Behavioral
Ecology
The official journal of the
ISBE
International Society for Behavioral Ecology
Behavioral Ecology (2014), 25(4), 802–812. doi:10.1093/beheco/aru057
Original Article
Residual correlations, and not individual
properties, determine a nest defense boldness
syndrome
Jon E. Brommer,a Patrik Karell,b,c Kari Ahola,d and Teuvo Karstinene
aDepartment of Biology, University of Turku, University Hill, FI-20014 Turku, Finland, bEnvironmental
Biology, Department of Biosciences, Åbo Akademi University, Artillerigatan 6, FI-20520 Turku, Finland,
cAronia Research and Development Institute, Åbo Akademi and Novia University of Applied Sciences,
Raseborgsvägen 9, FI-10600 Ekenäs, Finland, dTornihaukantie 8D 72, FI-02620 Espoo, Finland, and
eJuusinkuja 1, FI-02700 Kauniainen, Finland
Received 13 November 2013; revised 5 February 2014; accepted 10 March 2014; Advance Access publication 8 April 2014.
Different behavioral traits often covary, forming a behavioral syndrome. It is poorly known whether this covariance occurs on the
between-individual level and what its selective consequences are. We used repeated measures (N = 562 observation events) of individual tawny owl Strix aluco females (N = 237) to study the integrated effects of seasonal timing of reproduction and clutch size on
boldness displayed during defense of their clutch, in relation to plumage coloration, including local recruit production as a selective
force on these traits. Using a Bayesian multivariate mixed model, we quantified the covariances between these traits on phenotypic,
residual, and between-individual level and used a structural equation modeling approach to test the significance of presumed causal
relationship between these traits in an a priori hypothesized path. On the phenotypic level, boldness was determined through early timing of breeding and larger clutch size, and early breeding increased recruitment probability. However, this relationship was entirely due
to residual covariances and was not present on the between-individual level. The low individual-level correlations did not constrain the
capacity of the population to respond to evolution as quantified by average autonomy (a metric summarizing evolutionary constraint on
multiple traits). In the tawny owl, the association between early breeding and bold behavior, which is favored by selection, is solely due
to extrinsic, nonheritable factors. We conclude that phenotypic evidence is insufficient to demonstrate syndrome covariance.
Key words: animal personality, Bayesian statistics, linear mixed model, multivariate models, structural equation model, variance partitioning.
Introduction
In a wide array of taxa, individuals show repeatable variation in
metrics of behavior (Réale et al 2007; Bell et al. 2009). Repeatable
behaviors are considered measures of animal personality, and,
typically, multiple behaviors covary, a phenomenon termed “behavioral syndrome” (Sih et al. 2004). Covariation among traits may
even extend beyond behavioral traits to encompass physiological
and life-history traits (Koolhaas et al. 1999; Réale et al. 2010). In
particular, the “Pace of Life Syndrome” (Réale et al. 2010) places
behavioral syndromes within a much broader setting where also the
covariation of behaviors with physiological and life-history traits is
recognized. The existence of such syndromes implies that researchers must adopt a multivariate approach. The use of structural
Address correspondence to J.E. Brommer. E-mail: [email protected].
© The Author 2014. Published by Oxford University Press on behalf of
the International Society for Behavioral Ecology. All rights reserved. For
permissions, please e-mail: [email protected]
equation models (SEM) has been promoted as a valuable multivariate technique to describe syndrome structure in a nonexperimental
setting by comparing various alternative putative syndrome structures (Bentler 1980; Jöreskog 1993; Dingemanse et al. 2010).
Another line of research in animal personality emphasizes that
syndrome covariance is an essentially hierarchical process. The covariance between behaviors and other traits on the level of the phenotype (i.e., between the actual measurements taken) is a weighted
average of the covariances occurring on hierarchically deeper levels.
Especially, the between-individual level and the residual (or withinindividual) covariances are important components in syndrome
research (Dingemanse et al. 2012; Dingemanse and Dochtermann
2013). Indeed, Dingemanse et al. (2012) argue that animal personality research should focus on the between-individual variances and
covariances. Whereas analysis of between-individual variance (i.e.,
repeatability) is common in animal personality research, few studies
Brommer et al. • Hierarchical structure of a syndrome
quantify between-individual covariances (Dingemanse et al. 2012).
Traditionally, behavioral syndromes are not defined to occur only on
the between-individual level (Sih et al. 2004). Nevertheless, consideration of phenotypic covariances without further partitioning this
covariance to its underlying levels leads to what has been termed
the “individual gambit” (Brommer 2013), where researchers (implicitly or explicitly) assume that phenotypic correlations indeed capture the underlying individual-level correlations adequately. Under
the standard statistical assumption that residuals are random noise,
this assumption may qualitatively hold. On the other hand, a classic notion in life-history theory is that a trade-off occurs whenever
finite resource must be allocated in 2 or more traits but that the
direction of this trade-off may be masked when phenotypic covariance between traits is investigated (van Noordwijk and de Jong
1986; Price et al. 1988). This is because environmental conditions
are likely to affect multiple traits in the same direction, thereby leading to environmentally driven covariance which, whenever traits are
largely determined by environmental conditions, also largely determines the phenotypic correlation. Such a scenario could drive the
correlations in what on the phenotypic level appears to be a syndrome. In wild population, where environmental heterogeneity is
large and uncontrolled for, within-individual (i.e., residual) correlations could be strong and hence seem particularly likely to determine phenotypic associations between traits. For some behavioral
syndromes in the wild, we know that they have a genetic basis and
thus are determined (at least partially) by individual-specific properties (e.g., Brodie 1993; Duckworth and Kruuk 2009; Réale et al.
2010; reviewed by Dochtermann 2011). However, studies that are
not concerned with the genetic underpinning of syndrome covariances rarely dissect phenotypic covariances into underlying hierarchical levels (such as the between-individual and within-individual
correlations). It is, hence, currently not known whether phenotypic
covariances in general reflect between-individual covariances or not.
One powerful approach to include this hierarchy of levels affecting
a behavioral syndrome is to analyze repeated measures of behavioral
and other traits obtained on a set of individuals in a multivariate
803
mixed model framework (Lynch and Walsh 1998; Snijders and
Bosker 1999). In this article, we use this technique to implement a
multivariate hierarchical view of the boldness of tawny owl Strix aluco
females in defending their clutch. In general, nest defense is defined
as behavior where the individual risks its own survival for the protection of its offspring (Montgomerie and Weatherhead 1988). We use
34 years of scores of the boldness of tawny owl females in defending their clutch when an observer comes to check the status of their
brood. We expect that our score of nest defense boldness captures a
repeatable aspect of tawny owl behavior because nest defense intensity has been found to be repeatable in other birds (Duckworth 2006;
Kontiainen et al. 2009; Fresneau et al. 2014).
Multivariate models allow estimating the covariance between
several traits, which putatively form a syndrome. Joint interpretation of all pairwise covariances, however, is challenging. We,
therefore, investigate the observed associations in our syndrome by
means of a path analysis (Figure 1), which captures our a priori
hypotheses of how the various traits considered in our analysis are
related to each other. We hypothesize that variation in nest defense
boldness is driven by a number of other traits, which we graphically summarized in a path diagram (Figure 1, paths a1–a4), based
on the following lines of evidence. Firstly, clutch size of broods
produced early in the season is typically larger than that of broods
produced late in the season (the covariance a2 in Figure 1) and
this covariance has a genetic basis in some species and populations
(Sheldon et al. 2003, but see Husby et al. 2010). Secondly, early
and large broods are assumed to have a higher fitness value than
smaller broods produced later in the season. The fitness value of
the brood that parents defend is considered the main driver for
variation in nest defense (Montgomerie and Weatherhead 1988).
Hence, the timing of seasonal production and clutch size are
expected to drive variation in nest defense boldness (paths a3 and
a4 in Figure 1). Lastly, tawny owls show marked variation in plumage coloration, varying from pale gray to reddish brown (Brommer
et al. 2005), which is caused by differential deposition of pheomelanin in their feathers (Gasparini et al. 2009). In general, the same set
Figure 1
Hypothesized path depicting the relationships between boldness and the other focal traits. Arrows depict putative causal relationships between variables and
the double arrow indicates a covariance. Paths a1–a4 concern the influences of plumage coloration and life-history traits on nest defense boldness. Paths a5–
a8 describe the recruitment selection on each of the traits included.
Behavioral Ecology
804
of genes that increase the expression of melanism coloration also
affect aggression and other aspects of behavior, as documented in
a variety of organisms (reviewed by Ducrest et al. 2008). Hence,
we expect plumage coloration to affect nest defense boldness (path
a1, Figure 1). A path analysis implies causality by drawing directional relationships between traits (i.e., a1 and a2—a4 in Figure 1).
Provided a path model indeed fits the data, these directional relationships are only valid to the extent that the hypothesized paths
indeed provide a complete description of the system (Shipley 2002).
We wanted to quantify the selective forces acting on the nest
defense boldness–clutch size–laying date–color syndrome in tawny
owls. We, therefore, considered the probability that a brood produced offspring that were recruited back into the breeding population. In principle, each of the traits in the syndrome is expected to
be under recruitment selection (paths a5–a8 in Figure 1). In general, selection on animal personality is typically explored by considering how a single trait (e.g., aggression or exploration) maps to
fitness (e.g., Dingemanse et al. 2004; Duckworth and Badyaev 2007;
reviewed in Dingemanse and Réale 2005; Réale et al. 2007). The
existence of syndromes necessitates consideration of not only direct
but also indirect fitness consequence of variation in personality. We
may, for example, observe that individuals that defend their brood
more vigorously recruit more offspring, but is this because of their
capacity to defend their offspring or because they also tend to have
produced more offspring (cf. Kontiainen et al. 2009)? One of the
attractive features of path analysis is that both direct and indirect
effects are included. Thus, the path “a5” (Figure 1) denotes recruitment selection on nest defense boldness, after taking into account
how boldness is affected by clutch size, laying date, and plumage
coloration. Joint analysis of the integration of multiple traits and
the selection acting on such syndromes is considered the necessary
approach for gaining insight into the evolutionary forces determining the existence of syndromes (Sih et al. 2004).
Because our hypothesized path (Figure 1) consists of traits that are
measured each time an individual breeds, we can partition the phenotypic variances and covariances that characterize the paths into their
underlying between-individual and within-individual (co)variances
using standard mixed model methodology (Lynch and Walsh 1998;
Snijders and Bosker 1999). We here implement this mixed model in
a Bayesian framework, where we can use the posterior distribution of
the (co)variances to also take the uncertainty around the (co)variances
forward to quantify the uncertainty of the path coefficients.
Study of the associations between multiple traits (a syndrome)
tends to make inference of the biological relevance of observed
syndrome covariances increasingly problematic as the number of
traits considered increases. When there are many pairwise correlations, it becomes unclear what their overall consequences for the
population are. A meta-analysis by Dochtermann and Dingemanse
(2013) recently used the concept of average autonomy (Hansen
and Houle 2008) to demonstrate that most behavioral syndromes
tended to have an evolutionary relevance in constraining the capacity of the population to respond to selection. One defining feature
of considering evolution from a multivariate perspective is that we
need to consider the population-level consequences of the entire
correlational structure rather than interpreting pairwise correlations
(e.g., Agrawal and Stinchcombe 2009; Morrissey et al. 2012). Here,
we use the posteriors from our hierarchical mixed model to ask
whether the individual-level covariances that we estimate are biologically relevant in the sense that they could constrain evolution.
The above outlined approach allows us to answer 2 questions. 1) Is
the apparent syndrome between traits, as observed through phenotypic
covariance between traits, a true syndrome that generates individuallevel covariances between traits or does it arise merely through withinindividual covariances? 2) Does direct or indirect selection act on the
true (individual level) syndrome or are fitness associations merely due
to environmental conditions driving trait-fitness covariance? These are
core questions regarding syndrome research, which—to our knowledge—have not been previously studied in a single integrative approach.
Methods
General field protocol
The tawny owl S. aluco is a forest-dwelling nocturnal bird of prey
found in the temperate and southern boreal zone of Europe. In
Finland, tawny owls inhabit mixed and boreal forests where they
readily breed in nest-boxes. We studied tawny owls in a nest-box
equipped area of about 250 km2 in southern Finland between 1979
and 2012. There were between 15 and 55 active territories in the
area of which 50–80% bred depending on the vole abundance (cf.
Karell et al. 2009). Female tawny owls lay their clutch in March–
April and incubate their eggs approximately 30 days. The nestboxes were checked during the end of April or beginning of May
in order to get information on where the owls were breeding and
to quantify their clutch size. More regular visits were made around
the presumed date of hatching. After hatching, nestlings were measured (wing length with a ruler and body mass with a spring scale)
and their age was estimated on the basis of growth curve data in
order to estimate the hatching date. Laying date was estimated
by assuming that eggs were incubated for 30 days. Note that the
error inherent in this backdating procedure is small compared with
the phenotypic variation in laying date (>50 days). Tawny owls do
not have second clutches during their breeding season and do not
produce a replacement clutch after nest failure either. It should be
noted, however, that we only identify individuals late in the annual
breeding cycle (see below) and we hence cannot trace the actions of
individuals suffering nest failure early in the breeding period.
During nest-box checks, data on the owls’ behavior when
approaching the nest-box were collected (see Nest defense boldness behavior). When the chicks had hatched practically, all breeding female owls were caught and handled by netting them at the
nest-box entrance. A swing door trap was attached at the nestbox entrance and left there overnight in order to catch the males
when they delivered prey to the offspring. Nearly all breeding
males were caught each year. The unique ring number of female
and male parents were controlled (birds were ringed if unringed).
Individuals were weighed, measured, and their plumage coloration
was scored (see Karell et al. 2013 for details on the color scoring
method). Adult tawny owls ringed as nestlings can be exactly aged
and unringed adults can be aged on the basis of plumage characteristics because tawny owls typically molt only part of their flight
feathers (Karell et al. 2013). One-year olds still have their juvenile
plumage and 2-year olds typically have both juvenile- and adulttype flight feathers. Adults captured for the first time (first breeders)
with only adult-type flight feathers were assumed to be 2 years old.
This is warranted because nearly all tawny owls start to breed as a
1- or 2-year olds (Karell et al. 2009). This allowed an estimate of
minimal age (from here on age) for every individual in the population. All offspring were ringed prior to fledging approximately at
the age of 28 days. Offspring caught later in life as a breeding adult
were considered to have recruited. We here used recruitment on
the level of the brood as fitness measure. That is, for each brood,
Brommer et al. • Hierarchical structure of a syndrome
we scored whether at least 1 offspring recruited (1) or not (0). Note
that multiple recruits per brood were rare (see Results for descriptive statistics).
Nest defense boldness behavior
Nest defense boldness of individual female owls was scored after
egg laying. We here use behavioral data collected during the season’s first nest-box check in order to rule out any possible effects
of habituation during the season. Boldness of the females was thus
scored in the latter half of the incubation period. During nest-box
checking, a standard sequence of actions was followed each time a
nest was visited and the stage of this sequence at which the female
escaped from the nest-box when an observer approached the nest
was noted. We assumed that bolder individuals are those that
remain in their nest longer in order to protect their offspring and,
thus, scored female nest defense boldness as follows:
1. Female is already outside when arriving to the nest tree or she
jumps out before the observer reaches the nest-box tree.
2. Female jumps out of the nest-box when clapping and scraping
the nest-box tree, which simulated a potential predator starting
to climb the nest-box tree.
3. Female jumps out when the observer was climbing the nestbox tree.
4. Female jumps out of the nest-box when opening the lid of the
nest-box.
5. Female jumps out after being touched or stays in the nest-box
during the duration of the check.
In case there were multiple checks during the incubation phase, we
used the boldness score at first nest-box check in our analyses in
order to rule out any possible effects of habituation during the season. On average, we made 2.35 ± 0.04 standard error (SE; range
1–6, N = 551) nest-box checks where we scored nest defense boldness of individual female owls. The same standard sequence of
actions for data collection was followed in all study years and the
data were largely (>95%) collected by the same observers between
1979 and 2012 (K.A. and T.K.). Between years, these observers
changed the nest-boxes they were responsible for checking, and,
hence, any putative differences between these observers in scoring
nest defense boldness were assumed to be random with respect to
the individual they scored.
Mixed model procedure
Our primary interest was to understand whether our hypothesized
path (Figure 1) depicted relationships observed on the phenotypic
level (i.e., associations between the actual measured values) or
whether these associations were also present on the between-individual and/or residual levels. We, therefore, needed to partition
the phenotypic covariance matrix P into a matrix denoting the
between-individual covariances ID and a matrix containing the
residual covariances R, where P = ID + R. Partitioning was done
using a multivariate mixed model, where an individual’s individualspecific trait values are assumed to be individual-specific deviations
from the overall fixed effect mean for each trait. In general, for
traits X and Y, observed trait value z of individual n in year t was
modeled as
(1)
z X ,n ,t = µ X + i X ,n + ε X ,n ,t , zY ,n ,t = µ Y + iY ,n + ε Y ,n ,t ,
where μ denotes the overall fixed effect mean, i the individualspecific trait value, and ε the residual value. The values of i and
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ε are assumed to stem from a multivariate Gaussian distribution
with zero means and (co)variance matrices ID and R, respectively.
Laying date, clutch size, coloration, and nest defense boldness were
assumed to themselves approximate a Gaussian distribution and
recruitment was modeled as a binomial trait on the logit scale, such
that the linear equation on the right-hand side of Equation 1 could
be applied. Covariances across individuals were modeled by including individual as a random effect in the mixed model procedure.
Residual variances and covariances between all traits were also
included. The resulting matrix defined on level L (i.e., phenotypic
matrix P, between-individual matrix ID, and residual matrix R),
therefore, has elements

 VL
 LLD

L
 C LD,CS

VCS
 L

L
L
 C LD,COL C CS
,
V
, COL
COL
 L

L
L
L
 C LD,BOLD C CS

VBOLD
C COL ,BOLD
, BOLD
 L

L
L
L
L
 C LD, REC C CS , REC C COL,REC C BOLD, REC VREC 

 (2)
where the upper triangle (which is not presented here) is symmetrical with the lower triangle and VXL denotes the variance in trait X on
level L, and C XL ,Y the covariance between traits X and Y on level L.
Traits are laying date (LD), clutch size (CS), coloration (COL), nest
defense boldness (BOLD), and recruitment (REC). The elements of
matrix Equation 2 were estimated on the between-individual level
(ID) and the residual (i.e., within-individual) (R) level. The phenotypic covariance matrix P was then calculated as the sum of these
2 matrices. The last row of the matrix in Equation 2 denotes the
fecundity selection on the different levels on the various traits. This
estimate of fecundity selection here denotes the covariance between
trait and the logit of the probability that a recruit was produced.
This covariance can be interpreted on the phenotypic and residual
levels as the covariance between a brood’s phenotypic or residual
value for CS and LD and the brood’s mother phenotypic or residual COL and DEF value, and the brood’s probability to recruit
offspring (on the logit scale). On the individual level, this covariance concerns the covariation between the individual-specific trait
values and the individual’s propensity (on the logit scale) to produce
a recruit during 1 breeding attempt. Nonlinear selection was not
considered because this is not easily implemented in the approach
followed in this article. Correlations were calculated from the covariance matrices on the different levels, following the standard definition of a correlation (i.e., rX,Y = CX,Y /√(VX × VY).
The multivariate mixed model was implemented in a Bayesian
framework using Markov chain Monte Carlo (MCMC) sampling in
the package “MCMCglmm” (Hadfield 2010) in R (R Core Team
2012). As fixed effects, we included year and the age of a female
in order to correct for annual variation and age-specific effects.
Because binomial variances are fixed through the statistical properties of the binomial distribution, we fixed residual variance for
the binomial trait “recruitment” at 1. MCMCglmm uses inverseWishart distributed priors for variances. We here specified proper
priors with parameter “V” for the variances in R set at the rawdata phenotypic variances for each trait (except recruitment, which
was necessarily fixed at 1) and “V” for variances in ID at 0.1 times
the raw-data phenotypic variances. We specified a relatively strong
degree of belief (parameter “nu” was equal to the number of variances to be estimated in R and ID). Details on parameter definitions and implications are provided by Hadfield (2010). R code
for all procedures in this article is provided in the Supplementary
Behavioral Ecology
806
Material. Because the raw-data phenotypic variance of the trait
“laying date” was much higher than the variances for the other
traits, values for laying date were divided by its standard deviation
(SD, i.e., laying date was expressed in units of 1 SD) in order to
aid in convergence of the MCMC chain. The MCMC chain had a
burn-in of 10 000, followed by 500 000 iterations with a thinning
interval of 500, which produced a chain with decently low autocorrelations in the posteriors. Bayesian implementation of multivariate mixed models is challenging because noninformative priors for
variances may be informative for the covariances. Autocorrelation
in the chain was carefully assessed. We also reran the model using
different sets of priors constructed on the same premises as outlined
above, but with differing degree of belief parameter “nu.” These
produced qualitatively the same results. In addition, a frequentist
implementation of the multivariate model based on all traits except
recruitment in the program ASReml (VSN International, Hempel
Hemstead, UK) produced results that were in agreement with the
model outcome presented here.
As point estimate for all statistics derived from the mixed model,
we calculated the mode of the posteriors, and we used the 95%
Highest Posterior Density as a measure of its 95% credible interval (95% CRI). Repeatability (R) for each Gaussian trait was
calculated using the posteriors; for trait X, R = VXI / (VXI + VXR ).
Repeatability of the binomial trait recruitment was calculated on
the latent scale by taking the expected variance of a binomial trait
I
I
/ (VREC
+ 1 + π 2 / 3).
into account as RREC = VREC
Path analysis
We analyzed our hypothesized path (Figure 1) within the general
framework of SEM carried out on the correlation matrices (scaled
covariance matrices) P, ID, and R using the procedure “sem” of
the sem package (Fox 2006) implemented in the program R (R
Core Team 2012). We calculated the loadings (path coefficients) in
our hypothesized path for each of the posteriors of matrices P, ID,
and R scaled to correlations and calculated the posterior mode and
95% CRI of these loadings (R code provided in Supplementary
Material). Applying SEM directly to the posteriors to calculate
the loadings and their uncertainty has at least 1 advantage above
applying SEM to the estimated point estimates (posterior mode)
of the respective matrices. Uncertainty of the loadings (but not
the estimate of the loading itself) in a frequentist SEM is based on
the effective sample size specified to underlie the covariance matrix
under analysis. In a mixed model analysis, it is not obvious what
this sample size would be, especially on the between-individual versus residual levels. Statistically, this relates to the open question of
how many degrees of freedom a random effect actually has (e.g.,
Snijders and Bosker 1999). This issue is particularly problematic
for data collected in wild populations on marked individuals, where
individuals vary in the number of repeated measures collected and
the total number of individuals with data is usually restricted to
lie in the range where specifying different interpretations of sample
size has a strong effect on the estimated uncertainty.
Although our objective was not to explore alternative models, we
did want to confirm that our hypothesized path was a reasonable
description of the data. We used the posterior mode of the matrices P, ID, and R scaled to correlations to fit, in addition to our
hypothesized path (Figure 1)—also a model where all variables were
assumed uncorrelated and one where all variables were assumed to
be affected by a single underlying (latent) factor. Model fit of these
3 models was compared using Akaike information criterion (AIC).
Sample size for these alternative SEM models was set at the number of individuals.
Autonomy of the syndrome
Whenever the associations between more than 2 traits are considered, as we do here, it becomes challenging to interpret the biological relevance of all covariances between traits that are estimated.
This is because some covariances are likely to be relatively low,
whereas others may be strong. Given that we work in a multivariate framework, we would ideally want to quantify the biological
relevance of the whole covariance structure rather than trying to
interpret pairwise correlations. In this section, we describe a quantitative approach to capture whether the estimated between-individual covariances between traits (contained in matrix ID) are of such
magnitude that we can consider them biologically relevant.
We here used average autonomy a (Hansen and Houle 2008) as a
metric for describing the evolutionary relevance of our ID matrix.
Average autonomy was originally developed for testing whether
evolutionary constraints acted on associations between multiple
traits. In short, the average autonomy a of a matrix containing the
additive genetic (co)variances (G matrix) of k traits can be thought
of as the average constraint on a population’s capacity to respond
to all possible stabilizing selection gradients in all k directions.
When G is unconstrained and all k traits can evolve to the same
magnitude and completely independently from each other, a = 1.
When a falls below unity, the evolutionary trajectory is constrained
to some extent. When a = 0, the effective dimensionality of G is
<k (one or more of the eigenvalues of G equals zero). Hence, average autonomy is a metric, which quantifies an evolutionary relevant
property of the whole (co)variance matrix.
We cannot estimate G in our study system and, therefore, we
used between-individual (co)variances matrix ID as a proxy for
G (see Discussion for details on this assumption). We calculated
the autonomy of the between-individual (co)variance matrix IDS
between laying date, clutch size, coloration, and nest defense boldness, that is, IDS is the matrix of Equation 2 on level ID but without the bottom row (recruitment). Following standard practices in
Bayesian statistics, we calculated a for each of the 1000 posterior
IDS (co)variance matrices. Hansen and Houle (2008) advocated the
use of both mean trait standardization of the (co)variance matrix
and of variance standardization. Mean trait standardization of
posterior matrix IDS was done by using the posterior trait-specific
intercept, thereby taking forward both the uncertainty in the matrix
IDS and in the mean. Variance standardization was performed
by using the sum of the posterior VXI and VXR for each trait X as
estimate of phenotypic variance and hence integrates uncertainty
of both between-individual and phenotypic variances. Our results
are qualitatively the same for average autonomy of a nonscaled
matrix, but this latter is not informative as the various traits are
measured on different scales (Hansen and Houle 2008) and is
hence not reported. A general R script to calculate autonomy of
nonscaled, mean-scaled, and variance-scaled matrices is provided
in the Supplementary Material.
We inferred whether the observed correlational structure formed
an evolutionary constraint by comparing the estimated autonomy
aS based on the full IDS matrix to the autonomy expected if the
between-individual variances were the same, but covariances were
set to 0 (termed null autonomy a0, following Brommer 2014). For
the pth posterior (co)variance matrix IDS, p, aS , p = a ( IDS , p ) and
a0, p = a ( IDS , p * I ) , where “*” denotes the element-by-element
matrix product and I is an identity matrix (matrix with a diagonal
Brommer et al. • Hierarchical structure of a syndrome
807
to be high. Repeatability of clutch size and laying date was about
half the repeatability of nest defense boldness score. Most (83.4%,
457/548) of broods did not recruit any offspring to the breeding population, whereas 13.9% (76/548) recruited 1 and 2.7%
(15/548) recruited 2 offspring. We here consider recruitment as
a binomial process (recruited one or more offspring or not). The
probability of recruitment had, as expected for a measure of fitness, the lowest repeatability.
of 1s) of the same dimension as IDS (IDS,p * I is thus a matrix
having within its diagonal the same variances as in IDS but all
covariances set to 0). The lower 90% CRI of a0 was compared
with the upper 90% CRI of aS . The 90% CRI was used because,
by definition, a0 ≥ aS . This is because the average autonomy of a
matrix (when keeping the variances the same) is maximal when all
its covariances are zero. Hence, 1-tailed testing should be applied
(Brommer 2014). We here infer that the syndrome’s correlational
structure constrains the independent evolution of all traits significantly when a falls significantly below a0 (cf. Dochtermann and
Dingemanse 2013).
Multivariate analysis
Investigation of the phenotypic matrix revealed 4 strong correlations for which the CRI did not include 0 (Table 2). First, the size of
broods that were produced later in the season was smaller. Second,
broods that were produced later in the season were associated with
a lower nest defense boldness of the mother. Third, larger brood
sizes were associated with bolder mothers. Fourth, broods that were
produced later in the season had lower probabilities to recruit offspring later in life. These 4 correlations were also significant on the
within-individual level. On the between-individual level, however,
the CRI of all correlations overlapped with 0. Hence, the apparent
syndrome between boldness and the production of large clutches
early in the breeding season, for which there is strong evidence on
the phenotypic level, was not present on the between-individual
level but was driven by within-individual correlations.
The relationships on these different levels can be illustrated by
considering the raw data. Consider, for example, the negative phenotypic correlation between boldness and laying date (corrected
for annual variation) for all observations (Figure 2a). For individuals with repeated measures of both these traits (N = 115), we can
calculate the individual-specific means as a proxy estimate for i in
Equation 1. The individual-specific means of these traits do not
show a strong correlation (Figure 2b). For this same set of individuals, the within-individual (i.e., residual) correlation can be illustrated as the correlation between the difference between observed
(phenotypic) values and the individual-specific means of both traits,
which is clearly negative (Figure 2c).
Ethical note
Data analyzed in this article were collected as part of a long-term
project on tawny owls carried out by K.A. and T.K. from 1977
onward and from 2006 onward together with P.K. Checking of
nest-boxes during incubation, as well as trapping and handling
of birds, falls under the ringing licenses of these persons. Nesting
adult tawny owls were only caught and handled after their eggs had
hatched in order to avoid desertion due to human disturbance.
Results
Descriptive statistics
We used data consisting of 562 observation events (i.e., visits to the
nest where at least one of the trait considered was observed) of 237
individuals between 1979 and 2012. All traits were not measurable at each occasion leading to minor variation in the number of
observations and individuals (Table 1). Approximately 115 of the
individuals were measured repeatedly (2–9 times per individual,
and 1 individual 15 times).
All traits considered were repeatable (Table 1). Repeatability of
nest defense boldness was 0.32, which is typical for behavioral traits
(Bell et al. 2009). On average, nest defense boldness was scored
18.9 ± 0.4 SE (N = 544; 7 observations could not be dated) days
after laying the first egg. This repeatability analysis (Table 1) was
based on the first scoring of nest defense boldness for an individual during each year it was observed. Nevertheless, nest defense
boldness was also repeatable within years (Supplementary Table
S1). Furthermore, nest defense boldness was not affected by the
number of days between assaying it and the laying of the first
egg (Supplementary Table S1). We hence assume that the season’s
first score of nest defense boldness is representative for the individual during that year. Plumage coloration is a highly heritable
trait in tawny owls (Brommer et al. 2005; Gasparini et al. 2009;
Karell et al. 2011), and as expected, its repeatability was confirmed
Path analysis
We used the (co)variances between traits to analyze the explicit
hypothesis that variation in nest defense boldness was driven by laying date, clutch size, and plumage coloration and that this behavior
was under direct or indirect recruitment selection using path analysis (paths depicted in Figure 1). Path analysis concerned the full
posterior distribution of the matrices estimated by the multivariate
mixed model (as summarized in Table 2) and thus took the uncertainty in the covariance matrices forward into the path analysis.
Table 1
Descriptive statistics and repeatabilities
Trait
Nind
Nobs (1/2/3/4/5+)
Median
SD
Range
R (95%CRI)
Laying date
Clutch size
Coloration
Boldness
Recruitment
225
237
235
237
236
545 (110/42/29/11/33)
560 (121/41/31/11/33)
547 (121/43/27/12/32)
551 (120/46/29/10/35)
548 (122/44/27/11/20)
−2
4
7
3
12.77
1.06
2.61
1.06
−44 to +38
0 to 9
4 to 14
1 to 5
0 to 1
0.16 (0.10, 0.26)
0.17 (0.09, 0.26)
0.91 (0.88, 0.93)
0.32 (0.23, 0.42)
0.04 (0.01, 0.12)
Laying date is expressed as the deviation to the long-term average (0 = 31 March). Nind = number of individuals; Nobs = number of observations where the
number of individuals with 1, 2, 3, 4, and 5 or more observations are presented within brackets. The median, raw-data SD, and extreme values of the data are
given. Repeatability (R) and its 95% CRI were based on the posteriors for variance components in a multivariate Bayesian mixed model as detailed in the text.
Behavioral Ecology
808
Table 2
Correlation matrices of trait associations on different levels
LD
Panel A
Phenotypic correlations
CS [CRI]
−0.20 [−0.29, −0.12]
Col [CRI]
−0.003 [-0.12, 0.09]
Bold [CRI]
−0.16 [−0.26, −0.08]
Rec [CRI]
−0.17 [−0.43, −0.03]
LD
CS
0.09 [−0.03, 0.17]
0.16 [0.08, 0.25]
−0.01 [−0.18, 0.30]
CS
Panel B
Residual correlations and between-individual correlations
LD [CRI]
−0.08 [−0.39, 0.33]
CS [CRI]
−0.24 [−0.33, −0.15]
Col [CRI]
0.02 [−0.08, 0.16]
0.04 [−0.07, 0.16]
Bold [CRI]
−0.21 [−0.34, −0.13]
0.15 [0.03, 0.25]
Rec [CRI]
−0.23 [−0.53, −0.05]
0.07 [−0.17, 0.38]
Col
0.10 [−0.01, 0.21]
0.21 [−0.13, 0.34]
Bold
−0.10 [−0.37, 0.08]
Col
Bold
Rec
−0.03 [−0.31, 0.20]
0.12 [−0.16, 0.35]
−0.01 [−0.33, 0.31]
0.34 [−0.07, 0.54]
0.15 [−0.05, 0.37]
0.06 [−0.53, 0.35]
−0.09 [−0.58, 0.45]
0.39 [−0.31, 0.79]
−0.43 [−0.80, 0.34]
0.06 [−0.05, 0.17]
0.05 [−0.16, 0.26]
−0.10 [−0.41, 0.19]
In panel A, phenotypic correlations are shown below the diagonal and in panel B, between-individual level correlations are shown above the diagonal and
residual correlations below the diagonal. Point estimates of correlations are the mode of the posterior correlations, and the 95% CRI is provided within
square brackets. Correlations for which the CRI does not overlap with 0 are indicated in bold and are considered as statistically significant. Abbreviations: Col,
plumage coloration; Bold, nest defense boldness; CS, clutch size; LD, laying date; Rec, recruitment. Full covariance matrices are presented in Supplementary
Table S2 and fixed effect estimates in Supplementary Table S3.
Our hypothesized path fitted the data satisfactorily on the phenotypic, between-individual, and the within-individual level (Table 3).
Furthermore, AIC comparisons between our hypothesized path
model and the alternative of no correlations and of a single latent
factor underlying all trait values also supported our hypothesized
path (Table 3).
Investigation of the path loadings (based on carrying out a path
analysis on each posterior scaled covariance matrix) demonstrated
no support for any path on the individual level (Table 4). In contrast, there was strong support for a negative correlation between
clutch size and laying date, as well as for a negative loading of laying date on nest defense boldness on the phenotypic and withinindividual levels (Table 4). Path analysis demonstrated that clutch
size did not significantly affect boldness on the within-individual
level after controlling for the strong within-individual covariance
between laying date and clutch size. Residual effects on laying date
thus drive variation in nest defense boldness.
Autonomy based on covariances
The average autonomy a (Hansen and Houle 2008) of the
between-individual (co)variances of laying date, clutch size, coloration, and nest defense boldness was 0.491 (upper 90% CRI
0.674) and 0.697 (upper 90% CRI 0.768) for mean standardized
and variance standardized (co)variances, respectively. The CRI for
both measures included the lower 90% CRI of average autonomy
a0 based on assuming that all covariances were 0, which were 0.400
and 0.724, respectively. Hence, there was no evidence for evolutionary constraints due to the observed between-individual covariances.
Discussion
We have explored variation in nest defense boldness, quantified as
the tendency of a female to stay on her nest protecting her eggs
during a standardized assay, which simulates attack by a predator.
Our objective was to explore whether this behavior forms a syndrome with other traits, as well as how direct and indirect selection
acts on all of these traits within a multivariate hypothesis-driven
framework. We formalize our hypothesis as a specific path, which
denotes—based on literature studies—how we believe these traits
are causally related. We quantify the coefficients in this path on
the phenotypic level and on the between-individual and withinindividual levels using Bayesian methodology, which allows us to
consider path coefficients and their uncertainty, while partitioning the phenotypic covariance matrix into these latter levels. This
approach hinges on the information provided by making repeated
measures on all traits. The main message of our findings is that the
strikingly strong phenotypic correlations between clutch size, laying
date, nest defense boldness, and fitness, which we expected to find,
are largely due to processes occurring on the residual level, thereby
capturing processes creating within-individual (co)variation. Hence,
there is no true syndrome as based on covariation of the individualspecific values i (Equation 1) for the various traits considered here.
We thus find no evidence that a female with an individual-specific
value for early breeding also will, on average, be bold when defending its clutch and have a high individual-specific fitness value in
terms of offspring recruitment, despite the fact that the phenotypic
associations between these traits are strong. Instead, residual, and
thus within-individual, variation in laying date covaries with withinindividual variation in nest defense boldness and recruitment. This
within-individual covariance produces the phenotypic pattern
where broods produced early in the season are defended by bolder
mothers and recruit more offspring. Because these associations are
absent on the individual level, it implies that they may have little
implications for understanding the evolution of individual mean
trait values. Our findings thus illustrate how nonheritable (and
hence evolutionary transient) processes can lead to erroneous conclusions regarding the evolutionary relevance of syndrome covariation when analyses of trait–trait and trait–fitness associations are
performed on the phenotypic level.
What are within-individual correlations?
We find clear evidence for strong correlation and path loadings
on the within-individual level between clutch size–laying date and
Brommer et al. • Hierarchical structure of a syndrome
Figure 2
Illustration based on the raw data of the relationship between nest defense
boldness and laying date on (a) the phenotypic, (b) between-individual,
and (c) residual levels. Note that this is an illustration and that the analysis
is based on a multivariate mixed model reported in Table 2. Observed
laying date and nest defense boldness were corrected for annual effects by
subtracting the annual mean. (a) Phenotypic values based on data on all
individuals (correlation r = −0.19). (b) Individual-specific estimates (i in
Equation 1) were approximated as the mean values for nest defense boldness
and laying date for 115 individuals with multiple observations (r = −0.048).
(c) Residual values were approximated for these same individuals by the
deviation between the observed value minus the individual-specific mean
values (r = −0.24).
laying date–nest defense boldness. In addition, the strong fecundity
selection on laying date operates exclusively on the within-individual level. What drives these within-individual covariance and
809
path loadings? Residuals are statistically defined as the deviation
between the measured trait value and the value expected on the
basis of the fixed effects and the individual-specific effect (Equation
1). The statistical null assumption is that these deviations are random noise and that they therefore, by extension, are also uncorrelated between traits. Nevertheless, effects caused by factors that
are not put in the model (latent factors) also end up in the residuals.
Within a multivariate framework, it is conceivable that a latent factor affects multiple traits (including fitness) and, thereby, causes a
residual (i.e., within-individual) covariance. Conceptually, multiple
traits (laying date, boldness, and recruitment) can be thought of as
traits which jointly show a plastic response to the same latent factor, leading to covariation of these traits on the within-individual
level. Thus, under better than average environmental conditions, a
tawny owl female lays earlier than her individual-specific trait value
i (Equation 1) for laying date and also defends her nest bolder than
her individual-specific value for boldness, and her offspring recruit
better than expected from her individual-specific value for recruitment. Under below-average environmental conditions, a female
lays later, is less bold, and recruits less offspring than expected on
the basis of her individual-specific values for these traits. Indeed,
this pattern of within-individual covariance is one classic explanation for why strong phenotypic selection for earlier laying (which
is found in a plethora of organisms) does not lead to evolution
of the timing of laying (Price et al. 1988). We here focus on the
individual-specific mean trait values i, which conceptually form
the elevations of individual-specific reaction norms (Nussey et al.
2007). As such, within-individual covariance has no impact on the
evolutionary dynamics of the mean trait. Nevertheless, the joint
plasticity of multiple traits in response to environmental conditions,
as we observe here, may still constrain the population’s capacity to
respond to changes in its environment. Furthermore, from an ecological perspective, it will be of interest to understand the driver of
this plasticity.
Because we include year and a female’s age in the mixed model,
we are assured that the residual correlations are not due to annual
or age-specific effects. Residual correlations are also not caused by
environmental effects, which are permanently associated with an
individual because these appear in the individual-level correlation
(so called permanent environmental effects). For example, tawny
owls defend territories in which they stay year-round and typically
during their entire breeding career (Saurola 1987). Hence, if territories vary in their quality on a temporal scale long enough that they
can be considered as fixed with respect to the breeding life span of
a female (typically 1–4 years), this “territory effect” becomes part of
the variance between individuals. Conceivably, for a predator as the
tawny owl, variation in local environmental conditions during its
life span is likely caused by spatial variation from year to year in the
abundance of its prey, small mammals, and birds. A given territory
may, in 1 year, contain more food resources than the annual average
but may be poorer than the annual average in the next year. This
type of variation may then affect multiple traits, leading to earlier
laying and bolder behavior as well as a higher recruitment relative
to the individual-specific values for these traits in years of aboveaverage local conditions and vice versa in years of below-average
local conditions. Although local food resources are a good candidate for causing the residual correlation we observe, it should be
noted that other elements of “local environmental conditions” (e.g.,
abundance of parasites and local abiotic winter conditions) could
also be at play and that these factors are not mutually exclusive.
An experimental approach where the putative local environmental
Behavioral Ecology
810
Table 3
Goodness of fit of the hypothesized path model (Figure 1), and its AIC comparison to the alternative models of “no correlations
between traits” and of “a single underlying latent factor”
Test
Phenotype
Individual
Residual
Model fit
Path versus no correlations
Path versus single latent factor
χ2 = 1.93, P = 0.38
ΔAIC = 29.9
ΔAIC = 16.2
χ2 = 3.42, P = 0.18
ΔAIC = 134.7
ΔAIC = 27.0
χ2 = 0.75, P = 0.69
ΔAIC = 32.5
ΔAIC = 4.2
Likelihood based on path analysis of the correlation matrix between all traits as derived from the posterior modes of the mixed model (co)variances (Table 2).
ΔAIC values are the AIC deviations from the path model. Model comparisons are shown on the phenotypic level (Phenotype), between-individual level
(Between), and residual level (Residual).
Table 4
Path loadings (partial correlation coefficients) and their CRIs derived from a path analysis
Association
Path
Phenotype [CRI]
Individual [CRI]
Residual [CRI]
Col → Bold
CS ↔ LD
CS → Bold
LD → Bold
Bold → Rec
LD → Rec
CS → Rec
Col → Rec
a1
a2
a3
a4
a5
a6
a7
a8
0.07 [−0.02, 0.20]
−0.20 [−0.29, −0.12]
0.14 [0.04, 0.22]
−0.14 [−0.24, −0.06]
−0.18 [−0.42, 0.03]
−0.29 [−0.47, −0.06]
0.02 [−0.21, 0.25]
0.22 [−0.12, 0.35]
0.06 [−0.08, 0.36]
0.08 [−0.39, 0.33]
0.20 [−0.07, 0.56]
0.07 [−0.26, 0.39]
−0.35 [−0.82, 0.32]
−0.15 [−0.50, 0.37]
−0.15 [−0.52, 0.48]
0.45 [−0.31, 0.80]
0.08 [−0.05, 0.17]
−0.24 [−0.33, −0.15]
0.12 [−0.03, 0.20]
−0.21 [−0.33, −0.11]
−0.17 [−0.47, 0.12]
−0.30 [−0.56, −0.08]
−0.01 [−0.22, 0.33]
0.08 [−0.13, 0.27]
The paths and their corresponding parameters are illustrated in Figure 1. Coefficients with their 95% CRI in square brackets are shown on phenotypic level
(Phenotype), between-individual level (Individual), and residual level (Residual). Abbreviations: Col, plumage coloration; Bold, nest defense boldness; CS, clutch
size; LD, laying date; Rec, recruitment.
driver is manipulated in order to study its consequences for laying
date and nest defense boldness is required to critically test specific
hypotheses.
Partitioning covariances: power and biologically
relevant effect sizes
Whether we can or even should aim to understand associations
between traits on the individual level is the subject of current
debate in behavioral ecology (Dingemanse et al. 2012; Garamszegi
and Herczeg 2012; Brommer 2013). Partitioning the phenotypic
covariance matrix requires repeated measures on various traits.
This data structure means there will always be more observations
than individuals (subjects). Hence, there is more information to estimate the phenotypic and residual covariances than the individuallevel covariances. This fact transpires from our results, where the
95% CRIs of the residual correlations tend to be about half of
the interval of the corresponding individual-level ones. In general,
reasonable power and precision of estimates of between-individual correlations require >100 subjects to be measured repeatedly
(Dingemanse and Dochtermann 2013). In our case, we have information accrued during 34 years covering approximately 237 individuals of which approximately 115 were measured repeatedly.
Hence, one caveat of our findings is whether we indeed have the
power to reduce the uncertainty of between-individual correlations
or whether this uncertainty is so large that it will obscure all except
the largest effect sizes. Simulations suggest that our data structure
provides a power of ≥15%, ≥60%, and ≥95% to detect a significant individual-level correlation of 0.1, 0.3, and 0.5 respectively
(Figure 1 in Dingemanse and Dochtermann 2013). Thus, our data
have limited power to detect statistically significant between-individual correlations falling below 0.3. It, therefore, remains possible
that further measurements would decrease the uncertainty around
some of our correlations to such an extent that they would deviate
significantly from 0. At the same time, however, we believe that our
inferences regarding syndrome structure occurring on the residual
but not on the individual level are robust to the inclusion of more
data. This is because the point estimates for our path coefficients on
the clutch size–laying date–coloration–boldness syndrome on the
between-individual level are all close to 0 (with the possible exception of the effect of clutch size on nest defense boldness).
The other side of the issue of considering statistical power is at
what magnitude individual-level correlations in a syndrome become
biologically relevant. We here explored this issue by calculating the
average autonomy (Hansen and Houle 2008) of the clutch size–laying date–coloration–boldness syndrome. Average autonomy captures the general capacity of a population to respond to selection
in multivariate space and is defined for the additive genetic (co)variance matrix G. We have not estimated G, but we here make the
assumption that the between-individual (co)variance matrix ID is
a decent description of G for these traits. This assumption breaks
down to assuming 1) that all traits in the syndrome are heritable
and 2) that permanent environmental effects (which are included
in ID) do not distort the correlational structure of G. By removing
R and using the between-individual covariance matrix ID, we are
1 hierarchical step closer to G (which is a further partitioning of
matrix ID). In general, however, the use of ID as a proxy for G is
related to making the “phenotypic gambit,” which is the assumption that phenotypic (co)variance matrix P captures G (Grafen
1984; Brommer 2013). Testing this assumption requires estimation
of G, which we cannot at present do. Hence, our inferences regarding average autonomy should be interpreted with caution.
We find that the between-individual correlations in the clutch
size–laying date–coloration–boldness syndrome do not significantly
impair the average autonomy of the population compared with the
average autonomy value expected if all correlations were 0. A recent
compilation of average autonomy of behavioral syndromes suggests
Brommer et al. • Hierarchical structure of a syndrome
that syndrome structure tends to constrain the average autonomy
below the expected value for average autonomy (Dochtermann
and Dingemanse 2013). In our study, however, the uncertainty
around the elements of the (co)variance matrices is taken forward in estimating the uncertainty in average autonomy, which
is not possible in literature-based studies. It would be instructive to also explore the autonomy of the syndrome to the actual
selection gradients acting on it, but this requires to (apart from
recruitment selection) also integrate survival selection into the
current approach. In any case, the nonsignificant reduction in
average autonomy suggests that the low correlation characterizing our syndrome’s structure has no evolutionary relevance (to
the extent that between-individual (co)variances can be considered a proxy for additive genetics ones).
Conclusions
Many behavioral syndromes described to date are based on phenotypic correlations between traits. Such studies make the “individual gambit” (Brommer 2013) by assuming that phenotypic
correlations are representative of underlying individual-level correlations when considering behavioral traits and selection on these.
We find clear evidence that the individual gambit does not hold
in our case: Despite clear phenotypic correlations, associations
between laying date, nest defense boldness, and recruitment are
not due to covariation of the individual-specific values for these
traits (i.e., between-individual correlations) but are instead strongly
determined by unidentified environmental conditions generating
residual (i.e., within-individual) correlations in these traits. Clearly,
this finding does not rule out that the individual gambit works in
the wild. For example, Kluen et al. (2014) found an absence of
residual covariance between a number of behavioral, physiological,
and morphological traits in a wild passerine. It is difficult, however,
to a priori know whether the individual gambit will hold or not.
It seems particularly likely that residual covariance is strong when
it involves behaviors closely associated with fitness. Heterogeneity
in environmental conditions experienced by an individual during
its life span will then likely lead to joint expression of both traits
in the direction of increased fitness when environmental conditions are favorable and vice versa under adverse conditions (van
Noordwijk and de Jong 1986). Little conclusive can be said on this
issue, however, until there are more studies that dissect phenotypic
correlations into underlying between-individual and residual ones.
The approach detailed in this article is a potentially versatile technique, which can be applied to other systems in order to tackle this
interesting issue.
Supplementary Material
Supplementary material can be found at http://www.beheco.
oxfordjournals.org/
FUNDING
This work was partly supported by the Academy of Finland (J.E.B.,
P.K.).
We thank Prof. N.J. Dingemanse for suggestions on implementing the
Structural Equation Model within a Bayesian multivariate mixed model.
Comments by P.-O. Montiglio and 1 anonymous reviewer greatly improved
811
the manuscript. All members of Kimpari Bird Projects (KBP) are thanked
for their assistance in the field. This is publication nr 16 from KBP. K.A.,
T.K., and P.K. collected the data, J.E.B. and P.K. analyzed the data, and
J.E.B. and P.K. wrote the manuscript.
Handling editor: Alison Bell
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