitude of change with age in the form of parameter estimates. However, this approach is unable to quantify proportionate contributions of selective disappearance and within-individual effects in the same way as the decomposition approach, and assumes a predefined functional form of age-specific change. Similarly, although describing variation in age-specific means from model predictions using GAMs allows description of patterns of ageing without assuming a specific functional form, it cannot quantify the effects of selective disappearance or investigate sources of individual variation in ageing patterns. It therefore represents a method for describing relatively complex patterns of ageing-related change but may not allow meaningful conclusions to be drawn about the manner of individual-level change. The decomposition method (Rebke et al. 2010) has the advantage of being able to quantify contributions of individual-level change and selective disappearance to population-level change across the life span and even at individual ages. A limitation is that it requires complete information on every individual for it to provide an accurate decomposition, and a major problem of studies of natural populations is of repeatedly sampling individuals, especially at older ages (Nussey et al. 2008), and some traits of interest (e.g. birth weight) may not be defined in a given year. A further limitation is that it cannot investigate individual variation in ageing (e.g. Nussey et al. 2007; Reed et al. 2008; Hayward et al. 2009) or test for terminal effects. The respective merits of these techniques suggest that applying more than one analytical approach may be beneficial in studies of senescence.
A further consideration is the decision whether to include, as fixed effects in mixed-effects models, variables which affect the response variable of interest, but which themselves change with age. Where the variables are on the same scale, this can provide a method for partitioning senescence (e.g. Bouwhuis et al. 2009), but when on different scales, interpretations may change depending on the fixed effects controlled for in GLMMs. We chose to analyse ageing in reproductive traits without accounting for body weight and parasite burden, hence describing the age-specific pattern; in the Supporting Information, we analysed reproductive traits including body weight, describing ageing once effects of body weight on reproductive traits and age-specific changes in body weight were accounted for. The ageing patterns were not affected despite body weight being positively associated with all of the reproductive traits, but this is a potentially important decision in analysis of age-specific change, and we urge researchers to consider the implications of including such effects.
Our results provide evidence for age-related changes in four aspects of reproductive performance in a natural population of Soay sheep. The results illustrate the complexity of variation in ageing patterns across traits and that senescence may not be detectable in all traits. A major limiting factor in the study of ageing in natural populations is the quality, depth and detail of data; studies with detailed longitudinal data on multiple traits are rare and are extremely valuable in identifying variation in ageing rates (e.g. Nussey et al. 2009; Lecomte et al. 2010; Massot et al. 2011). There was considerable variation in the population-level ageing-related patterns, and the contributions of selective disappearance and individual senescence also varied between traits. Our results also indicate that senescence is not ubiquitous across all aspects of reproductive performance, and therefore should not be assumed to always occur. Incorporating estimates of the importance of ageing, selective mortality and terminal effects on multiple traits will aid understanding of ageing in natural populations and help identify general patterns and population-specific processes.
We thank the National Trust for Scotland and Scottish Natural Heritage for permission to work on St Kilda, and the Royal Artillery Range (Hebrides) and QinetiQ for logistical support. We thank M. Festa-Bianchet, J.-M. Gaillard and one anonymous reviewer for comments on a previous draft, which greatly improved the manuscript. We thank D.H. Nussey, P. Monaghan, A. Pedersen and G. Asher for discussion. We also thank the many volunteers who have collected field data. The long-term data collection on St Kilda has been funded by the Natural Environment Research Council, the Wellcome Trust, the Biotechnology and Biological Sciences Research Council and the Royal Society, through grants to T.H.C.-B., J.M.P., L.E.B.K., B.T. Grenfell, M.J. Crawley, T. Coulson, and S. Albon. The work presented was funded by a Biotechnology and Biological Sciences Research studentship to A.D.H.