Phenotypic plasticity is an important mechanism via which populations can respond to changing environmental conditions, but we know very little about how natural populations vary with respect to plasticity. Here we use random-regression animal models to understand the multivariate phenotypic and genetic patterns of plasticity variation in two key life-history traits, laying date and clutch size, using data from long-term studies of great tits in The Netherlands (Hoge Veluwe [HV]) and UK (Wytham Woods [WW]). We show that, while population-level responses of laying date and clutch size to temperature were similar in the two populations, between-individual variation in plasticity differed markedly. Both populations showed significant variation in phenotypic plasticity (IxE) for laying date, but IxE was significantly higher in HV than in WW. There were no significant genotype-by-environment interactions (GxE) for laying date, yet differences in GxE were marginally nonsignificant between HV and WW. For clutch size, we only found significant IxE and GxE in WW but no significant difference between populations. From a multivariate perspective, plasticity in laying date was not correlated with plasticity in clutch size in either population. Our results suggest that generalizations about the form and cause of any response to changing environmental conditions across populations may be difficult.
An important series of questions in evolutionary biology is how well populations are adapted to the environment they experience, whether they can adapt if the environment changes and, if so, how rapidly. Recent global change in climatic conditions and the associated impact on the phenology and behavior of a wide variety of species (reviewed in Parmesan 2006) has caused an increased interest in these fundamental questions (e.g., Stenseth et al. 2002; Orr and Unckless 2008; Visser 2008). Although numerous empirical studies have revealed changes in average phenotype across changing environmental conditions for a wide variety of characters (e.g., for avian clutch size [CS] adjustment in relation to population density, see Both et al. 2000; for laying date (LD) in relation to increasing temperatures, see Dunn 2004), the causes behind such responses are rarely explored. One important mechanism by which individuals can adjust to changing environmental conditions is through phenotypic plasticity, which simply refers to a (genotype's) change in phenotypic expression across an environmental gradient (Scheiner 1993). Although phenotypic plasticity can be fundamental in allowing populations to deal with environmental change (Price et al. 2003; reviewed in Ghalambor et al. 2007; Lande 2009), we know relatively little about the extent to which plasticity varies between individuals in natural populations and whether such variation (if present) has a genetic component (Nussey et al. 2007). Such knowledge is important to determine how quickly natural populations may respond to environmental changes they might experience. In particular, it is of interest to know if variation in plasticity itself is heritable and so might have the potential to evolve under selection (Visser 2008).
Several recent studies of variation in plasticity in natural populations have focused on how breeding time (LD) of birds responds to changes in spring temperature and whether there is a genetic basis to this variation in plasticity (e.g., Nussey et al. 2005; Brommer et al. 2008; Charmantier et al. 2008). This interest is not surprising as it is particularly important to understand how life-history traits closely related to fitness, like timing of reproduction and/or number of young produced, will change with the changing environment. Separating the average population-level pattern into individual-level patterns can be achieved using longitudinal studies, where repeated measures of the same individuals under a range of environmental conditions are available, and a linear mixed model framework for data analysis (Nussey et al. 2007). Longitudinal studies also frequently facilitate the construction of a multigenerational pedigree (Pemberton 2008) and this pedigree information allows the application of quantitative genetic methods such as the animal model (Henderson 1950; Kruuk 2004) to separate the genetic and nongenetic components of variance in the traits under study. Similarly, we can partition variation in plasticity into its genetic and nongenetic component: for instance, a genetic basis to variation in plasticity (GxE interaction) would mean that plasticity itself is heritable (Nussey et al. 2007). An individual's change in phenotype across the environment is often termed its “reaction norm” which can be characterized by an intercept (elevation) and a slope (see Via et al. 1995 and Methods).
Importantly, the animal model is not restricted to the study of single traits, but can readily be extended to incorporate multiple traits (Kruuk 2004). For instance, a bivariate animal model allows us to partition variance in two traits as well as the covariance between them and we can thus estimate the genetic correlation between the two (or more) traits. This is important as adaptation is an inherently multivariate process (Lande and Arnold 1983; Blows 2007) and so knowledge about genetic constraints is crucial if we want to understand evolutionary change. Although the use of bivariate animal models to estimate genetic correlation between traits (both within and across sexes) in natural populations has increased (e.g., Jensen et al. 2003; Wilson et al. 2007; Garant et al. 2008; Robinson et al. 2009), to date, to our knowledge, studies of phenotypic plasticity in the wild have only concentrated on a single trait (e.g., Brommer et al. 2005; Nussey et al. 2005; Wilson et al. 2006; Brommer et al. 2008; Charmantier et al. 2008; but see Robinson et al. 2009). This is somewhat surprising as it is well known that genetic correlations between traits can constrain or speed up the rate of adaptation (Lande and Arnold 1983) and, similarly, between-trait correlations in plasticity also have the potential to speed up or delay adjustment to environmental changes. For instance, we know very little about the extent to which individuals in natural populations plastic for one trait are also plastic for other traits, i.e., if there is such a thing as a “generally plastic” genotypes, or what has been termed “phenotypic integration” (Schlichting 1986). Yet, if this was the case, it could allow rapid adjustment to changes in the environment.
Despite recent methodological advances in the field and the increasing number of studies demonstrating that phenotypic plasticity can be an important mechanism for adapting to changing environmental conditions (e.g., Reale et al. 2003; Charmantier et al. 2008), we know little about the generality of observed patterns. For example, two recent studies of phenotypic plasticity in two populations of great tits (Parus major) from the Hoge Veluwe (HV) in The Netherlands and Wytham Woods (WW) in the UK both reported population-level response, with average LD advancing with increasing spring temperatures (Nussey et al. 2005; Charmantier et al. 2008). However, the individual-level patterns were strikingly different. While the study of the Dutch population found large between-individual variation in the response to temperature, and also a genetic basis to this plasticity (Nussey et al. 2005), that of the UK population found no significant between-individual variation in the response, and also no genetic basis to the variation in plasticity (Charmantier et al. 2008). Direct comparison of the results from these two studies is, however, not straightforward because of differences both in the definition of the environment (mean temperature used in the Dutch study and the sum of daily maximum temperatures (warmth sum) in the UK study) and in the data structure (females who bred twice or more in the Dutch study and females who bred three times or more in the UK study).
Our aim in this study was to increase our understanding of phenotypic and genetic between-population variation in plasticity patterns by comparing data from the two long-term study populations of great tits at the HV, the Netherlands (van Balen 1973) and at WW, UK (Perrins 1965). Our goals were: first, to explore the multivariate patterns of plasticity for two key life-history traits closely linked to fitness, LD, and CS. These two traits often covary negatively (e.g., Sheldon et al. 2003) generating a clear a priori reason for examining the multivariate patterns of variation in plasticity and for comparing the multivariate reaction norm patterns between the two populations. Second, we wanted to eliminate some of the problems related to methodological issues when comparing studies on plasticity by directly comparing two populations of the same species using the same time series and same methodology.
Materials and Methods
STUDY SPECIES, POPULATIONS, AND DATA COLLECTION
Great tits are small (14–22 g) monogamous hole-breeding passerines occupying most of Europe as well as parts of Asia and North Africa (Gosler 1993). Data have been collected in the HV National Park, the Netherlands and in WW, Oxford, UK continuously since the early 1950s. However, because a storm damaged the study area in HV during winter 1972/73 and nestboxes were subsequently relocated, and because we wished to compare the two populations over the same time period, we only used the years from 1973 to 2006 for both populations. There is evidence to suggest that climate-change related impacts are only apparent in recent decades (e.g., McCleery and Perrins 1998), further justifying the restriction to the later period. Table 1 summarizes information about the two populations.
Table 1. Summary information about the two populations. Laying date (LD, day 1=1 April) and clutch size (CS): data are from 1973 to 2006 inclusive. Note that the sample sizes for the two traits are slightly different in the Wytham Woods population due to missing data.
Number of records
Number of individuals
In both areas nest boxes were visited at least once every week during the breeding season (April–June). The LD of the first egg of a female's clutch (LD) was calculated from the number of eggs found during the weekly checks, assuming that one egg was laid per day. Number of eggs in the nests was counted (CS) and when the young were 7–10 days old, the parents were caught on the nest using a spring trap. We excluded individual records of females who had their CS manipulated during egg-laying (i.e., before clutch completion) in the HV population (n= 138). For the WW population there were no such manipulations.
Laying dates are presented as the number of days after 31 March (day 1 = 1 April, day 31 = 1 May). We only used information on the first clutch for both populations, defined as any clutch started within 30 days of the first laid egg in the respective population in any given year. Replacement and second clutches (which comprise less than 3% of breeding attempts in Wytham (Charmantier et al. 2008) and are currently also rare (less than 5% of breeding attempts) in the HV population (Husby et al. 2009)) were excluded from the analysis. More details about the HV study population can be found in van Balen (1973) and about the WW population in Perrins (1965) and Perrins and McCleery (1989).
To test for plastic responses in CS and LD we used the population-specific local temperature records as a description of environmental conditions. We used a “sliding window” approach to decide on the climatic time window that best predicted the onset of mean LD for the two populations. We thus correlated the average temperature within periods of varying start date (beginning with 1st January), end date (30 April) and length (10-day intervals, ranging from a minimum of 10 days to a maximum of 120 days) to the mean LD in the population each year. The population-specific period with the highest R-squared value was then used for testing for plastic responses. Temperature data for the HV population were obtained from the De Bilt weather station of the Royal Dutch Meteorological Institute (KNMI, http://www.knmi.nl/klimatologie/daggegevens) and for the WW population from the Radcliffe Observatory, Oxford, UK (Charmantier et al. 2008). For both populations we used the daily average temperature ((minimum + maximum)/2). For the HV population the period 13 March–20 April was the best predictor for the onset of laying (R2= 0.656), whereas the equivalent period for the WW population was 15 February–25 April (R2= 0.669).
Following the framework outlined by Nussey et al. (2007), we first quantified the average population-level association between LD and CS for both populations in relation to the most informative temperature period for each population (see above).
INDIVIDUAL-LEVEL VARIATION IN PLASTICITY (TESTING FOR IxE)
By adopting a linear mixed effects model framework we can partition any population-level association into individual-specific changes to test whether individuals differ in their response to spring temperature. We thus used phenotypic information to estimate (1) the between-individual variation in average LD and CS (elevations of reaction norms), and (2) the between-individual variation in the response to environmental variation (slope of reaction norms), as well as (3) the covariance between elevation and slope for each trait.
GENETIC BASIS TO VARIATION IN PLASTICITY (TESTING FOR GxE)
To estimate the genetic basis of IxE variation, a pedigree was constructed for the two populations where all ringed females known to have bred were assigned to their social mother and father if these were known. In cases where brood manipulation experiments had been carried out and chicks had been moved between nests, we assigned the genetic parent rather than the social parent. If only one parent was known, we “dummy coded” the missing parent to preserve sibship information (note that we did not assign a phenotype to this parent). The rate of extra-pair paternity (EPP) has been estimated to be 14% in the WW population using two allozyme loci (Blakey 1994), but the rate is unknown in the HV population. The EPP rate is, however, generally found to be low (3–9%) in other populations of great tits (Verboven and Mateman 1997; Lubjuhn et al. 1999). EPP rates of less than 20% have been shown to have a negligible impact on heritability estimates given sufficient sample sizes (Charmantier and Reale 2005). The full pedigree for the HV population included 6907 individuals with 1271 dams and 1295 sires, whereas the full pedigree for the WW population included 11,117 individuals, with 3161 and 3298 dams and sires, respectively. However, because the full pedigree is not necessarily informative for the particular analysis carried out (Morrissey and Wilson, in press) we pruned each pedigree to contain only links that were informative for the available data used here. This reduced the HV pedigree to contain 2691 individuals with 936 maternities, 703 paternities, 309 full sibs and a mean maternal and paternal sibship size of 1.502 and 1.766, respectively. Similarly, the pruned WW pedigree contained a total of 6592 individuals with 3845 maternities, 3344 paternities, 1907 full sibs and a mean maternal and paternal sibship size of 1.784 and 1.968, respectively. A discussion of the benefits of reporting information from a pruned versus a full pedigree can be found in Morrissey and Wilson (in press).
Univariate random regression models
Phenotypic variation in LD and CS was partitioned using an “animal model” (Henderson 1950; Lynch and Walsh 1998; Kruuk 2004) to give between-individual phenotypic variation (VI); this variation was subsequently decomposed into its additive genetic (VA) and, based on repeated measures on individuals across multiple years, permanent environmental variance (VPE). To explore patterns of variation in plasticity for LD and CS, we first analyzed each trait separately using a univariate “random regression animal model” (RRAM). These models use covariance functions to estimate covariances between the regression coefficients (Meyer 1998) in an animal model framework (Lynch and Walsh 1998; Kruuk 2004). The individual breeding values can thus be modeled as linear (or higher order) functions along some continuous scale (the environmental variable, i.e., spring temperature in this case). Thus, LDs and CS records of individual i in each standardized annual temperature measurement were analyzed using Legendre polynomials (Kirkpatrick et al. 1990; Gilmour et al. 2006). Temperature measurements were standardized to be within the range −1 to +1, as Legendre polynomials are only defined within this range (e.g., Huisman et al. 2002), using the following equation: −1 + 2(temperature value – minimum temperature value)/(maximum temperature value – minimum temperature value). We only fitted polynomial functions (φ) of a zero and first order (n= 0 or n= 1) due to problems with model convergence, and thus considered linear reaction norms only; however, population-level responses to temperature are apparently linear (Fig. 1C,D). A first order function, φ(indi, n, T), applies a linear reaction norm model for individual-specific values across temperature (T) such that variances in elevation and slope of reaction norms are estimated, as well as the covariance between them (resulting in a 2×2 variance covariance matrix for each random effect).
Thus our model was:
where yi is the vector of the individual trait values (CS or LD) and X, Z1, Z2, and Z3 are the design and incidence matrices relating to the fixed effects and random effects of the additive genetic (ai), permanent environment (pei), and year (yri) observations, respectively. Fixed effects (bi vector) included age as a two level factor (first year breeder or older) to correct for the fact that LD generally advances with increasing age in great tits (e.g., Wilkin et al. 2006) and that CS is often larger in older females (Kluijver 1951; Perrins 1965). In analyses of CS (but not LD) we also fitted terms for population density as it has been shown previously in great tits (e.g., Both et al. 2000; Wilkin et al. 2006) that population density often has a negative effect on CS (but not LD). Population density was defined in both populations as the within-population sector-specific density in breeding pairs ha−1 and ranged from 0.04–2.05 (mean = 0.849) in the WW population and 0.2–1.88 (mean = 0.840) in the HV population. The use of this more local measure of density is justified by its correcting for sector-specific differences in the density of nest boxes, thus local variation in population density will be corrected for. Population-specific (see above) standardized spring temperature (T, on the range −1 to +1) was included as a fixed effect covariate to account for the population-level response in mean trait value. Year (yr vector) was included as a random effect to model variation among years not explained by spring temperature. φ(ai, n1, T) is the random regression function of order n1 of the additive genetic effect of individual i and similarly φ(pei, n2, T) is the random regression function of order n2 of the permanent environment effect. We included a permanent environment effect (pei vector) because of the repeated sampling of the same individuals (Kruuk 2004) and this also reduces inflation of estimates of the additive genetic variance due to environmental factors (Kruuk and Hadfield 2007). The error term (e vector) was partitioned into three decade specific (1973–1983, 1984–1994, 1995–2006) groups, thus allowing residual error variance to vary between decades. In general, using a heterogeneous error variance structure gave a substantially better fit compared to a model with homogenous error variance (HV; LD: χ22= 11.56, P= 0.003, CS: χ22= 19.78, P < 0.001, WW; LD: χ22= 26.34, P < 0.001, CS: χ22= 1.34, P= 0.512). We also tried modeling the error variance with year-specific estimates but, due to the large number of parameters involved, some of the models failed to converge and thus we do not present the results here.
Bivariate random regression animal model
A bivariate random regression animal model is an extension into two-dimensional space of the univariate model described above and allows the estimation of covariance structures between the two traits. Hence for each individual (i) our model was:
where all parameters are as defined for the univariate random regression model. This model estimates the variation in reaction norm components in each trait as well as the between-trait covariances. For instance, a first order function (n1= 1) for the additive genetic effect (ai) would estimate the additive genetic variance–covariance matrix:
where σ2CSe refers to the variance in reaction norm elevation, e, for CS, σ2CSs refers to the variance in reaction norm slopes, s, for CS and σCSes refers to the covariance between the two. Similarly, σ2LDe refers to the variance in LD elevation, σ2LDs to the variance in LD slope and σLDes to the covariance between the two. These parameters are all as fitted in the trait-specific univariate models (see above). However, in addition to the within-trait variances, we also estimated the between-trait covariances, where σCSe, LDe is the covariance between CS elevation and LD elevation, σCSe, LDs the covariance between CS elevation and LD slope, σCSs, LDe the covariance between CS slope and LD elevation, and finally σCSs, LDs is the covariance between the slopes for CS and LD (and so estimates the covariance in plasticity between the two traits).
Residual variance was defined as for the univariate models, thus using a heterogeneous structure. This provided a substantially better fit compared to a model with homogenous error variance for both populations (χ26= 38.00, P < 0.001 and χ26= 44.04, P < 0.001 for the HV and WW population, respectively). Note that we also fitted the covariance between the two traits for the residual and year variance, as not fitting these will cause the estimate of the additive genetic covariance to be inflated (in a similar way that not fitting a permanent environment effect will inflate the additive genetic variance in a univariate model).
To explicitly test whether the size of the variance components and the plasticity patterns in the two populations were significantly different from each other, we combined the datasets and pedigree information from both populations. Each trait in the two populations was then used in two separate bivariate random regression models (i.e., CS-HV and CS-WW in one bivariate model, and, similarly, LD-HV and LD-WW in a different bivariate model) extended to incorporate the combined dataset and pedigree from each population, and using the measures of temperature from each population. Because gene flow between the two populations is negligible, we constrained all covariances between the population-specific traits to be zero. The residual variance was modeled as three (decade-specific for each population) 2×2 unstructured matrices (with covariances constrained to zero). Hence this will model the same residual variance as described above under the univariate analysis. We also modeled population-specific fixed effects (see detailed description under the univariate model).
The population-specific comparison was done by constraining the respective variance components in the two populations to be equal and then optimizing the likelihood under this model. We then used a likelihood ratio test (LRT, see below) to compare the likelihood of this model to that of a model in which they were unconstrained. For more details concerning the use of LRTs to compare matrices, see Shaw (1991).
All models were fitted using REML in ASReml v 2.0 (Gilmour et al. 2006). For all models we first fitted a homogenous residual structure, and then a heterogeneous residual structure (see above). To partition the average population-level response into individual-level variation in plasticity, we used a linear mixed effect model framework with increasingly complex variance structure; this logic was also followed for the multitrait model. In the few cases where the estimated variance components were negative, mainly when assessing slope variance for CS in the HV population, we constrained the matrix to be positive definite; the estimates from the CS analysis in HV should thus be treated with some caution.
In the multitrait models we additionally fitted the covariance terms between the random regression coefficients, i.e., testing associations between plasticity components and elevation components between the two traits. We first estimated the full 4×4 matrix (see matrix (3) above) and compared this to a model in which all four between-trait covariances were constrained to be zero, thus giving a single test for the significance of sources of between-trait genetic or environmental covariances. Second, we constrained all between-trait covariances except that between the elevations of the two traits (i.e., σCSe, LDe) to zero to assess the significance of the between-trait phenotypic and genetic covariance.
All significance testing of (co)variance component(s) was done by calculating the log likelihood ratio and testing against a chi-square distribution with degrees of freedom equal to the difference in degrees of freedom between the two models tested (Pinheiro and Bates 2000). Thus, LRT =−2(L2−L1), where L1 is the log likelihood of the initial model and L2 the log likelihood of the model with (co)variance component(s) added.
Although we are using the “reaction norm approach” here to assess the genetic basis of variation in plasticity, GxE can also be thought of from a “character state” view. That is to say that the estimated genetic variance–covariance matrix of the reaction norm components (i.e., elevation and slope) can be transformed to give environment specific trait values of VA for the underlying trait (CS or LD). In the presence of GxE, VA is expected to change across the environmental axis and thus the character state approach provides a useful way to visualize the change in VA across the environmental conditions. To this end we calculated the environment-specific additive genetic covariance matrix, G, which was obtained as G=zQzT, where z is the vector of orthogonal polynomials evaluated at values of standardized temperature measures in the two populations and Q is the additive genetic variance–covariance matrix of the random regression parameters for elevation and slope (obtained under model 6 in Table 2). Approximate standard errors for the (co)variance components of G as a function of the environmental values were calculated according to Fischer et al. (2004), with confidence intervals defined as twice the standard errors. We also calculated the coefficient of variation (CV = var0.5/mean) for the additive genetic variance component according to Sokal and Rohlf (1995).
Table 2. Results from the univariate random regression analysis of laying date and clutch size in the HV and WW populations. Reported chi-square values and df are for comparison with the previous model and the P-value for the associated LRT. For each population, we used the population-specific temperature period (see Methods). All models were fitted with decade specific error variance (see Methods). VI is the between-individual variance which is split into VPE (permanent environment variance) and VA (additive genetic variance). IxE is the phenotypic variance–covariance plasticity matrix when no additive genetic variation in plasticity is fitted, PExE is the permanent environment variance–covariance plasticity matrix and GxE refers to the additive genetic variance–covariance plasticity matrix.
(A) Laying date
(B) Clutch size
In both populations, spring temperatures increased over the study period at similar rates (HV: b = 0.055, SE = 0.019, F1,32= 8.475, P= 0.007, Fig. 1A; WW: b = 0.050, SE = 0.015, F1,32= 10.66, P= 0.003, Fig. 1B). The onset of laying was also closely related to temperature in both populations (HV: b =−3.256 days °C−1, SE = 0.421, F1,32= 59.85, P < 0.001, r2= 0.652, Fig. 1C; WW: b =−5.158 days °C−1, SE = 0.635, F1,32= 66.05, P < 0.001, r2= 0.674, Fig. 1D), although the response was significantly weaker (t62= 2.496, P= 0.007) in HV than in WW. The close relationship between LD and spring temperature and the increase in spring temperatures over the study period led to an advancement in LDs for both populations (HV: b =−0.196 days yr−1, SE = 0.079, F1,32= 6.128, P= 0.007, Fig. 1E; WW: b =−0.367 days yr−1, SE = 0.090, F1,32= 16.48, P < 0.001, Fig. 1F); as expected given the stronger response to temperature, the advancement for the WW population was about twice the rate of that in the HV, although the slopes were not significantly different (t62= 1.428, P= 0.079). We therefore have clear evidence of a population-level response of average lay date in relation to variation in spring temperature. In contrast, CS did not show significant population-level response to spring temperature (HV: F1, 32= 0.191, P= 0.66; WW: F1, 32= 0.267, P= 0.267) and nor any evidence of temporal change (HV: F1, 32= 0.236, P= 0.63, Fig. 1G; WW: F1, 32= 1.252, P= 0.27, Fig. 1H).
Univariate random regression animal model analysis: laying date
The results from the univariate models of LD in the two populations provided strong support for the existence of significant between-individual variation in LD (Table 2A, model 3) and evidence that this variation had a genetic component, i.e., LD was heritable (Table 2A, model 4). Individuals also differed in their response to changing environmental conditions, i.e., in their reaction norm slope, thus there was significant IxE in both populations (Table 2A, model 5). However, we did not find statistical support for a heritable basis of the variation in plasticity (no GxE; Table 2A, model 6) in either population, although there was more improvement in the model when fitting GxE in HV than in WW (compare model 6 in Table 2A for HV and WW). We are thus unable to statistically exclude the possibility that the observed IxE is entirely environmentally driven. Nevertheless, IxE must arise from GxE and/or nongenetic PExE sources and while not a significant better fit than model 5, model 6 provides our best estimate of the relative contribution of these sources. We therefore visualized the predictions from the GxE model, using the character state approach, as shown in Table 3 and Figure 2. This shows a qualitative pattern of increasing VA with temperature in HV and no increase in the WW population. The estimated size of the additive genetic variance components for slope in the HV was 3.315 compared to 0.837 in the WW population (see Table S1 for more details). We reiterate that the decomposition of the IxE term was not statistically significant in either population and that any interpretation of GxE is therefore preliminary. This is also reflected by the wide confidence intervals depicted in Figure 2.
Table 3. Variance components of laying date evaluated at different standardized spring temperatures for the HV and WW population under model 6 in Table 2A. Note that there are no records in the dataset at exactly 0 standardized temperature and thus the sample size and mean laying date value is given for the nearest temperature record (HV: −0.0019, WW: −0.0012). No standard errors are available for VPE in the HV populations as the associated variance components were fixed at the edge of the parameter space (thus VP is also without standard errors). VP is the sum of the variance components (phenotypic variance), VA the additive genetic variance, VPE the permanent environment variance component VYR the year variance, and VR the residual variance. Note that VR is the same for some temp values if they happen to fall within the same decade. CVA is the coefficient of variance for the additive genetic variance.
Univariate random regression analysis: clutch size
Although neither of the populations showed a population-level relationship between average CS and spring temperature, this does not preclude the presence of variation in plasticity at the individual level (e.g., if reaction norms are crossing (see, e.g., fig. 2G in Nussey et al. 2007). Hence, we also explored individual-level variation in CS in relation to temperature. For the HV population, individuals differed in their average CS (Table 2B, model 3) and part of this variation was due to genetic differences between individuals, i.e., CS is heritable (Table 2B, model 4). However, we found no indication that individuals differed in how they responded to spring temperature, i.e., there was not any significant variation in plasticity (Table 2B, model 5), and there was no improvement in the model when trying to fit a GxE model (Table 2B, model 6).
For the WW population we also found a difference between individuals in their average CS (Table 2B, model 3) and evidence that this difference was partly genetically determined (Table 2B, model 4). In contrast to the HV population, however, individuals also differed in how they adjusted their CS in relation to the temperature (IxE, Table 2B, model 5). Furthermore, we found statistical support for the hypothesis that some of this variation has a genetic basis, i.e., there was significant GxE for CS (Table 2B, model 6). See Table 4 and Figure 3 for an illustration of how the additive genetic variance for CS changes with temperature.
Table 4. Variance components for clutch size evaluated at the different standardized temperatures for the HV and WW population under model 6 in Table 2B. Note that the variance components were evaluated at different standardized spring temperatures for the WW population due to the significant GxE interaction. As there was no IxE and no GxE for clutch size in the HV population the total number of records, overall mean and variance components are reported. As there were no records in the dataset at exactly 0 standardized temperature, sample size, and mean laying date value are given for the nearest temperature record (−0.0012). CVA is the coefficient of additive genetic variance.
Bivariate random regression animal model in HV population
Comparison of the full 4×4 phenotypic matrix to a model in which all between-trait covariances were constrained to be zero, indicated that the two traits showed significant sources of within-individual phenotypic covariance(s) (χ24= 18.60, P < 0.001). We subsequently tested, first, the significance of the between-trait covariance in reaction norm elevations (σCSe,LDe). This showed a strong negative phenotypic correlation between CS and LD (χ21= 18.60, P < 0.001, rp=−0.264, SE = 0.047), i.e., individuals that on average lay early have larger average CS. Second, we tested all three other covariances, but there was no indication of any other covariance term being significant (χ23= 0.00, P= 1.00), indicating that the phenotypic covariance did not show a significant change with the environmental conditions.
At the genetic level, the model that included covariance between all four genetic reaction norm components was not a significant improvement over the phenotypic model and thus none of the four between-trait genetic covariances were significant (χ24= 6.20, P= 0.18). When explicitly testing the genetic correlation between LD and CS (σCSe,LDe), we found it was positive, although nonsignificant (χ21= 3.00, P= 0.08, rG= 0.560, SE = 0.387; note that this is slightly different to the estimate given in Table S1 due to convergence problems, see Methods for further details), and so of opposite sign to the phenotypic correlation between LD and CS found above. Furthermore, a separate test for the three other genetic covariances also did not show any significant effect (χ23= 3.20, P= 0.36) suggesting that there was no significant change in the genetic correlation with environmental conditions. The lack of significant genetic covariances when tested separately is thus consistent with the result from the model in which all genetic covariances were tested simultaneously. For a full breakdown of the bivariate phenotypic and genetic (co)variance plasticity matrices see Table S1.
Bivariate random regression model in WW population
As for the HV population there was a strong indication that some of the phenotypic between-trait covariances were significant (χ24= 16.18, P= 0.003). As above we subsequently tested, first, the between-trait covariance in CS elevation and LD elevation (σCSe,LDe) which showed a highly significant negative correlation (χ21= 13.40, P < 0.001, rP=−0.341, SE = 0.029). Thus, as for the HV population, early breeding birds have on average larger CS than late breeding individuals. When we tested the other three phenotypic between-trait covariances, to see if the phenotypic correlation would change over the range of environmental conditions, they were not significant (χ23= 2.78, P= 0.427) indicating that the phenotypic correlation remained more or less constant.
Testing all additive genetic between-trait covariances there was, in contrast to the HV population, a significant effect (χ24= 12.32, P= 0.015), indicating that one or more of the covariances were significant. As above, we explored, first, the additive genetic covariance between CS elevation and LD elevation (σCSe,LDe) and this was, in contrast to the HV population, significant (χ21= 9.02, P= 0.003, rG=−0.310, SE = 0.090). Furthermore, when we tested the three other between-trait covariances, i.e., the covariance between CS elevation and LD slope (σCSe,LDs), between CS slope and LD elevation (σCSs,LDe) and between CS slope and LD slope (σCSs,LDs), there was no indication that these were significant (χ23= 3.30, P= 0.348).
Our results thus suggest that plasticity for LD and plasticity for CS are not statistically associated and that the phenotypic and genetic covariances between LD elevation and CS elevation did not change with the environment. There is a full decomposition of the phenotypic variance–covariance plasticity matrix in Table S1.
To compare the reaction norm patterns in the two populations we fitted LD and CS in the two populations in two separate random regression models. Thus, the first bivariate model treated LDs in HV and WW as two separate traits (with no covariance between them) while the second bivariate model treated CS in HV and WW as two separate traits (again with no covariance between them).
There was significantly more between-individual variation in the average LDs (VI) in the WW population than in the HV population at the phenotypic level (χ21= 15.14, P < 0.001), but no suggestion that this was the case at the genetic level (χ21= 1.90, P= 0.168), although the estimated additive genetic variance was higher in the WW population than in HV. This implies no significant difference in additive genetic variance for LD (in the average environment) between the two populations.
As a direct test for differences in IxE pattern for LD between the two populations, we constrained the population-specific variance–covariance matrices to be equal and compared this with a model in which they were unconstrained (see Methods). This test was highly significant (χ23= 19.02, P= 0.0003), confirming that the between-individual reaction norm patterns in these two populations are very different. When we repeated this test on the genetic level, i.e., when comparing the GxE patterns in the two populations, the test was marginally nonsignificant (χ23= 7.50, P= 0.058). This may reflect a lack of power, but in any case we are thus unable to rule out the possibility that the between-population difference is genetic rather than environmental. Nevertheless, this does lend some support to the observations from the univariate random regression animal models that the observed (albeit nonsignificant) GxE pattern is different in these two populations (Fig. 2).
Phenotypic variation in CS (elevation) reaction norms did not differ between HV and WW (χ21= 3.39, P= 0.065), and when comparing the additive genetic variance in reaction norm elevation for CS between the populations there was also no suggestion of a significant difference (χ21= 0.15, P= 0.702). Furthermore, the reaction norm plasticity matrices for CS in the two populations were not significantly different, at the phenotypic level (χ23= 4.60, P= 0.204), or at the genetic level (χ23= 2.40, P= 0.494).
We explored and compared the multivariate genetic basis of variation in phenotypic plasticity in response to changing environmental conditions in two long running individual-based study populations of great tits. Very few studies have compared the multivariate patterns of plasticity, and to our knowledge this study is the first to do so in natural populations using the random regression animal model framework (but see Robinson et al. 2009). We found that, although both populations exhibited similar population-level trends in average LD (see Fig. 1E,F) and CS (Fig. 1G,H), they differed in their pattern of IxE for LD, although when we partitioned this further any difference in GxE was marginally nonsignificant.
The bivariate random regression models showed little indication that individuals that were plastic for LD also showed plasticity in CS: thus in these two populations there was little evidence for phenotypic integration between individual-level variation in LD and CS plasticity. Interestingly, the multivariate analysis indicated that the genetic correlation between CS and LD in the two populations was of opposite sign, despite a similar phenotypic correlation. A significant negative phenotypic and genetic correlation was found in the WW population, but in the HV population the phenotypic correlation was negative and the genetic correlation positive (although nonsignificant).
Furthermore, when we compared the reaction norm patterns for LD in the two populations there were significant differences among individuals in their plastic responses to temperature (IxE); at the genetic level (GxE) this was marginally nonsignificant. For CS, however, we did not find any significant difference in reaction norm patterns at the phenotypic (IxE) or at the genetic level (GxE), although the population-specific univariate models suggested IxE and GxE in the WW population whereas in the HV population neither was significant (Table 2B). Hence, our results highlight the need to be cautious about extrapolating results from one population to other populations of the same species when understanding, or predicting, responses to climate change.
Although there has been a similar increase in spring temperatures over the study period in both populations (Fig. 1A,B), there was a stronger relationship between onset of laying and spring temperatures in WW (Fig. 1D) than in HV (Fig. 1C), as well as more rapid advancement in mean LDs in WW (Fig. 1F) than in HV (Fig. 1E); these results agree with previous analyses (McCleery and Perrins 1998; Visser et al. 1998; Gienapp et al. 2006; Garant et al. 2008). Spring temperature has been shown to have a profound impact on seasonal timing of reproduction in birds in general (reviewed in Dunn 2004), as well as in these two populations in particular (Visser et al. 1998; Charmantier et al. 2008), and so represents a reasonable environmental variable with which to examine phenotypic plasticity in LD. Although it may be less clear that this is a good measure with which to examine plasticity in CS, we emphasize that we are concerned here with the effect increasing spring temperatures have on general plasticity patterns. However, this clearly does not mean that CS could not respond to other environmental factors (e.g., density, Both et al. 2000; Wilkin et al. 2006). Similar to our results, a number of North American bird species also show a population-level association between LD and temperature, but not between CS and temperature (Martin 2007).
Individual-level variation in plasticity
In common with other studies that have estimated components of variance in LD (e.g., Sheldon et al. 2003; Brommer et al. 2005), we found that females differed significantly in their average (phenotypic) LD (significant VI component, Table 2A) and that a significant amount of this variation was due to additive genetic effects (VA, Table 2A). The estimated heritabilities for LD in HV and WW (Table 3) correspond well with what has been shown previously for these two populations (Gienapp et al. 2006; Garant et al. 2008).
We found that there was significant between-individual variation in phenotypic plasticity (IxE) for LD in both populations (see Table 2A), indicating that females differ in how they adjust their LD in relation to the spring temperature. This supports the findings from an earlier study in the HV population (Nussey et al. 2005), but is in contrast to a recent study in the WW population that did not find statistical support for IxE (Charmantier et al. 2008). There are several possibilities as to why our results differ from those of Charmantier et al. (2008), some of which we can exclude. For instance, we used a heterogeneous error structure (see Methods) whereas Charmantier and colleagues used a homogenous error structure, but rerunning the models with a homogenous error structure gave the same conclusion of IxE (although P= 0.016 compared to P= 0.008 with a heterogeneous error structure). The number of years included in this study is also different (1960–2008 vs. 1973–2006 in our study), but again this is unlikely to be the cause of the difference, unless birds from the period 1960–1973 were much less plastic than individuals from the later part, which seems unlikely. Furthermore, Charmantier et al. (2008) only used females that bred three times or more whereas we used all breeding females (i.e., also those that only bred once). Although this should not influence the estimate of variance in plasticity itself, as it is only females with at least two breeding records that provide information on plasticity, it may still influence the statistical power to detect IxE because including all females will increase sample size and thus the precision of the estimated variation in elevations. Finally, as mentioned above, we used a different environmental measure (mean temperatures) whereas Charmantier et al. (2008) used the “warmth sum” (sum of daily maximum temperatures during the period 1 March–25 April). Repeating the analysis using “warmth sum” instead of mean temperature over the period 15 February–25 April (i.e., the same period as for mean temperature used in this study) gave identical results to those reported in Charmantier et al. (2008), i.e., no support for any IxE interaction (χ2= 0.02, df = 2, P= 0.99, compared to a standard animal model) and the estimated slope variance was essentially zero (σ2s < 0.0001). Furthermore, using the “warmth sum” over the period 1 March–25 April (as used by Charmantier and colleagues) again yielded no support for IxE and estimated slope variance close to zero in agreement with that reported by Charmantier et al. (2008). Thus, it is very likely that the use of mean temperatures instead of maximum temperatures is the reason for the different conclusions reached between our study and that by Charmantier et al. (2008). Note, however, that we did find evidence for differing degrees of plasticity (IxE) in the two populations.
Interestingly, the temperature periods that correlated best with the onset of breeding in the two populations differed in length. For the WW population the period that explained most of the variation in onset of laying was from 15 February–25 April, whereas for the HV population this period was substantially shorter, 13 March–20 April. Although we do not presently understand why the two periods are different we examined how differences in the temperature period may influence our results here by rerunning the population-specific random regression models using the “other” temperature period (i.e., for HV we ran an analysis using the mean temp for the period 15 February–25 April as environmental measure and, similarly, for WW using 13 March–20 April as environmental variable). In general this did not change our conclusions presented here, with the exception that GxE for CS in the WW population was no longer significant (χ22= 2.08, P= 0.35) and the IxE for LD was marginally non-significant (χ22= 5.42, P= 0.07). The fact that using different temperature periods can change our conclusions of IxE and GxE again highlights the difficulty of comparing patterns of plasticity between populations.
In many ways the different conclusions about IxE we reach using the two different (but still highly correlated, rs= 0.963, P < 0.001) environmental variables are a cause for concern. Although it is clear that plasticity is only defined in relation to a particular environment (Scheiner 1993), it also raises the question of how we can draw general conclusions from different studies that use different environmental measures. This is just as much a concern for laboratory-based studies as precise replication of environments is extremely difficult: further work will need to be carried out assessing the sensitivity of random regression models to detect patterns of IxE (and GxE) for different environmental variables if we are to be able to generalize patterns of plasticity across populations and species. In particular, finding the actual cue that triggers the response should be an important goal of future studies.
Although population-level patterns in CS are frequently reported (e.g., Both et al. 2000), we are only aware of one other study looking at between-individual variation in CS plasticity, Przybylo et al. (2000) found that collared flycatchers (Ficedula albicollis) differed in their adjustment of CS in relation to the winter NAO-index (North Atlantic Oscillation), with a high NAO value (indicating warm moist winters in Scandinavia) resulting in higher CSs. In this study we found support for between-individual variation in CS plasticity and a genetic basis to the variation in plasticity in the WW population, but not in the HV population (Table 2B, Table 4). The individual variation in CS plasticity found in the collared flycatcher population and in the great tits in WW contrasts with the lack of such plasticity in the great tits in the HV population, suggesting that inter-population differences, for example, due to characteristics of the experienced environmental conditions, may be important.
Genetic basis to phenotypic plasticity variation
Both populations showed IxE for LD, but when we tried to separate the IxE variation into its genetic (GxE) and environmental (PExE) effects we found that such a model was not significantly better (Table 2A), suggesting that we might not have the statistical power to separate the two. Nonetheless, provisionally accepting as our best estimate the partition of IxE under the full model, then the majority of variation in plasticity is due to additive genetic effects in the HV population whereas this was not so in the WW population (Table S1). This difference was also apparent when we visualized the change in VA with increasing spring temperature (Fig. 2) using the character state approach. Whereas there was qualitative (but nonsignificant) increase in additive genetic variance with spring temperature for LD in the HV population (Fig. 2A), there was no such pattern of change for the WW population (Fig. 2B). Thus our finding in the HV population is similar to the conclusions reached by Brommer et al. (2008) investigating the genetic basis of variation in LD plasticity in a population of common gulls (Larus canus), who also found IxE but no statistical support for GxE.
Our finding that the putative GxE for LD in HV was not statistically significant contrasts with the findings from Nussey et al. (2005) who estimated the genetic basis of variation in plasticity using a slightly different “two-step approach.” The “two-step approach” is different to a random regression approach in that one first runs a linear mixed effect model on the phenotypic values and extracts the “best linear unbiased predictors” (BLUPs) for elevation and slope, and then use these estimates in an animal model to estimate the genetic basis of elevation and slope. This approach ignores the large uncertainty associated with the BLUP estimates and is considered to be less robust than the direct estimation of GxE from a single model as performed here (Nussey et al. 2007; Brommer et al. 2008). For instance, Nussey et al. (2005) failed to find a significant heritability of elevation, only for slope, suggesting that LD itself is not heritable, but only its plasticity is. A similar result, using the same approach, was reported by Brommer et al. (2005) in a long-term study of collared flycatchers breeding on Gotland, Sweden, where there was no heritable basis for elevation (or slope). This lack of LD heritability contrasts with previous findings in the same population (Merilä and Sheldon 2000; Sheldon et al. 2003). Our results (Table 2A) clearly suggest a heritable basis of LD elevation in the HV (and WW) population, as has previously been shown (van Noordwijk et al. 1981; Gienapp et al. 2006). However, our finding that most of the variation in plasticity is due to additive genetic effects (Table S1) does lend some support to Nussey and coworkers’ findings, and, when repeating the “two-step approach” on our dataset (and environmental variable), we also found statistical support for GxE (A. Husby, unpubl. results). Thus, the lack of a significant GxE when using the random regression approach here is probably due to power limitations that were not adequately reflected in the methodology used by previous studies (Nussey et al. 2005). We agree with Brommer et al. (2008), however, that we need to be careful about equating a nonsignificant GxE with an absence of GxE. This is because, assuming all IxE to have a nongenetic basis is not necessarily conservative with respect to its implications for environment-specific heritabilities.
Interestingly, there was not only IxE variation but also GxE variation, and thus a heritable basis of plasticity, for CS in the WW population (Table 2B). In contrast to the change in VA for LD with temperature in the WW population and HV, the negative genetic covariance between CS elevation (σ2CSe) and CS slope (σ2CSs) generated a relatively large decrease in VA with temperature (Fig. 3). An overview of the results obtained from this study compared to the findings of Nussey et al. (2005) and Charmantier et al. (2008) is in Table 5.
Table 5. Summary table of results from this study compared to previous studies on the same populations. Note that both previous studies used a two-step model (see Discussion), whereas the results from this study use a random regression animal model.
The four between-trait covariances determine the degree to which the two traits and the plasticity in these traits are correlated and thus the populations’ multivariate reaction norm pattern. Our results indicate little evidence of any significant correlation between plasticity in the two traits. The presence of a negative phenotypic correlation between CS and LD is commonly found in a number of different populations and species of birds (e.g., Klomp 1970; Perrins and McCleery 1989; Winkler and Allen 1996). Interestingly, although both the HV and WW population showed a significant negative phenotypic correlation between CS and LD, the genetic correlation was positive (although nonsignificant) in the HV population and significantly negative in the WW population. There are surprisingly few studies that have estimated the genetic correlation between CS and LD in birds, and so far there seems to be no emergent pattern. A negative genetic correlation has been found in collared flycatchers and great tits (Sheldon et al. 2003; Garant et al. 2008), whereas a previous study in the HV population also found the genetic correlation to be non-significant (Gienapp et al. 2006). It is difficult to speculate as to the causes behind the divergent correlations observed, but genetic correlations are sensitive to allele frequencies and subject to rather large sampling variance and so can differ substantially between populations (Falconer and Mackay 1996).
Very few studies have investigated whether between-trait correlation structures are sensitive to environmental conditions. In our study such sensitivity would be manifest from statistical significance of one or more of the cross-trait covariances between elevation and slope, or the cross-trait covariance of reaction norm slopes. Robinson et al. (2009) studied how the phenotypic, additive genetic and environmental correlation between horn length and body weight, horn length and parasite load and between body weight and parasite load changed with environmental conditions in a wild population of Soay sheep (Ovis aries). In that population, the genetic correlation between horn length and body weight, and that between horn length and parasite load both showed a significant decline in more favorable environmental conditions, whereas the phenotypic correlation between horn length and body weight decreased with increasing environmental conditions, and that between horn length and parasite load showed a positive increase. Thus there seems to be no clear expectation as to how the environment should influence phenotypic and genetic correlations in the wild: it may simply be trait and population specific.
Although the concept of between-trait correlations in plasticity was first suggested over 20 years ago by Schlichting (1986), it has, perhaps due to experimental and statistical difficulties, received relatively little attention. A multivariate approach to studying the adaptive basis of plasticity was, however, carried out by Spitze and Sadler (Spitze and Sadler 1996) who examined plasticity in eight morphological traits in Daphnia pulex in response to presence/absence of a predator (Chaoborus americanus). Although covariances in plasticity between traits were not examined, the authors convincingly showed that single univariate analyses of the adaptiveness of plasticity could yield an incomplete and misleading picture of what traits contribute to adaptive phenotypic plasticity. They hence advocated a multivariate approach to examining plasticity.
Interestingly, some experimental work by Newman (1994), where between-trait correlations in plasticity were examined, suggests that these correlations may depend on the environmental variable used to study it. Newman (1994) collected families of spadefoot toads (Scaphiopus couchii) and raised them in the laboratory with different temperature and food availability regimes and showed that plasticity in size and plasticity in larval period were negatively correlated for the food regimes, but positively correlated under temperature variation. This clearly shows that even if we do find a between-trait correlation in plasticity this may be subject to change depending on the environmental variables we use in the context of studying plasticity. It is clear that the possibility of between-trait correlations in plasticity, or so-called phenotypic integration (Schlichting 1986), in natural populations requires much more study.
Although there was significantly more phenotypic variance in LD in WW than in HV, there was no indication that the amount of additive genetic variance was significantly different. However, when we compared the phenotypic IxE patterns, there was a clear difference between the two populations and this was also reflected at the genetic level by a marginally nonsignificant difference in the genetic reaction norm patterns (GxE pattern). The between-population comparison is interesting for several reasons: first, it demonstrates that although both populations showed IxE, there is considerable more within-population variance in the reaction norm slopes in HV than in WW. Second, this difference was also present, although marginally nonsignificant, when comparing the genetic reaction norm patterns, supporting the qualitative conclusions from the separate univariate analysis (see Table 2A and Fig. 2). It is unclear why there is more variation in plasticity between individuals in the HV population than in WW. A plausible reason may be that it is due to differences in environmental heterogeneity in these two populations. If the HV population has a more heterogeneous environment than the WW population this may lead to such (environmentally induced) variation. It has been shown in other systems that changes in environmental conditions may lead to an increase in phenotypic (and genetic) variance, particularly if the environmental conditions are outside what the population have previously experienced and thus there is no opportunity for selection to act (de Jong 2005; Ghalambor et al. 2007).
The population comparison also showed that the GxE pattern for CS that we detected in WW is not significantly different from that in the HV population. This probably reflects the fact that, although significant, variation in plasticity for CS was also low in the WW population. No comparison between the two populations was actually significant for CS, suggesting similarity rather than difference, contrary to what would be inferred from the univariate population-specific analyses.
In conclusion, we have demonstrated that changing environmental conditions may not have the same consequences in different populations of the same species, even when rates of environmental change are similar. Using a multivariate approach, we have shown that there was no significant correlation between plasticity for LD and plasticity for CS in these two populations.
Although our findings do not, as is the case in all quantitative genetics studies, allow us to dissect the molecular genetic basis of phenotypic plasticity they do suggest that, given the limited evidence for additive genetic variance in plasticity found in these two populations (and in WW in particular), a QTL approach (Lynch and Walsh 1998) to studying plasticity in natural populations might prove challenging, despite the recent development of genetic marker-based linkage maps for such populations (Backström et al. 2006).
Associate Editor: J. Wolf
The long-term population study in the Hoge Veluwe has been conducted under the directorships of H. N. Kluyver (1955–1968), J. H. van Balen (1968–1991), and A. J. van Noordwijk (1991–2002). The database has been managed by J. Visser and L. Vernooij. The data from the long-term study at Wytham have been collected by many hundreds of fieldworkers. We are grateful to Anne Charmantier for discussions and to two anonymous referees and Jason Wolf for their comments on the manuscript, and to Michael Morrissey for help with pedantics. This work was conducted as part of a GENACT Project studentship to AH, funded by the Marie Curie Host Fellowships for Early Stage training, as part of the 6th Framework Programme of the European Commission. DHN, AJW, and BCS are funded by the Natural Environment Research Council, MEV is supported by a NWO-VICI grant, and LEBK is funded by the Royal Society, London.