Quantitative genetics of age at reproduction in wild swans: Support for antagonistic pleiotropy models of senescence Anne Charmantier*, Christopher Perrins, Robin H. McCleery, and Ben C. Sheldon Edward Grey Institute, Department of Zoology, University of Oxford, South Parks Road, Oxford OX1 3PS, United Kingdom Edited by Joseph Felsenstein, University of Washington, Seattle, WA, and approved March 13, 2006 (received for review December 23, 2005)
evolutionary tradeoff 兩 genetic correlation 兩 heritability 兩 mute swan 兩 aging
T
he decline in reproductive performance in organisms of old ages is one component of the evolutionary paradox of aging (1). Aging, or senescence, is the drop in survival and兾or fertility probabilities in old individuals. It is often witnessed in laboratory conditions (e.g., see refs. 2–4) and, more rarely, in nature (5–7). For evolutionary biologists, the evolution of decreased performance and increased mortality with age, which should at first sight be counterselected, is a puzzle. The solution to this puzzle lies in the weaker force of natural selection for older individuals in age-structured populations (8), which allows for the evolution of aging. Two main genetic processes have been proposed as causal mechanisms underlying the evolution of senescence. The first assumes an accumulation of late-acting deleterious mutations as a result of weak selection late in life (referred to as the mutation accumulation theory) (1, 8). Alternatively, aging can be promoted by the active selection of alleles with late deleterious effects but beneficial effects early in life, when selection is strongest (9). This latter theory, known as the antagonistic pleiotropy (AP) theory of aging, can be considered an optimality theory (10) because the evolution of senescence is explained by fitness maximized by good performance early in life, at the expense of performance later. This type of pleiotropic effect is best illustrated in physiological or ecological tradeoffs such as that occurring between reproduction and survival. Indeed this theory has at times been called the ‘‘tradeoff’’ model (11). However, an important facet of the AP theory is that the pleiotropic alleles lead not only to phenotypic, but also to genetic, correlations between early and late life-history traits. Artificial selection experiments on Drosophila melanogaster have www.pnas.org兾cgi兾doi兾10.1073兾pnas.0511123103
repeatedly given support for the AP theory, showing negative genetic correlations between early fecundity and late fecundity or longevity (review in ref. 1). Our knowledge and understanding of the evolution of aging has benefited greatly from research on laboratory Drosophila (e.g., 12–14). However, artificial selection experiments potentially suffer from genotype-by-environment interactions because of, for example, environment-dependence of the difference in fertility between selected lines (15). Manipulative studies of reproduction in laboratory conditions make it possible to test multiple predictions from the theories of senescence evolution (such as a genetic tradeoff between reproduction and longevity), but it is difficult to determine the extent to which the observed life-histories are affected by the novelty of laboratory conditions. Long-term observational studies of vertebrates have recently started to provide sufficient data to investigate senescence in wild animals (5–7). These data sets provide an invaluable opportunity to determine whether results from lab studies are consistent with observations in natural populations on a wide range of taxa. In this article, we focus on senescence revealed through the decline in reproductive performance, namely the termination of reproduction. We use data collected from a free-ranging population of mute swans (Cygnus olor) to investigate natural selection on, and genetic determinants of, the age at first reproduction (AFR) and age at last reproduction (ALR). AFR is a surrogate of early reproductive effort, whereas ALR is an index of an individual’s rate of reproductive aging. Hence the AP model predicts that the rate of senescence will be stronger, i.e., ALR with be earlier, for birds that have invested heavily in early-life reproduction, i.e., have started reproducing early. This prediction is not shared by the mutation accumulation theory, which relies on uncorrelated age-specific effects of deleterious mutations (16); hence this comparison provides a direct test of whether the AP theory can be applied to the evolution of senescence in the wild. The aims of this study were as follows: (i) to test whether phenotypic differences between mute swans in the timing of when they start and when they stop to reproduce influences their lifetime reproductive success (hence to measure current selection on AFR and ALR); (ii) to test whether the phenotypic variation in these two traits has a heritable component; (iii) to determine the phenotypic and genetic covariance between these characters; and, finally, (iv) to discuss the implications of these findings with respect to life-history evolution and the evolution of senescence. Conflict of interest statement: No conflicts declared. This paper was submitted directly (Track II) to the PNAS office. Abbreviations: AFR, age at first reproduction; ALR, age at last reproduction; AP, antagonistic pleiotropy; ind, rate-sensitive individual fitness; LRS, lifetime reproductive success. *To whom correspondence should be addressed. E-mail:
[email protected]. © 2006 by The National Academy of Sciences of the USA
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Why do individuals stop reproducing after a certain age, and how is this age determined? The antagonistic pleiotropy theory for the evolution of senescence predicts that increased early-life performance should be accompanied by earlier (or faster) senescence. Hence, an individual that has started to breed early should also lose its reproductive capacities early. We investigate here the relationship between age at first reproduction (AFR) and age at last reproduction (ALR) in a free-ranging mute swan (Cygnus olor) population monitored for 36 years. Using multivariate analyses on the longitudinal data, we show that both traits are strongly selected in opposite directions. Analysis of the phenotypic covariance between these characters shows that individuals vary in their inherent quality, such that some individuals have earlier AFR and later ALR than expected. Quantitative genetic pedigree analyses show that both traits possess additive genetic variance but also that AFR and ALR are positively genetically correlated. Hence, although both traits display heritable variation and are under opposing directional selection, their evolution is constrained by a strong evolutionary tradeoff. These results are consistent with the theory that increased early-life performance comes with faster senescence because of genetic tradeoffs.
Fig. 1.
Distribution of AFR (a) and ALR (b) in female and male mute swans.
Results Mute swans varied considerably with respect to both AFR and ALR. AFR varied from 2 to 12 years of age, whereas ALR varied from 2 to 20 years of age. Part of the variation in ALR is linked with AFR, because it is inevitably true that ALR ⱖ AFR; we discuss the consequences of this in Heritability and Genetic Correlation. There was no difference in the time at which male and female mute swans started reproducing or finished reproducing [AFR(female) ⫽ 4.37, SD ⫽ 1.52, n ⫽ 525; AFR(male) ⫽ 4.53, SD ⫽ 1.64, n ⫽ 538, t1061 ⫽ 1.67, P ⫽ 0.10; Fig. 1a; ALR(female) ⫽ 7.99, SD ⫽ 3.78, n ⫽ 306; ALR(male) ⫽ 7.74, SD ⫽ 3.37, n ⫽ 342, t646 ⫽ ⫺0.87, P ⫽ 0.38; Fig. 1b]. Nor was there any evidence for sex-specific differences in selection gradients or heritabilities (data not shown). Hence, for all further analyses, we combined male and female records and present only the results on this pooled data set. Variation in AFR is not simply because of sampling error (e.g., due to some birds moving to the colony at an old age): For example, 76% of the birds that started reproducing after 7 years of age (n ⫽ 54) were seen in the colony in several years before their year of first reproduction. Therefore, these birds are most likely to be low-quality birds that wait many years before having access to a breeding site and partner.
Fig. 2. Selection on AFR (a) and ALR (b). Lifetime reproductive success (LRS) with respect to AFR and ALR for 529 birds, dead by 2005, that had stopped reproducing in 2000 or earlier (mean ⫹ SE).
Selection. When all 529 breeders that died before 2005 and that
did not reproduce after 2000 were included, linear and quadratic selection analyses showed strong negative directional selection on AFR and strong positive directional selection on ALR with a quadratic component pointing to stabilizing selection on the latter (Table 1 and Fig. 2 a and b). There was no evidence of correlational selection (Table 1): Hence, beginning to breed early is favored independently of the age at which a bird ceases to breed. The selection gradients estimated on these life-history components are very strong (e.g., compare with ref. 17), indicating close linkage with fitness for these traits. Heritability and Genetic Correlation. A significant proportion of the total phenotypic variance was explained by additive genetic effects and year of birth effects for AFR and ALR (Table 2), leading to small but significant heritability for both traits. AFR and ALR were significantly positively correlated, both at the phenotypic and at the genetic level in the initial animal model including all breeding birds (n ⫽ 648, Table 2). However, the phenotypic correlation (0.193, SE ⫽ 0.051) was more negative than that expected from the
Table 1. Selection on AFR and ALR Trait under selection AFR ALR
S⬘i (SE)
⫺0.412 (0.090)*** 1.020 (0.044)***
c⬘i (SE)
i⬘ (SE)
␥i⬘ (SE)
␥ij⬘ (SE)
⫺0.118 (0.086) ⫺0.099 (0.038)***
⫺0.433 (0.065)*** 0.972 (0.041)***
⫺0.068 (0.051) ⫺0.160 (0.036)***
⫺0.001 (0.084)
We used here dead birds that stopped reproducing before 2000, N ⫽ 529. Standardized selection differentials (linear models for directional selection, S⬘, and quadratic models for stabilizing兾disruptive selection, c⬘) and selection gradients (linear, ⬘, and quadratic, ␥⬘) were estimated using univariate and bivariate generalized linear models with a Poisson distribution and a log link function, and scaled deviance. ***, P ⬍ 0.001. 6588 兩 www.pnas.org兾cgi兾doi兾10.1073兾pnas.0511123103
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Table 2. Quantitative genetics on AFR and ALR from a bivariate animal model Statistic N VA ⫾ SE VYOB ⫾ SE VR ⫾ SE h2 ⫾ SE Trait mean ⫾ SD CVA
AFR
ALR
1,063 0.24 ⫾ 0.11* 0.58 ⫾ 0.19*** 1.88 ⫾ 0.12* 0.088 ⫾ 0.040* 4.45 ⫾ 1.58 10.94
648 1.07 ⫾ 0.64* 1.86 ⫾ 0.69** 9.90 ⫾ 0.80*** 0.083 ⫾ 0.049* 7.86 ⫾ 3.57 13.16
N number of breeding individuals included in the analysis. Estimation from an animal model fitting sex of breeder and rearing in/out pen as fixed effects. *, P ⬍ 0.05. **, P ⬍ 0.01. ***, P ⬍ 0.001, for one-tailed t tests.
mathematical dependence of ALR on AFR, as estimated from the permutation tests (mean of 500 simulations: 0.410, SD ⫽ 0.031). The phenotypic correlation is likely to be generated by a number of processes; these analyses suggest that variation in individual quality, with good quality individuals performing well both early in life (with an early AFR) and late in life (with late AFR, hence tending toward negative correlation), is an important component. This conclusion is in accordance with results showing that individual female mute swans with relatively long lives lay more eggs at any given age (R.H.M., C.P., and A.C., unpublished work). When restricting to birds with a reproductive lifespan longer than 1 year (n ⫽ 469), the phenotypic correlation was reduced, but the genetic correlation remained high, although only marginally significant, possibly because of low sample size (Table 3). Also, within the 500 permutation tests, although heritability of AFR remained significant with a mean of 0.155 (SD ⫽ 0.033), heritability of ALR was never significantly different from 0 (mean of 0.027, SD ⫽ 0.046), thereby confirming that our result cannot be explained by the effect of a necessary autocorrelation between the two traits. This independence is also expected given that the genetic covariance between two traits depends on those traits’ relationship across relatives, rather than within individuals, as is the case for the phenotypic correlation. Finally, when we restricted the analysis to birds that lived at least 1 year after their last reproductive attempt (n ⫽ 272), both correlations had similar values to that found with the original data set (Table 3). This confirms that the genetic correlation is between AFR and true reproductive senescence. Predicted Response. Although the genetic correlation between
AFR and ALR is strong, it is ⬍1 and hence allows independent evolution in both traits. If we disregard the stabilizing selection on ALR, which is small in comparison to the directional selection acting on AFR and ALR (Table 2), our multivariate selection and quantitative genetic analyses predict increases in AFR and ALR of 0.013 years and 0.095 years, respectively, per generation. Because mean generation time is 7.2 years in the swan (18), a change in mean ALR in Abbotsbury swans by 1
year might occur in ⬍80 years, but mean AFR would change little in the same period. The constraint on the evolution of AFR results from the strong genetic correlation, because, in the absence of genetic correlation, the mean AFR would decrease. Discussion Our analyses of selection and inheritance of the age at which birds start and stop breeding showed that both are under strong selection, in opposite directions, and that both possess additive genetic variation, but that the genetic covariance between the characters acts as a constraint on evolutionary responses for both traits. The finding that genetic variance associated with an early start to the reproductive life is associated with an early end to reproduction is as predicted by antagonistic pleiotropy models of the evolution of senescence. However, this finding contrasts with previous results from two studies of human populations, where AFR had a weak negative correlation with ALR (or menopause; see refs. 19 and 20). The difference could be explained by the importance of cultural and family effects, such as wealth in humans, compared with other animals. In this wild swan population, natural selection favors individuals that start to reproduce early and breed until an old age, resulting in strong positive selection on reproductive lifespan. Although the latter is quite a common finding (21, 22), direct selection for early AFR is more surprising. The usual finding is of no evidence for selection on AFR when using lifetime reproductive success (LRS) as a surrogate for fitness but evidence for selection favoring early AFR when using a ratesensitive individual fitness (ind) measure (e.g., 23–25). This rate-sensitivity is because the benefit of higher probability of realized fitness for individuals with early maturity can be balanced by associated fitness costs, such as shorter lifespan (26). Particularly in growing populations, LRS has been considered inadequate as a fitness measure, because selection on early AFR may be apparent only when considering differential timing by using ind (24). However, in our swan population, where population size has been increasing for more than two decades, there is strong directional negative selection for AFR using both LRS [selection differential (SE): S⬘i ⫽ ⫺0.412 (0.090)] or ind [S⬘i ⫽ ⫺0.219 (0.068)]. The concordance of selection estimates from rate-sensitive and rate-insensitive fitness measures is likely to result from the relationship between reproductive performance and age at the individual level: Strong senescence in reproductive output makes it advantageous for swans to start reproducing early, even when disregarding the demographic context, i.e., even when using LRS rather than ind. Two of the major findings of this paper are that ALR was heritable and that there is strong genetic covariance between the age at which birds started reproducing and their reproductive senescence; we tested the robustness of these results in several ways. First, randomization tests showed that genetic variance in ALR and the genetic correlation with AFR did not result from the necessary autocorrelation between the two traits. This
Situation tested All breeding swans dead by 2005 All breeding swans dead by 2005, and with ALR ⬎ AFR All breeding swans dead by 2005, and with age at death ⬎ ALR
No. of birds
Phenotypic correlation ⫾ SE
Genetic correlation ⫾ SE
648 469
0.193 ⫾ 0.051*** 0.118 ⫾ 0.060*
0.555 ⫾ 0.291* 0.560 ⫾ 0.404
272
0.191
0.495
For the first two data sets, the correlations were estimated using the animal model described in Materials and Methods. For the last data set, the Pearson correlation coefficient was estimated on the phenotypic data and on the breeding values from the full animal model.
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Table 3. Phenotypic and genetic correlation between AFR and ALR
conclusion is confirmed by the genetic correlation being almost three-fold larger than the phenotypic correlation and by the effect of removal of all birds with AFR ⫽ ALR, which reduced the phenotypic, but not genetic, correlation (Table 3). Second, some swans die of predation or accidental death before their reproductive performance is affected by senescence. In our initial analyses (Table 2), ALR can result from both reproductive senescence (if a bird stops reproducing but still lives) and兾or mortality (if a bird is not seen as a breeder because it has in fact died). When restricting the data set to birds that stopped reproducing but were still seen in the colony, i.e., birds that showed real reproductive senescence, breeding values showed a persistently high genetic correlation between both traits. This correlation confirms that reproductive senescence is genetically related to the age of the onset of reproduction, as predicted exclusively by the antagonistic pleiotropy theory of the evolution of senescence. Some studies of age-related reproduction in birds have uncovered cases where early reproductive performance was positively, rather than negatively, related to subsequent performance, presumably because of substantial variation in quality among individuals (see Selection hypothesis for age-specific reproductive performance in ref. 27). The classic explanation for such patterns is that if the amount of resources available varies across individuals then good performers early in life may live longer and reproduce faster as well (28); in our case, this positive covariance of fitness components would appear to lead to a negative relationship between AFR and ALR, rather than the positive relationship observed. In fact, we have evidence that this process is occurring in our study population. As the randomization procedures showed, a positive relationship between AFR and ALR is inevitable when the phenotypic correlation is considered, because ALR ⱖ AFR. Hence, the finding that the phenotypic correlation in the raw data is actually smaller (i.e., more negative) than that generated from randomization implies that early values of AFR are associated with late values of ALR more than expected. Hence, our data simultaneously reveal how these characters can covary in different directions at phenotypic and genetic levels. We have shown here that, in accordance with the antagonistic pleiotropy theory, genetic tradeoffs can explain the cessation of reproduction in old mute swans. Uncovering molecular processes such as oxidative stress or telomere shortening underlying the genetic correlation between early and late reproduction would necessitate a complementary, experimental approach, which might be best undertaken in a shorter-lived species, more amenable to manipulation. Knowing the physiological mechanism would be helpful especially to elucidate whether the described tradeoff between AFR and ALR is resulting from a covariance of both traits with a third unmeasured trait, such as the individual’s size or differing development time. Indeed, a classic tradeoff found in many species links growth, survival, and fecundity (29). In our case, an early AFR might result in a relatively small adult body size (because of a shorter growth period), which in return could explain the early ALR, because growth rate can be linked to lifespan and senescence rates by several physiological mechanisms (30). Materials and Methods Study Population, Data Collection, and Pedigree. The earliest
records of the colony of mute swans (C. olor) in Abbotsbury, Dorset, U.K., date back to the 14th century, but the colony may be older in origin (for a description of the study site see refs. 31 and 32). The first records of individually identifiable birds are from the late 1960s, although systematic banding of all birds in the colony started in 1976. Since 1990, all of the birds breeding in the colony (apart from 10% of immigrant breeding males and 5% of immigrant females) have been born after the start of the individual monitoring and are consequently of known exact age. 6590 兩 www.pnas.org兾cgi兾doi兾10.1073兾pnas.0511123103
Every 2 years since 1989, a roundup has been organized where all of the birds in the colony are captured and individually marked (or identified) with a unique metal ring as well as a plastic ring for quick identification in the field. As soon as swans start pairing up in March, the nesting area is visited daily to identify all breeding parents, and to record their breeding site, breeding dates, and clutch size. An individual is recorded breeding from the moment it is seen to start a breeding attempt (nest-building), irrespective of the success or failure of that particular breeding attempt. Consequently, the estimated AFR and ALR are very close, if not identical, to the real AFR and ALR, and they are not contingent on an individual producing surviving offspring. One or two days after hatching, the cygnets are marked individually with a web-tag, before being equipped with metal and plastic rings when they reach their full size in the autumn. From May to October, some families or individual cygnets are placed in pens to protect them from aggression from other swans. The fledgling survival of these protected cygnets is increased (31), possibly affecting their later condition and reproductive decisions. Hence, this ‘‘pen’’ effect was taken into account in our analyses. Since the early 1970s, the number of breeding pairs in the colony has ranged from 20 to a maximum of 163 in 2001, with a general trend for an increase in breeding density. Here, we use records of 1,147 individuals that bred in the colony between 1969 and 2005. All breeding birds were included in the pedigree used for quantitative genetics analyses. The pedigree has 237 identified fathers (770 father–offspring relationships), 215 identified mothers (772 mother–offspring relationships), and a maximum of six generations within a family. AFR and ALR were estimated only for swans for which the exact birth year was known. AFR was known for 1,063 birds (538 males and 525 females). ALR, lifespan, and LRS (or lifetime number of recruited offspring) were recorded only for the 648 birds considered dead by the end of the study period (2005), i.e., that were not breeding in 2004 or 2005, nor were recorded during the 2005 swannery roundup, nor sighted outside the swannery in 2004 or 2005. Inbreeding Levels and Potential Bias. The pedigree of 1,147 breed-
ing birds showed only two closely inbred individuals (i.e., the product of matings between half-siblings or closer relatives: individuals with inbreeding coefficients ⱖ0.125). When relaxing the inbreeding coefficient to ⱖ0.03125, it yields only 31 individuals (i.e., 2.7%). The results from the selection and quantitative genetic analyses were unchanged when these 31 individuals were removed from the data set, and a mixed model controlling for year, sex, and pen rearing showed no effect of inbreeding coefficient on AFR (t1,1027 ⫽ 0.00, P ⫽ 0.99) nor on ALR (t1,1027 ⫽ 0.30, P ⫽ 0.76). Hence, because of continued immigration, inbred individuals are very rare in the study population, and their exclusion does not alter the conclusions in any way. Estimating Natural Selection. We used univariate and multivariate
linear regressions of fitness on trait values to estimate selection gradients and differentials (33–35). For parameter estimation, we standardized AFR and ALR (zero mean, unit variance) within the subset of data on which the analysis was performed (36). Individual fitness was estimated only for birds dead by the end of the study period and which did not reproduce since 2000 (this truncation allows for the recruitment of offspring during a minimum of 5 years after birth). The chosen fitness estimate was total number of recruited offspring in the colony or LRS. Individual fitness was also converted to relative fitness (standardized average of 1). Standardized directional (S⬘) and stabilizing (c⬘) selection differentials were estimated by using univariate linear and second-order polynomial regressions, respectively (34). We fitted generalized linear models with a Charmantier et al.
Estimating Heritability. The pedigree of 1,147 birds relies exclusively
on social mating status, although there may be some extra-pair matings leading to extra-pair paternities (EPP). Consequently, additive genetic variance and heritability potentially may be underestimated in our analyses, although we expect the rate of EPP to be low (0% to 17% of extra-pair cygnets were found in other swan species; see refs. 39 and 40) and hence the bias to be small. Indeed, a recent study has shown that for life-history traits with typically low heritabilities, sample sizes of several hundred of male-offspring and female-offspring pairs will lead to insignificant biases even with 20% unaccounted pedigree errors (41). Finally, previous investigations of heritability of life-history traits using the same social pedigree have provided estimates that are consistent with the literature, implying that pedigree errors do not compromise its use in quantitative genetic analyses (18). To partition the phenotypic variance (VP) and estimate variance components and heritability, we used a restricted maximum likelihood (REML) mixed-model known as ‘‘the animal model’’ (42, 43), implemented in the software ASREML (44). The analysis combines pedigree information with phenotypic records to break down individual phenotypes in a sum of fixed and random effects. In its matrix form, an animal model can be described as: y ⫽ X ⫹ Zu ⫹ e,
[1]
where y is the vector of phenotypic observations,  is the vector of fixed effects, u is the vector of additive genetic effects, X and Z are design matrices relating the fixed and random effects to each individual, and e is the vector of residual errors. Compared with conventional methods such as parent-offspring regressions, these REML-based methods make fewer assumptions about the data, and they are more powerful because they accommodate unbalanced data sets and they exploit all relationships in the pedigree (45). The main disadvantage of these techniques is the computational complexity, which requires significant sample sizes. Preliminary generalized linear models showed that AFR and ALR were substantially influenced by the year of birth of an individual. In the following animal models, this factor was included as a random effect (33 levels between 1969 and 2002). The sex of the bird and its rearing inside or outside pens also influenced AFR, although not ALR; hence both bimodal factors were also added as fixed effects. Maternal random effects were initially fitted in the model but never proved significant; hence, they were removed. The phenotypic variance (VP) was therefore partitioned into the following components: VP ⫽ V A ⫹ V YOB ⫹ V R, Charmantier et al.
[2]
where VA is the additive genetic variance, VYOB is the variance attributed to differences in years of birth, and VR is the residual variance. When dealing with tradeoffs, it is essential that both traits be analyzed simultaneously, hence all animal models were bivariate. ASREML provided the best linear unbiased predictors (BLUPs) of each individual’s breeding value (42) for both traits. The additive genetic correlation between AFR and ALR was estimated with ASREML by using the bivariate animal model described above. Heritability (46) was estimated for each trait as h2 ⫽ VA兾VP. To enable comparison with other traits and populations, we also report the coefficient of additive genetic variance CVA (47) in which the ): additive genetic variance is scaled by the trait mean (X CVA ⫽ 100 ⫻
冑V A兾X .
[3]
Randomization to Test for Autocorrelation. There are two issues that
potentially influence the interpretation of our findings and for which we performed additional tests. The first one is whether the autocorrelation between AFR and ALR resulting from AFR ⱕ ALR will affect our results. This conjecture was tested (i) by using a restricted data set and (ii) by performing randomization procedures to estimate the degree of autocorrelation. First, because a correlation between AFR and ALR can be inflated by birds that reproduce only once and for which AFR ⫽ ALR, we removed these birds and ran a similar animal model as previously (n ⫽ 469). Second, using the relationship ALR ⫽ AFR ⫹ RLS ⫺1, where RLS is the reproductive lifespan, we performed tests where AFR was kept constant for each bird, but RLS was randomly permuted across individuals hence giving a new value of ALR for each bird at each permutation. A simple animal model partitioning the variance into VP ⫽ VA ⫹ VR was run after each of 500 permutations, thereby providing an upper limit to the amount of additive genetic variance in ALR that resulted from the autocorrelation with AFR (for example, due to this trait possessing genetic variance). The second concern is whether AFR is a good index of reproductive senescence or whether it is mainly determined by longevity. Indeed ALR can reflect the cessation of reproduction for a bird for various reasons, including accidental death. To investigate the genetic correlation between AFR and real reproductive senescence, we restricted the data set to birds that lived at least 1 full year after they were recorded having stopped breeding. The sample size for this restricted data set (n ⫽ 272) did not allow us to successfully run an animal model; however, we estimated the genetic correlation between AFR and ALR for these ‘‘senescing’’ birds by using the breeding values from the full animal model. The correlation between breeding values lies between the phenotypic correlation (if breeding values are estimated with no information on relatives) and the true genetic correlation (in the case of extensive information on relatives; see ref. 48). The Abbotsbury pedigree has proven to confer good accuracy thanks to high connectedness between individuals (18), which means the correlation in breeding values will be a good estimate of true genetic correlation. Predicting the Response to Selection. We predicted the response to
selection over one generation in both traits by using the equation (46): R ⫽ h12 1 ⫹ rg h1h22, where h12 is the heritability of the focal trait, 1 its standardized selection gradient, rg the genetic correlation coefficient, and h22 and 2 those of the other trait. This study was made possible by the long-term work of the swannery staff, especially Dave Wheeler, and many volunteers. Thanks to J. Brommer for useful discussions and to L. Kruuk, D. Promislow, and two anonymous referees for very helpful suggestions on the analyses and the manuscript. A.C. was supported by a Marie Curie Intra-European Fellowship. PNAS 兩 April 25, 2006 兩 vol. 103 兩 no. 17 兩 6591
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poisson error structure and logarithmic link function. Overdispersion occurred in all models and was controlled for by scaling the deviance to 1. Next, we accounted for indirect selection in multivariate regressions of AFR and ALR, which provided estimates of standardized directional (⬘) and nonlinear (␥⬘) selection gradients. In the multivariate analysis, we estimated the standardized correlational selection gradient (␥⬘ij), which measures the selection acting on the covariance between AFR and ALR, by fitting the cross product (33). Because the number of breeding birds in Abbotsbury has shown a steady increase over the years since the beginning of the study period (37), we repeated the selection analyses by using the ind estimate (24) instead of LRS. In agreement with the results of recent comparative analyses of ind and LRS by using data on the collared f lycatcher Ficedula albicollis and the Ural owl Strix uralensis (38), the two fitness estimates gave very similar estimates of selection. For this reason, only LRS estimates are detailed here, although ind results are brief ly discussed.
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