Partitioning of phenotypic covariance among lifehistory traits in the great tit Parus major
B.C. Sheldon1*, R.A. Pettifor2, W.J. Browne3,4, J. Rasbash3 & R.H. McCleery1
1.
Edward Grey Institute, Department of Zoology, University of Oxford, UK
2.
Institute of Zoology, Zoological Society of London, UK
3.
Multilevel Models Project, Mathematical Sciences, Institute of Education, London, UK
4.
Mathematical Sciences, University of Nottingham, Nottingham, UK
*To whom correspondence should be addressed at:
EGI, Department of Zoology, University of Oxford, Oxford OX1 3PS Tel: +44 1865 281069 Fax: +44 1865 271168 E-mail:
[email protected]
Abstract Studies of variation in individual reproductive fitness in natural populations have been important in the development of life-history biology, in particular for our understanding of the evolution of reproductive scheduling, reproductive effort and the individual optimisation of fitness. Most long-term studies of marked individuals are characterised by complex data sets, where repeated observations of individuals, distributed over a range of environments, make the determination of the important sources of variation between individuals difficult. In addition, many traits measured in individuals show strong phenotypic covariance, which can arise for numerous reasons; distinguishing between these explanations is difficult without experimentation. In this paper we apply Bayesian cross-classified multivariate models to data from a long-term study of the great tit Parus major to partition the covariance between different reproductive parameters (life history traits) within and between differing sources of variance. Our analyses provide evidence for the importance of the environment in structuring patterns of phenotypic covariance between pairs of lifehistory traits. Additionally, these analyses reveal patterns of antagonistic covariance at different levels of the analysis, which seem to reflect the opposing influence of (i) individual variation (particularly among females) in acquisition of resources and (ii) trade-offs between life-history traits. We argue that the multi-level partitioning of covariance offers some alternative perspectives as a means of causal analysis of lifehistory variation, and suggest some additional approaches that could be taken using this method.
Keywords: fitness, life history, multivariate mixed model, optimisation, trade-off, variance decomposition
Introduction
Explaining variation between individuals in reproductive traits relating to fitness, such as their timing of reproduction, the number of offspring they produce, and the number of descendents they leave remains a long-term goal of evolutionary ecology. Many approaches have been used to answer these questions, ranging through development of theoretical models, comparative analyses, laboratory selection experiments, quantitative genetics and experimentation in the field (reviewed in: Stearns 1992; Bennett & Owens 2002; Roff 2002). Many of the observations that led to the initial development of modern life-history biology were derived from observations of animals and plants in natural populations (e.g. Lack 1954, 1966). In terms of understanding the sources of variation in traits, observational studies have a number of well-known weaknesses when compared to experimental approaches, foremost among which are the difficulty in assigning causality to observed relationships, and the possibility that covariance at different levels obscures underlying relationships of interest (Reznick et al. 2000). For example, it is commonly observed that traits that might be expected to be negatively correlated, such as fecundity and mortality, or clutch size and egg size, are in fact positively correlated at the level of the phenotype in natural populations. This covariance can be explained as resulting from variation across individuals in the extent to which they possess, or can acquire, limiting resources (e.g. van Noordwijk & de Jong, 1986; Bernardo 1996; Reznick et al 2000; Roff 2002).
Despite these well-known limitations, observational studies also offer some advantages over other methods. Foremost among these are the larger sample sizes,
3
and longer time series, that are often available for study. If selection on life-history traits is weak, then very large sample sizes may be needed to detect it (Kingsolver et al. 2001), and it may require sample sizes in the order of thousands to make confident statements about the presence or absence of selection on a character. In addition, if environments fluctuate, then long time series of data may be needed in order to detect effects that have important consequences for explaining characteristics of populations (e.g. Sinervo & Lively 1996; Grant & Grant 2002). Also, in many cases the environmental sources of variation that are of interest fluctuate at an annual scale (Tinbergen et al. 1985; Boyce & Perrins 1987), in which case a data set collected over many years is required. A further advantage of long-term studies of unmanipulated populations is that many such studies have already been running for decades, meaning that large amounts of data are already available for analysis. Retrospective analyses of such data have provided some important examples of ecological and evolutionary phenomena in action in natural populations (e.g. Keller et al. 1994; Kruuk et al. 1999; Coulson et al. 2001; Merilä et al. 2001; Veen et al. 2001; Grant & Grant 2002).
Our aim in this paper is to present analyses, using a novel statistical method applied to a long-term study of a marked population, which circumvent some of the difficulties associated with covariance among different levels of data, while making use of the large amount of data that are available. In this paper we partition the covariance between different traits at a number of different levels. A companion paper (Pettifor et al. MS) provides additional background information, and addresses the partitioning of variance among different levels of the same data set.
4
Partitioning covariance: rationale Our aim in this section is to explain the rationale behind our seeking to partition covariance between traits at different levels. We illustrate this with two hypothetical examples, both of which are closely related to the analyses reported below.
A common finding in studies of life-history variation in the wild is that two traits covary (e.g. Bérubé et al. 1999; Reid et al. 2003). For example, in many species of birds, breeding time and clutch size are negatively correlated, with late-breeding birds laying smaller clutches than earlier breeding birds (Fig. 1a). This negative covariance is usually explained as reflecting a decline in the food available for rearing offspring over the course of the avian breeding cycle, with the result that the optimum clutch size is smaller for birds that breed later (e.g. Perrins 1970; Daan et al. 1989). In that sense, the observed negative covariance between laying date and clutch size is an example of adaptive phenotypic plasticity. An alternative explanation might be that only females in prime condition are able to breed early, and that such females are able to lay larger clutches because they are in better condition (c.f. Price et al. 1988), in which case the association between clutch size and laying date would be incidental. Both explanations would be consistent with the negative phenotypic covariance between clutch size and laying date, and would require careful experimentation to distinguish them; such experiments may in fact be very difficult to perform (Sheldon et al. 2003). However, the two hypotheses make different predictions about how the covariance between these traits will be partitioned between different levels of a structured data set (Fig 1a).
5
If the covariance between these two traits were largely the result of adaptive phenotypic plasticity, then we would expect a relatively large proportion of the covariance to be attributable to specific environmental effects. These effects might reflect differences between individual nest-boxes (e.g. if some territories are consistently associated with early breeding, then we would expect clutch size to be adjusted in response), or effects at the level of individual observation (e.g. stochastic effects specific to individual breeding attempts cause a female to lay late, and clutch size is adjusted in response to timing). Alternatively, if the covariance were largely due to variation in the properties of individual females, we would expect a relatively large proportion of the covariance to be due to differences between individual females. Similar scenarios could be constructed to explain covariance between combinations of traits at other levels.
A second insight that can be obtained from partitioning covariance at different levels, concerns the ability to detect covariances of opposite sign at different levels that tend to cancel each other out when combined at the level of the simple, gross phenotypic correlation (Fig 1b). Life-history theory predicts that some life-history traits should show negative covariances, reflecting optimal trade-offs between fitness components that cannot simultaneously be maximized (Stearns 1992; Roff 2002). For example, a trade-off between investment in current reproduction and investment in future reproduction is one of the two major kinds of trade-off that are thought to structure the evolution of life-histories (Williams 1966; Lessells 1991; Stearns 1992; Roff 2002). Such a trade-off might be sought as a negative correlation between clutch size (current reproduction) and subsequent parental survival (future reproduction). It is well known that raw phenotypic correlations tend to give results that are hard to
6
interpret, with more positive covariances among traits predicted to show negative covariances than expected (Bernardo 1996; Glazier 1999). In fact, such positive covariances are expected if individuals differ in the amount of resources they have available to allocate to competing functions (van Noordwijk & de Jong 1986; Fig 1b). The realisation that individual variation can mask underlying trade-offs is part of the rationale behind experimental approaches to studying life-history trade-offs in natural populations, where the individual variation is assumed to be controlled for by random allocation to experimental treatments. Hence, a field experiment to test the idea that current and future reproduction trade-off against each other might take the form of manipulating brood size and measuring the subsequent survival of parents rearing manipulated broods (Pettifor et al. 1988, Doligez et al. 2002).
Brood manipulation experiments conducted in the field, such as that described above, have a number of difficulties, foremost amongst which is the likelihood that the expected effects may be small, and easily swamped by environmental sources of variation. This may then necessitate impractically large sample sizes in order to statistically detect an effect. Multi-level partitioning of covariance offers an alternative way to approach trade-offs between life-history traits. If the positive covariance between traits that are expected to show a negative covariance were due to variation between individuals in resource availability, then we would expect to find differing patterns of covariance at different levels of the analysis. At the level of differences between individual females, the covariance should be positive: some females are able to lay large clutches and are inherently more likely to survive to the following breeding season. However, at the lowest level (i.e. at the unit of observation, namely between breeding attempts), we may expect to see a negative
7
covariance. That is, once the effect of variation between individuals is removed, we might expect that we are able to detect the antagonistic effects of investment in two competing life-history traits (see Fig 1b). In this case, the experimental and the analytical approach aim to determine the same quantity: the sign of the relationship, holding individual variation constant, between two life-history traits.
Materials and Methods Data The data analysed here were collected as part of a long-term population study of the great tit Parus major, breeding in nest-boxes in Wytham Wood, near Oxford, UK. More details concerning the general methods and traits considered are given in the companion paper (Pettifor et al. MS), and in references therein; only brief details are given here.
Great tits were studied breeding in nest-boxes (>1000) erected throughout the wood; the position of the nest-boxes has remained unchanged over the course of the study period analysed here (1964 – 1997, although wooden boxes were replaced by concrete ones in 1974-76 due to heavy predation by weasels Mustela nivalis). Birds were identified from ring numbers applied either as nestlings, or when trapped as adults. Recruitment was determined through the recapture of birds, previously ringed as nestlings, as breeding adults. Six traits, and their covariance, are analysed here: (i)
Clutch size: the number of eggs laid in each completed clutch.
(ii)
Laying date: the date on which the first egg of the clutch was laid.
(iii)
Mean nestling mass: the mean mass of nestlings per brood.
8
(iv)
Nest success: a binary variable with the value of either 0 or 1 depending on whether any ringed young from that breeding attempt were recaptured as breeding adults in subsequent years (0 = none recaptured).
(v)
Female survival: a binary variable with the value of either 0 or 1 depending on whether an individual female was recaptured in subsequent years (0 = not recaptured).
(vi)
Male survival: a binary variable with the value of either 0 or 1 depending on whether an individual male was recaptured in subsequent years (0 = not recaptured).
We chose five classifications with which to partition the covariance among these traits: (1) Year of breeding attempt (2) Individual nest-box (the position of each was fixed over the course of the study) (3) Individual female (4) Individual male (5) Individual breeding attempt.
A total of 4165 observations had complete records for each of the six response variables - see the companion paper for more details (Pettifor et al. MS; nests subject to experimental manipulation were excluded). The choice of these particular classifications is self-explanatory, with the possible exception of nest-box. Our aim in choosing this classification was to have a fine-grained measure of the specific environment in which individual breeding attempts occurred, although other spatial
9
scales could have been chosen. However, our reason for choosing the level of individual next-box was an expectation on our part that quite small-scale effects might be rather important in contributing to variation in life-history traits. For example, the suitability of a particular nestbox for rearing young might be determined by the phenology of trees growing in the immediate vicinity of the box. Tits generally forage for food for their young quite close to the nest-site (90% of foraging within 45m of the nest: Naef-Daenzer & Keller 1999), and individual trees often show highly repeatable phonologies between years (Mopper et al. 2000). In general there has long been an expectation that ‘territory quality’ effects may be important in explaining variation between individuals in breeding success. As we had no information about the exact boundaries of territories in this study, we chose nest-box as likely to represent roughly the same information. It is likely, of course, that there are other environmental effects that are not captured by our classification. For example, we may expect individual nest-boxes that are close to one another to share more similar environments than those that are far apart. At present, this source of potential covariance between characters is not explored by our analyses, but determining the spatial scale which results in environmentally-induced covariances between traits is beyond the scope of this study.
Statistical Analysis
In the companion paper (Pettifor et al. MS), we used Markov chain Monte Carlo (MCMC) estimation of cross-classified multivariate models to quantify the variance present in life-history traits of known pairs of great tits Parus major, into that attributable to five separate random effects. In these data, the individual observations
10
consist of six responses (clutch-size, lay-date, nestling mass, successful recruitment per nest and parental [mother and father] annual survival) for each individual breeding attempt. Each of these breeding attempts is nested within four separate higher classifications (male parent identity (i.d.), female parent i.d., nestbox i.d. and year) which do not themselves exhibit any nesting structure, resulting in a four-way crossclassified structure at level 2, alongside the level 1 residual error.
We use a standard multivariate normal distribution, resulting in the following model:
( 2) ( 3) ( 4) ( 5) yi = β + u male ( i ) + u female ( i ) + u nestbox ( i ) + u year ( i ) + ei ( 2) ( 3) u male ( i ) ~ MVN (0, Ω u ( 2 ) ), u female ( i ) ~ MVN (0, Ω u ( 3) ), ( 4) ( 5) u nestbox ( i ) ~ MVN (0, Ω u ( 4 ) ), u year ( i ) ~ MVN (0, Ω u ( 5 ) ), ei ~ MVN (0, Ω e )
where yi is a vector of six responses, as are β, and the four sets of higher-level random-effects (u(2) ... u(5)) and an individual error (residual) term, ei. Details of this model are given in Pettifor et al. (submitted), including the use of latent variables for the binomially distributed data, which through the probit link results in a normal distribution for the latent variables (see Browne 2002). We use MCMC algorithms for fitting these models (Browne et al. 2001), and firstly constructed prior distributions for the unknown parameters. This was achieved by calculating the variances of the six responses and dividing these variances by approximately 5, i.e. assuming a priori that the variance is evenly split between the 5 classifications (see Pettifor et al. MS). We then used these values as prior estimates for the variance terms and assumed a priori that the covariance terms were all zero. This results in the same prior for each of the four higher-level variance matrices. We assumed uniform priors for the fixed effects, β, and the unconstrained elements of the residual variance matrix, Ωe.
11
Having constrained the variances of the binary response variables at level 1 to equal 1.0 (i.e. the diagonal cell values of the residual variance matrix Ωe), we are able to use MCMC sampling to fit the model (implemented in a beta version of the MLwiN software package – Rasbash et al. 2000; Browne 2002). The MCMC algorithm works by first splitting the unknown parameters into several sets; in the case of our model we have 5 variance matrices, 4 sets of higher level residuals and 1 set of fixed effects making 10 sets in total. We allocate ‘starting values’ for all the parameters and then consider each of the ten sets of unknown parameters in turn assuming that our current values for all the other parameters are correct. We are able to then calculate the conditional posterior distribution of each set of unknown parameters and take a random draw from this conditional posterior distribution. This random updating procedure is repeated for each of the 10 sets and once all parameters have been updated we repeat the same procedure many times over to produce chains of parameter estimates. After discarding a suitable ‘burn-in’ period where we allow the chains to converge to the underlying posterior distributions we subsequently have a sample of draws from each parameter’s posterior distribution that we can use for statistical inference of the model.
In reality in our model we also include latent variables for the binary responses in the model which can be treated as an additional set of unknown parameters making 11 sets in total. Full details of the MCMC algorithm will be given in Browne et al. (in preparation). Models were run on both the raw data and with the continuous traits standardised to zero mean and unit variance prior to analysis, with the phenotypic correlations subsequently calculated as
12
r ( x, y ) =
CoV ( x, y ) Var ( x, x) × Var ( y, y )
or as CoV ( x, y ) (1.0) × (1.0)
for the raw and standardised values respectively. Note that the correlations and covariances are equivalent with standardised data.
Results
Single-level covariances As a first step we investigated the simple covariances between the different traits that we have analysed here (Table 1; Fig 2a) – in other words, we ignored the multilevel structure within the data, and simply determined the gross correlations between the life-history traits using a single-level model. These phenotypic correlations show a fairly typical pattern for these traits in wild bird populations (e.g. Stearns 1992). While the covariances are generally quite low (absolute values do not exceed 0.29), the majority (13/15) achieve individual statistical significance. We found relatively strong negative covariance between clutch size and laying date, and between laying date and the probability of successful recruitment, but strong positive covariance between nestling mass and the probability of successful recruitment, and between clutch size and the probability of successful recruitment (Table 1; Fig. 2a). These inter-relationships between traits are commonly found in populations of temperate-
13
zone breeding birds: birds that breed early lay larger clutches, and large, early, clutches are more likely to be successful in producing surviving nestlings, as are broods with heavier nestlings than average.
More interesting single-level covariances can be seen between maternal survival and what might be taken as measures of reproductive investment. Females that laid larger clutches, and that laid earlier in the season, were in both cases significantly less likely to be recaptured in the following year (Table 1; Fig. 2a), although both covariances are relatively weak. These observations might be taken to indicate evidence of costs of laying large clutches and breeding early. However, in contrast, females that produced heavier broods were more likely to survive to the next year, and the subsequent survival of both sexes of parents was positively related to the success of the current breeding attempt in producing recruiting offspring. Since the production of heavier offspring, or offspring with a higher chance of surviving to reproduce can be thought of as requiring a transfer of reproductive value from parents to offspring, these results are of the opposite sign to those that would be expected if all individuals were identical in terms of their resources.
Partitioning of covariance at different levels: general results The general patterns of covariance across the different classifications in our analysis are shown in Fig 2b-f, and in Appendix 1. In general, most of the covariances attributed to the between year and nestbox classifications were not significantly different from zero, although the confidence intervals are rather broad in the case of year. Of the four covariances that were statistically different from zero for the year classification, three involved covariances between estimates of either adult or juvenile
14
survival to the following year. These positive covariances might reflect two processes: (i) the effect of annual variation in success in capturing adults, since this would affect the survival rate of both parents and offspring similarly, and (ii) environmental differences between years (e.g. beech mast crop, winter weather) affecting both adult and juvenile survival. The other significant covariance due to the effect of differences between years was between clutch size and the probability of successful recruitment of offspring. Across years, larger clutches were associated with higher recruitment of offspring from those clutches. This positive covariance might represent the influence of density-dependent adjustment of clutch size: clutch sizes are larger during years of low population density, which also allows high recruitment of juveniles in the following year due to more territory vacancies.
At the classification of the individual nest-box there was again little evidence of significant covariance between characters; in fact only 3/15 estimates reached statistical significance (Appendix 1). Two of these cases were between laying date and clutch size, and between laying date and the probability of successful recruitment; both were negative. Hence, this suggests that part of the covariance between laying date and clutch size in the single-level analysis is due to specific effects of territories: some territories are associated with later breeding and smaller clutch sizes. Some territories are also associated with higher recruitment and earlier breeding. This suggests that the relationship between breeding date and recruitment success can partly be attributed to differences between territories.
Differences in patterns of covariance at different levels
15
We attempted to adjust for the differing degree of statistical confidence in the covariances estimated among the different classifications in the analysis by asking what the correlations were between the estimated mean covariances at the different levels (Table 2). This showed that the patterns of covariance detected due to differences among years, nest-boxes, and observations were all rather similar to each other, and to the covariance at the gross phenotypic level (r between 0.588 and 0.778). These three classifications (year, nest-box, observation) might all be considered to be aspects of the environment experienced by great tits (though operating at different spatial and temporal scales). Hence, this analysis suggests that different environmental scales have rather similar effects on the covariances between traits, and that their overall effect is detectable at the level of the raw phenotypic correlations between traits.
A different pattern was observed when the covariances at the level of individual male and female were correlated with those at the other levels (Table 2). Here there was little evidence of similarity in the covariance among different traits, suggesting that the processes affecting covariance among traits at the level of individuals are quite different from those at the level of environmental influences. In the case of males, the lack of concordance is not surprising, since there was very little evidence that differences between males contribute to the covariance between traits (or to their variance: Pettifor et al. MS). However, there were several significant covariances at the level of individual female; similarly, reasonable amounts of the variance in these traits could be partitioned to differences between individual females (Pettifor et al. MS).
16
Antagonistic patterns of covariance In addition to the cases described above, there were several cases where the covariance was of opposite sign at different levels; these are summarised in Table 3. For example, there was significant positive covariance between clutch size and female survival at the between female classification (Fig 2e, Appendix 1), but significant negative covariance between clutch size and female survival at the lowest level (Fig 2f, Appendix 1); the covariance between these traits in the single level analysis was weakly (but significantly) negative. Hence, when individual females are considered, laying a large clutch is associated with elevated survival, while at the level of individual nesting attempts laying a large clutch is associated with reduced survival. These effects will tend to cancel each other when the covariance between characters is assessed for all of the data combined.
Similarly antagonistic covariances (i.e. significant covariances of opposite sign) were seen for several other combinations of traits (Table 3). Nestling mass and laying date were negatively related at the level of observation, but positively related at the level of individual females (weakly negative in the single-level analysis). In contrast, laying date and female survival were positively related at the level of observation, but strongly negatively related at the level of individual females; again, the single-level covariance agreed with that at the level of observation.
Discussion
By partitioning the covariance among a series of life-history traits to a number of different sources, we detected several interesting patterns, which provide significant
17
insights into the relationships between life-history traits in this population. First, while the simple phenotypic correlations between traits exhibited some familiar patterns (for example, higher success of early breeding females which laid large clutches, and which produced heavy nestlings), these patterns were not present for all of the classifications across which we partitioned the data. In general, the patterns of covariance at levels that could reflect the action of environmental factors were rather similar to those seen in the single level unpartitioned phenotypic data. In contrast, the pattern of covariance among traits between individual males and females was, for some key combination of traits, quite different from that in the unpartitioned data. While there was no evidence of effects of males on covariance among these lifehistory traits, there were some strong covariances due to the effects of individual females. Perhaps most interesting was the existence of antagonistic patterns of covariance at different levels of the analysis. These all took a rather similar form: pairs of traits were related in the opposite direction when differences between individual females were considered relative to the level of individual breeding attempts (i.e. within female differences), and to their relationship in the unpartitioned phenotypic data. We discuss some implications of these results below.
Environmental effects on life-history covariances Although we found little evidence of significant covariance among life-history traits at two of the three different environmental classifications (year and nest-box), this conclusion is tempered by large confidence intervals in the case of year. When we compared the estimated covariances among classifications irrespective of their statistical significance, rather similar patterns of covariance were found to result from the effects of differences between years, nest-boxes and observations. In turn, these
18
patterns of covariance were rather similar to those found in the single-level analyses (i.e. the overall phenotypic correlations). Our interpretation of these patterns is that a substantial part of the general pattern of covariance among these life-history traits results from the influence of the environment.
Year, and nest-box clearly represent two kinds of environmental variable, although with rather differing expected pathways by which they could affect life-history traits in these birds. Many studies have demonstrated the effects of similar sorts of environmental variable on the variance among life-history traits (reviewed in Newton 1998). In the present population, previous work suggests that important differences among years are in: (i) spring temperature (McCleery & Perrins 1998), with birds laying earlier clutches in warmer springs; (ii) the extent of the previous autumn’s beech mast crop (Lack 1966; Perrins 1966) and (iii) the population density of both great tits and their congener, the blue tit Parus caeruleus, with which they compete for breeding sites (Minot & Perrins 1986). There is also evidence of important spatial effects on life-history traits. For example, van der Jeugd & McCleery (2002) showed, for this population, that the resemblance between female great tits and their offspring is higher if both individuals nest relatively close together within the study plot.
The pattern of covariance among traits at the level of observation was also similar to that at the level of nest-box and year; it is likely that this reflects a third source of environmental variation. For example, changes in vegetation structure over time, stochastic variation in local phenology of trees, presence of competitors, are all factors that might influence the life-history traits analysed at the level of each
19
individual breeding attempt, and the influence of these characters will be captured at the ‘observation’ level (see Pettifor et al. MS for further discussion).
Influences of males and females on life-history covariances Variation between individual parents is important for the pattern of covariance of some characters, but statistical significance was established only in the case of females. This pattern is very similar to the case for the analyses of variances in these life-history traits (Pettifor et al. MS), where males only influenced relative nestling mass (which may be due to males contributing genes to offspring that determine mass and or size, or to consistent differences among males in the rate at which they provision their offspring). As for the analyses partitioning variance in these lifehistory traits to different levels, there are potential mechanisms by which males could influence the covariance between pairs of life-history traits that might, at first sight, appear to be obviously determined by the female. For example, if territories differ in quality, males compete to possess territories of high quality, males differ in their ability to sequester high quality territories, and variation in habitat quality affects the optimal combination of pairs of life-history traits, then males might have a direct influence on the covariance between pairs of characters. Alternatively, a number of experimental studies, including of birds, suggest that females adjust their reproductive investment in response to the perceived quality of their mate (reviewed in Sheldon 2000), for example by breeding earlier, laying larger clutches, or providing more parental care to offspring. Such differential allocation might influence the covariance between life-history traits. Our analyses provide no evidence that either process is important in this population.
20
There are several potential sources of covariance at the level of females. For example, genetic covariance between pairs of life-history traits (e.g. clutch size and laying date) will be detected as covariance due to differences between females. In addition, however, sources of individual variation in allocation to life-history characters will also be captured by the between individual female term. In general, we found evidence to suggest that variation in females is an important determinant in the pattern of covariance of life-history traits.
Detecting individual variation and life-history trade-offs We found several cases where the covariance between pairs of life-history traits differed in sign at different levels of the analysis. The general pattern was that the sign of the covariance at the level of individual females was opposite to that at levels that capture variation in the environment (year, nest-box and particularly individual observation). For example, annual parental survival and clutch size covaried positively at the level of females, but negatively at the level of observation (and also weakly negatively in the single-level analyses). Our interpretation of these antagonistic covariances is that partitioning the covariance among these traits at different levels allows us to detect different processes operating. High female survival associated with laying a large, early clutch, when other sources of covariance between these traits are held constant may reflect detection of variation in condition, or quality, across females. In contrast, at the level of observation, we detect the cost of laying a large, early, clutch in terms of reduced female survival. It is notable that while the covariance between survival and clutch size was relatively weak in the single-level analyses (-0.067), the ‘antagonistic’ covariances are much stronger (+0.45 across individual females; -0.20 at the level of observation). Hence, it appears that variation
21
among females exerts a substantial influence on the way in which survival and clutch size, and survival and breeding time, covary.
Many studies have attempted to reveal phenotypic trade-offs between current and future reproduction by manipulating clutch or brood size in birds, and analysing subsequent survival of females; there are relatively few cases in which such transgenerational trade-offs have been detected due to experimental manipulations (Møller & Lindén 1989; Roff 2002). Our analyses suggest that such trade-offs do occur, and can be detected, because when we analyse the relationship between clutch size and survival at the level of individual nesting attempts (i.e. controlling for major environmental sources of variation and, more importantly, for variation among individual females) we detect quite strong negative covariance between these traits. Given the strong covariance in the opposite direction at the level of females, and also fluctuating survival probabilities between years (Pettifor 1993a,b), and the confounding of parental survival with dispersal (Doligez et al. 2002) any effect of experimental manipulations of individual effort may be very hard to detect. In addition, the sample sizes available for the type of analysis we have performed are an order of magnitude larger than the most extensive experimental studies. These results are, therefore, what we would expect if within this population individual females were optimising reproductive decisions in order to maximise their fitness (Pettifor et al. 1988; 2001).
Conclusions Covariance, at both phenotypic and genetic levels, among pairs of life-history traits is important in determining the joint evolutionary trajectories of these traits (Roff 2002).
22
However, understanding why particular pairs of traits show particular patterns of covariance is difficult, but fundamental to our understanding of life-history variation within and across species. We have shown here how an ability to partition the covariance among traits to its different sources offers some interesting insights into the causes of the patterns of covariance. In some instances, these analyses could be used to suggest experimental manipulations that would provide tests of the underlying causal structure. In other cases, experiments will be very difficult, and detailed analyses of large, already-existing, data sets may provide the most fruitful means of making further progress in understanding.
Acknowledgements
BCS is a Royal Society University Research Fellow.
23
Literature cited
Bernardo, J. 1996. The particular maternal pattern of propagule size, especially egg size: patterns, models, quality of evidence and interpretation. Amer. Zool. 36, 216236. Bérubé, C.H., Festa-Bianchet, M. & Jorgenson, J.T. 1999. Individual differences, longevity, and reproductive senescence in bighorn ewes. Ecology 80, 2555-2565. Browne, W.J. 2002. MCMC Estimation in MlwiN. London, Institute of Education. Browne, W.J., Goldstein, H. & Rasbash, J. (2001) Multiple membership multiple classification (MMMC) models. Statistical Modelling 1, 103-124. Coulson, T.N., Catchpole, E.A., Albon, S.D. Morgan, B.J.T., Pemberton, J.M., Clutton-Brock, T.H., Crawley, M.J. & Grenfell, B.T. 2001. Age, sex, density, winter-weather, and population crashes in Soay sheep. Science 292, 1528-1531. Daan, S., Dijkstra, C., Drent, R.H. & Meijer, T. 1989. Food supply and the annual timing of avian reproduction. Pp. 392-407 in: Acta XIX Congressus Internationalis Ornithologici, Ottawa, 1986 (H. Ouellet, ed.). Doligez, B., Clobert, J., Pettifor, R.A., Rowcliffe, J.M., Gustafsson, L., Perrins, C.M. & McCleery, R.H. 2002. Costs of reproduction: assessing responses to clutch/brood size manipulation on life-history and behavioural traits using multistate capture-recapture models. J. Appl. Stats. 29, 407-423. Glazier, D.S. 1999. Trade-offs between reproductive and somatic (storage) investment in animals: a comparative test of the van Noordwijk & de Jong model. Evol. Ecol. 13, 539-555.
Grant, P.R. & Grant, B.R. 2002. Unpredictable evolution in a 30-year study of Darwin’s finches. Science 296, 707-711.
25
Keller, L.F, Arcese, P., Smith, J.N.M., Hochachka, P.W. & Stearns, S.C. 1994. Selection against inbred song sparrows during a natural population bottleneck. Nature 372, 356-357. Kingsolver, J.G., H.E. Hoekstra, J.M. Hoekstra, D. Berrigan, S.N. Vignieri, C.E. Hill, A. Hoang, P. Gibert, & P. Beerli, 2001. The strength of phenotypic selection in natural populations. Amer. Nat. 157, 245-261. Kruuk, L.E.B., Clutton-Brock, T.H., Albon, S.D., Pemberton, J.M. & Guinness, F.E. 1999. Population density affects sex ratio variation in red deer. Nature 399, 459461. Lack, D. 1954. The Natural Regulation of Animal Numbers. Clarendon Press, Oxford. Lack, D. 1966. Population Studies of Birds. Clarendon Press, Oxford. Lessells, C.M. 1991. The evolution of life histories. Pp 33-68. In: Krebs, J.R. & N.B. Davies. (Eds). Behavioural Ecology – An Evolutionary Approach. 3rd Edn. Blackwells, Oxford. Lindén, M. & Møller, A.P. 1989 Trends Ecol. Evol. 4, 367-371. McCleery, R.H. & C.M. Perrins, 1998 ... temperature and egg-laying trends. Nature 391, 30-31.
Merilä, J., L.E.B. Kruuk and B.C. Sheldon. 2001. Cryptic evolution in a wild bird population. Nature 412: 76-79. Minot, E.O. & Perrins, C.M. 1986. Intraspecific interference competition – nest sites for blue tits and great tits. J. Anim. Ecol. 55, 331-350. Mopper, S., Stiling, P., Landau, K., Simberloff, D. & van Zandt, P. 2000. Spatiotemporal variation in leafminer population structure and adaptation to individual oak trees. Ecology 81, 1577-1587. 26
Naef-Daenzer, B. & Keller, L.F. 1999. The foraging performance of great and blue tits (Parus major and P. caeruleus) in relation to caterpillar development, and its consequences for nestling growth and fledging weight. J. Anim. Ecol 68, 708-718. Newton, I. 1998. Population limitation in birds. Academic Press, San Diego, Calfornia. Perrins, C.M. 1966. The effect of beech crops on great tit populations and movements. British Birds 59, 417-432. Perrins, C.M. 1970. The timing of birds’ breeding seasons. Ibis 112, 242-255. Pettifor, R.A. 1993a. Brood manipulation experiments. I. The number of offspring surviving per nest in blue tits (Parus caeruleus). J. Anim. Ecol. 62, 131-144. Pettifor, R.A. 1993b. Brood manipulation experiments. II. A cost of reproduction in blue tits (Parus caeruleus)? J. Anim. Ecol. 62, 145-159. Pettifor, R. A., Perrins, C.M. & McCleery, R.H. 1988. Variation in clutch size in great tits: evidence for the individual optimisation hypothesis. Nature 336, 160-162. Pettifor, R. A., Perrins, C.M. & McCleery, R.H. 2001. The individual optimization of fitness: variation in reproductive output, including clutch size, mean nestling mass and offspring recruitment, in manipulated broods of great tits Parus major. J. Anim. Ecol. 70, 62-79. Pettifor, R.A., Sheldon, B.C., Browne, W., Rasbash, J. & McCleery, R.H. MS. Partitioning of phenotypic covariance among life-history traits in the great tit Parus major. Submitted MS (companion to this MS). Price, T., M. Kirkpatrick and S.J. Arnold. 1988. Directional selection and the evolution of breeding date in birds. Science 240, 798-799.
27
Rasbash, J., Browne, W.J., Goldstein, H., et al. 2000. A User’s guide to MlwiN, 2nd Edition. London, Institute of Education. Reid, J.M., Bignal, E.M., Bignal, S., McCracken, D.I. & Monaghan, P. 2003. Environmental variability, life-history covariation and cohort effects in the redbilled chough Pyrrhocorax pyrrhocorax. J. Anim. Ecol. 72, 36-46. Reznick, D., Nunney, L. & Tessier, A. 2000. Big houses, big cars, superfleas and the costs of reproduction. Trends Ecol. Evol. 15, 421-425. Roff, D.A. 2002. Life History Evolution. Sinauer, Sunderland, Mass. Sheldon, B.C. 2000. Differential allocation: tests, mechanisms and implications. Trends Ecol. Evol. 15, 397-402. Sheldon, B.C., Kruuk, L.E.B. & Merilä, J. 2003. Natural selection and inheritance of breeding time and clutch size in the collared flycatcher. Evolution 57, 406-420. Sinervo, B. & Lively, C.M. 1996. The rock-paper-scissors game and the evolution of alternative male strategies. Nature 380, 240-243. Stearns, S.C. 1992. The Evolution of Life Histories. Oxford University Press. Tinbergen, J.M., van Balen, J.H. & van Eck, H.M. 1985. Density-dependent survival in an isolated great tit population: Kluyver’s data reanalysed. Ardea 73, 38-48. van der Jeugd, H.P. & McCleery, R.H. 2002. Effects of spatial autocorrelation, natal philopatry, and phenotypic plasticity on the heritability of laying date. J. evol. Biol. 15, 380-387.
Van Noordwijk, A.J. & de Jong, G. 1986. Acquisition and allocation of resources: their influence on variation in life-history tactics. Amer. Nat. 128: 137-142.
28
Veen, T., Borge, T., Griffith, S.C., Sætre, G.-P., Bures, S., Gustafsson, L. & Sheldon, B.C. 2001. Hybridization and adaptive mate choice in flycatchers. Nature 411, 4550.
Williams, G. C. (1966) Natural selection, the costs of reproduction and a refinement of Lack's principle. American Naturalist, 100, 687 - 690.
29
Table 1 Covariances among life-history traits based on single-level models using
standardised data; values in parentheses are 95% confidence intervals; underlined covariances are significantly different from zero.
Trait
Clutch Size
Laying Date
Mean Nestling Mass
Successful
Male Survival
Recruitment
Laying Date
-0.291 (-0.330 – -0.254)
Mean Nestl. Mass Successful Recruitment Male Surv.
Female Surv.
-0.105
-0.040
(-0.143 – -0.068)
(-0.078 – -0.003)
0.186
-0.184
0.146
(0.140 – 0.232)
(-0.229 – -0.138)
(0.099 – 0.192)
-0.024
0.065
0.030
0.058
(-0.070 – 0.023)
(0.019 – 0.111)
(-0.016 – 0.076)
(0.000 – 0.115)
-0.067
0.067
0.049
0.076
-0.060
(-0.113 – -0.020)
(0.021 – 0.113)
(0.003 – 0.100)
(0.018 – 0.133)
(-0.118 – -0.002)
30
Table 2 Correlations between covariances estimated for each classification from 105
iterations of the five-level cross-classified multivariate MCMC model and a single level MCMC model, with the trait values standardised to zero mean and unit variance. Values in bold with an asterisk are significantly different from zero.
Level
year
year
1.000
nestbox
0.778*
male
-0.045
nestbox
male
female
observation
Singlelevel
1.000 0.307
1.000
female
0.570*
0.474
0.016
1.000
observation
0.622*
0.588*
-0.209
-0.025
1.000
Single-level
0.693*
0.658*
-0.220
0.355
0.730*
1.000
31
Table 3 Pairs of antagonistic covariances at different classifications
Pair of traits
Classification
Estimated
95% CI
covariance (1) Laydate & nestling mass Female
0.222
0.02 – 0.041
Observation
-0.188
-0.25 - -0.13
Female
0.447
0.264 – 0.614
Observation
-0.199
-0.271 - -0.125
Female
-0.695
-0.806 - -0.560
Observation
0.114
0.052 – 0.188
(2) Clutch size and female survival
(3) Laydate and female survival
32
Appendix 1. Phenotypic covariances obtained from the multivariate cross-classified models of the six life-history traits in great tits. The traits were standardised to zero mean and unit variance before analysis; values are means (95% confidence intervals). Estimates that are significantly different from zero are marked with an asterisk. Trait Clutch-size
Random Effect Year
Clutch-size
Nbox
Clutch-size
Male
Clutch-size
Female
Clutch-size
Obs
Lay-date
Year
Lay-date
Nbox
Lay-date
Male
Lay-date
Female
Lay-date
Obs
Mean Nestl. Mass Mean Nestl. Mass Mean Nestl. Mass Mean Nestl. Mass Mean Nestl. Mass
Year Nbox Male Female Obs
Successful Recruitment Successful Recruitment Successful Recruitment Successful Recruitment Successful Recruitment
Year
Male Survival Male Survival Male Survival Male Survival Male Survival
Year
Nbox Male Female Obs
Nbox Male Female Obs
Lay-date -0.317 (-0.589 - 0.026) -0.455 (-0.607 - -0.267)* -0.158 (-0.427 - 0.104) -0.443 (-0.547 - -0.339)* -0.21 (-0.280 - -0.155)*
Mean Nestl. Mass 0.218 (-0.145 - 0.529) 0.112 (-0.154 - 0.365) 0.090 (-0.280 - 0.376) -0.319 (-0.461 - -0.174)* -0.127 (-0.196 - -0.055)*
Successful Recruitment 0.592 (0.307 - 0.781)* 0.236 (-0.070 - 0.500) -0.135 (-0.464 - 0.280) 0.355 (0.127 - 0.591)* 0.071 (-0.009 - 0.147)
Male Survival 0.068 (-0.309 - 0.431) 0.305 (0.027 - 0.545)* 0.240 (-0.056 - 0.514) 0.065 (-0.162 - 0.306) -0.057 (-0.121 - 0.012)
Female Survival 0.019 (-0.349 - 0.386) 0.075 (-0.209 - 0.367) -0.025 (-0.547 - 0.354) 0.447 (0.264 - 0.614)* -0.199 (-0.271 - -0.125)*
0.135 (-0.214 - 0.461) -0.129 (-0.357 - 0.118) -0.056 (-0.328 - 0.225) 0.222 (0.022 - 0.407)* -0.188 (-0.249 - -0.127)*
-0.231 (-0.533 - 0.125) -0.394 (-0.596 - -0.148)* 0.187 (-0.132 - 0.516) -0.495 (-0.687 - -0.264)* -0.194 (-0.267 - -0.119)*
-0.013 (-0.384 - 0.361) -0.215 (-0.472 - 0.071) -0.333 (-0.546 - 0.003) -0.149 (-0.425 - 0.200) 0.054 (-0.015 - 0.118)
0.071 (-0.303 - 0.420) 0.040 (-0.225 - 0.303) -0.076 (-0.367 - 0.295) -0.695 (-0.806 - -0.560)* 0.114 (0.052 - 0.188)*
0.298 (-0.076 - 0.595) 0.182 (-0.133 - 0.440) -0.125 (-0.454 - 0.230) -0.230 (-0.515 - 0.112) 0.236 (0.152 - 0.319)*
0.033 (-0.359 - 0.416) 0.085 (-0.231 - 0.398) 0.039 (-0.252 - 0.349) -0.202 (-0.504 - 0.217) 0.060 (-0.011 - 0.122)
0.140 (-0.260 - 0.493) 0.174 (-0.131 - 0.459) 0.188 (-0.261 - 0.454) -0.071 (-0.330 - 0.184) 0.0419 (-0.028 - 0.109)
0.409 (0.023 - 0.683)* 0.102 (-0.237 - 0.417) -0.061 (-0.468 - 0.358) 0.235 (-0.273 - 0.548) 0.020 (-0.055 - 0.096)
0.374 (-0.009 - 0.657) 0.159 (-0.215 - 0.476) 0.078 (-0.308 - 0.473) 0.387 (0.016 - 0.641)* 0.024 (-0.052 - 0.101) 0.501 (0.146 - 0.737)* 0.238 (-0.116 - 0.516) 0.013 (-0.298 - 0.332) 0.052 (-0.287 - 0.416) 0.203 (0.139 - 0.266)*
33
Figure Legends
Figure 1: Illustration of partitioning among levels of covariance between two phenotypic traits. (a) Clutch Size and Laying Date: Two models exist to explain a decline in clutch size with laying date: (i) a causal effect of the environment, where declining prospects for young produced late in the season reduce the optimal clutch size, and (ii), a female condition effect, where females that are in good condition are able to breed earliest, and to lay the largest clutch sizes, producing a negative correlation between clutch size and laying date. The two models make different predictions about how the two phenotypic traits will covary at different levels. If the covariance is due to a causal effect of the environment, then negative covariance should be seen at the level of territory (for each territory, optimal clutch size declines as date progresses), and individual observation (stochastic processes will influence each individual breeding attempt, delaying or advancing it, and hence changing the optimal clutch size). In contrast, variation among females should not affect the covariance between clutch size and date, because the covariance results from the action of the environment (each female is assumed to experience this in the same way). In contrast, if the phenotypic covariance is due to the effect of variation in the condition of individual females, variation in the environment should have little effect on the covariance between clutch size and laying date, and negative covariance should exist at the level of females. Two different scenarios could be constructed for the expectation of the covariance at the level of individual breeding attempt under this hypothesis. If variation in female condition is largely determined early in life, then annual differences within females will be unimportant and there will be little or no covariance at the level of observation. Alternatively, if there are large fluctuations in
34
condition within females between years, there may be (b) Survival and Fecundity: The simple expectation from life-history theory is that increased fecundity will result in reduced survival. However, at the level of the raw phenotypic correlation, other patterns are often observed; in this case no relationship between the two characters. This absence of effect can be explained if individuals differ in the resources they have available to invest into these two traits. However, within individuals, we would still expect high levels of investment to be associated with reduced survival. Partitioning covariance between and within females allows the detection of both processes.
Figure 2: Correlations between the six life-history traits derived from the variancecovariance matrices of the (a) single-level model, and (b-f) the separate classifications of the multi-level MCMC multivariate model.
35
t
c
h
Figure 1
b
u C
L
y
i
n
a
t
e
F
c
u
n
(i) Female
Survival
Clutch Size
Clutch Size
Clutch Size
Clutch Size
Laying date
e
partitioning of covariance at different levels
Laying date
Laying date
(iii) Observation
d
Laying date
Laying date
(ii) Female
g
(2) Female condition effect
[partitioning of covariance at different levels]
Clutch Size
(i) Territory
a
Clutch Size
(1) Causal environmental effect
Raw phenotypic correlation
Survival
l
Raw phenotypic correlation
Fecundity (ii) Observation
Laying date
Survival
a
Fecundity
36
d
i
t
y
1.0 cs*ld cs*nm cs*nsucc cs*msurv cs*fsurv ld*nm ld*nsucc ld*msurv ld*fsurv nm*nsucc nm*msurv nm*fsurv nsucc*msurv nsucc*fsurv msurv*fsurv
cs*ld cs*nm cs*nsucc cs*msurv cs*fsurv ld*nm ld*nsucc ld*msurv ld*fsurv nm*nsucc nm*msurv nm*fsurv nsucc*msurv nsucc*fsurv msurv*fsurv
-1.0
cs*ld cs*nm cs*nsucc cs*msurv cs*fsurv ld*nm ld*nsucc ld*msurv ld*fsurv nm*nsucc nm*msurv nm*fsurv nsucc*msurv nsucc*fsurv msurv*fsurv
1.0
a)
0.5 0.5
0.0 0.0
-0.5 -0.5
c) 1.0
0.5 0.5
0.0 0.0
-0.5
-1.0
e) 1.0
0.5 0.5
0.0 0.0
-0.5
Female
-1.0
Trait
cs*ld cs*nm cs*nsucc cs*msurv cs*fsurv ld*nm ld*nsucc ld*msurv ld*fsurv nm*nsucc nm*msurv nm*fsurv nsucc*msurv nsucc*fsurv msurv*fsurv
cs*ld cs*nm cs*nsucc cs*msurv cs*fsurv ld*nm ld*nsucc ld*msurv ld*fsurv nm*nsucc nm*msurv nm*fsurv nsucc*msurv nsucc*fsurv msurv*fsurv
1.0
cs*ld cs*nm cs*nsucc cs*msurv cs*fsurv ld*nm ld*nsucc ld*msurv ld*fsurv nm*nsucc nm*msurv nm*fsurv nsucc*msurv nsucc*fsurv msurv*fsurv
Correlation (mean +/- 95% ci)
Figure 2
1.0 b)
Single level -1.0
Year
d)
Nestbox -0.5
-1.0
Male
f)
-0.5
-1.0
Observation
37
