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Research
Cite this article: Sæther B-E, Visser ME,
Grøtan V, Engen S. 2016 Evidence for r- and
K-selection in a wild bird population:
a reciprocal link between ecology and
evolution. Proc. R. Soc. B 283: 20152411.
http://dx.doi.org/10.1098/rspb.2015.2411
Received: 8 October 2015
Accepted: 4 April 2016
Subject Areas:
evolution, ecology
Keywords:
density dependence, density-dependent
selection, environmental stochasticity, great tit,
phenotypic evolution, r- and K-selection
Author for correspondence:
Bernt-Erik Sæther
e-mail: [email protected]
Evidence for r- and K-selection in a wild
bird population: a reciprocal link between
ecology and evolution
Bernt-Erik Sæther1, Marcel E. Visser3, Vidar Grøtan1 and Steinar Engen2
1
Centre for Biodiversity Dynamics, Department of Biology, and 2Centre for Biodiversity Dynamics, Department of
Mathematical Sciences, Norwegian University of Science and Technology, Trondheim 7491, Norway
3
Department of Animal Ecology, Netherlands Institute of Ecology (NIOO-KNAW), PO Box 50, Wageningen 6700
AB, The Netherlands
Understanding the variation in selection pressure on key life-history traits is
crucial in our rapidly changing world. Density is rarely considered as a selective agent. To study its importance, we partition phenotypic selection in
fluctuating environments into components representing the population
growth rate at low densities and the strength of density dependence, using a
new stochastic modelling framework. We analysed the number of eggs laid
per season in a small song-bird, the great tit, and found balancing selection
favouring large clutch sizes at small population densities and smaller clutches
in years with large populations. A significant interaction between clutch size
and population size in the regression for the Malthusian fitness reveals that
those females producing large clutch sizes at small population sizes also are
those that show the strongest reduction in fitness when population size is
increased. This provides empirical support for ongoing r- and K-selection in
this population, favouring phenotypes with large growth rates r at small population sizes and phenotypes with high competitive skills when populations
are close to the carrying capacity K. This selection causes long-term fluctuations around a stable mean clutch size caused by variation in population
size, implying that r- and K-selection is an important mechanism influencing
phenotypic evolution in fluctuating environments. This provides a general link
between ecological dynamics and evolutionary processes, operating through
a joint influence of density dependence and environmental stochasticity on
fluctuations in population size.
1. Introduction
One of the central issues in ecology has been the influence of density dependence
upon fluctuations in population size, which lead to controversies lasting for several decades [1]. An important contribution was provided by May and co-workers
who showed that even simple population models could produce extremely complicated population dynamics [2] and that most populations showed patterns in
population fluctuations that clearly indicated regulatory effects of density dependence [3]. However, even though ecologists have for a long time realized the
importance of density dependence, estimating the form of density regulation
and strength of density dependence in natural populations have proved difficult
[4,5]. This occurs because a large sample covering the full range of variation in
population size is necessary for obtaining reliable estimates of how a change in
population size affects the population size the following year(s) [6]. This requires
long time series, preferably based on precise population estimates [7].
In population genetics, classical models assume a constant population size. In
an attempt to include more ecological realism in population genetic models
MacArthur [8] showed that in a stable environment under density-dependent
selection, evolution will maximize equilibrium population size or the carrying
capacity of the population. This important result formed the foundation for the
introduction by MacArthur & Wilson [9] of r- and K-selection as an important
selective agent in natural populations. Based on the assumption of a trade-off
& 2016 The Author(s) Published by the Royal Society. All rights reserved.
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2. Material and methods
(a) Study population and field procedures
We analyse selection on the number of eggs produced per season
based on data from a long-term (1955–present) population study
of great tits at the Hoge Veluwe National Park, the Netherlands.
The area consists of mixed pine-deciduous woodland on poor
sandy soils. To ensure that availability of artificial nest sites did
not limit population size, we provided a surplus of nest-boxes
[31]. The adult survival rate of great tits in this population was
around 0.40 [32], strongly dependent on the beech crop cycle.
The population dynamics of great tits is dependent on a
2
Proc. R. Soc. B 283: 20152411
to analyse how phenotypic selection depends upon population size. We choose the total number of eggs produced
per female during the breeding season as the phenotypic
trait studied. Previous studies have shown stabilizing selection around an intermediate clutch size in great tits [25,26],
which is affected by variation in population size [27]. We
use the model of Engen et al. [21] to analyse the joint process
for mean character and log population size in a fluctuating
environment. A general result obtained from this model is
that with reasonable trade-offs preventing unlimited growth
of fitness, evolution approaches stationary fluctuations of
the mean character in the population, with the expected
response always in the direction that increases average population size. Hence, the mean phenotype during a long time
interval represents a compromise between phenotypes with
large growth rates at small population sizes and those with
weak density regulation [21,28]. In addition, stochastic effects
make the mean fluctuate continuously, generating fluctuations
in population size. This provides a tool for empirical analyses
of density-dependent selection if the strength of density dependence g(z) is not constant among phenotypes. For r- and
K-selection to occur, there must exist a trade-off between the
growth rate at low densities r and g (or between r and K)
because otherwise the evolution of the mean phenotype
would always increase the mean growth rate r and decrease
the mean strength of density regulation g, resulting in correlated selection for large r and K. Thus, the requirements of
such phenotypic trade-offs between major life-history characters means that empirical analyses of evolution by means of
r- and K-selection are challenging because obtaining reliable
estimates of density-dependent selection as well as genetic
covariances among phenotypic characters are in general difficult in natural populations [29]. Here we provide evidence
that fluctuations in population size can act as an important
selective agent of mean clutch size z in great tits. We show,
using a novel approach based on a parametrizing of a model
for r- and K- selection including realistic ecological dynamics
[21], that there is phenotypic variation in the strength of density
regulation g
as well as in the population growth rate r at small
densities. More importantly, we show that there is an interaction effect between population size N and mean phenotype
on the Malthusian fitness. Consequently, when the population
size fluctuates, this generates r- and K-selection as predicted by
MacArthur & Wilson [9], resulting in evolution towards an
intermediate clutch size that varies little through time. The evidence for such density-dependent selection is important
because it provides empirical support for a general mechanism
for a reciprocal coupling between ecological and evolutionary
processes [30].
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between traits affecting selection at small population sizes
and those favoured at larger population sizes, they argued
that high population growth rates should be favoured when
the number of individuals was small (r-selection). By contrast,
at large population sizes selection should favour highly
competitive phenotypes, resulting in an increased carrying
capacity (K-selection).
This introduces a complication different from that in ecological analyses of density dependence; density-dependent
selection requires that changes in population size affect the fitness of different phenotypes differently. For example, the
occurrence of r- and K-selection in a population requires that
the fitness of phenotypes favoured at small population sizes
are more strongly influenced by a change in population size
than the fitness of those phenotypes with high mean individual
fitness close to the carrying capacity K. Thus, analyses of
density-dependent selection must include time series of how
fitnesses of different phenotypes are affected by fluctuations
in population size, which requires estimates of second-order
interaction effects between population size and phenotypic
variation on fitness that may be small compared with the
first-order effects. In addition, as in ecology, the effects of
density dependence should be separated from the influence
of environmental variation on the distributions of phenotypes.
Consequently, this makes data requirements for statistical analyses of density-dependent phenotypic selection in natural
populations extensive because long time series of individual
phenotype-specific differences in fitness are needed.
A central focus in evolutionary biology has been to understand factors affecting the rate of phenotypic evolution [10].
A large number of studies covering a wide variety of taxa document that phenotypic selection acting on quantitative
characters occurs regularly in natural populations [11–13],
yet processes explaining variation in the strength of this
selection in time and space are poorly known [11,13–15].
Because populations of even closely related species may
show large differences in the magnitude of population variability [16,17], density-dependent selection may provide a general
mechanism with important implications for how fast phenotypes will change over time. For instance, if there is no
density dependence, the long-run growth rate of the population is maximized [18] and stasis will only occur when
there is balancing selection around an intermediate optimal
phenotype (see Chevin et al. [19] and references therein for
analyses of the effects of stabilizing selection on phenotypic
evolution in a fluctuating environment). Basically, this corresponds in the terminology of MacArthur & Wilson [9] to a
form of r-selection. By contrast, selection may also favour individuals with phenotypes that are little affected by population
density and thus produces K-selection. Although these cases
represent r- and K-selection, this does not necessarily imply
that there are fluctuations within a population between these
two types of selection. However, if there is genetic variation
in growth rate as well as strength of density regulation with a
trade-off between phenotypes favoured at small population
sizes and those that are less affected by population density,
fluctuating r- and K-selection around an intermediate phenotype, dependent upon the environmental stochasticity may
occur [20–23]. Thus, the influence of fluctuations in population
size on phenotypic selection may be crucial for understanding
basic features of phenotypic evolution [24].
Our aim with the present study is to use a unique longterm demographic dataset of great tits in the Netherlands
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Our analysis is based on females’ individual fitness W ¼ I þ B/2,
which is an individual’s contribution to the next year’s population. Here I is an indicator of female survival with value 1 for
survival and otherwise 0, while B is its number of recruits of
both sexes entering the breeding population the following year
or later. Individual fitness is a stochastic variable [38] with some
distribution expressing stochastic variation among individuals
within years, representing demographic stochasticity, depending
on phenotype z, population size N as well as the environment defined by some vector 1. Writing the expected fitness of
an individual of phenotype z at population size N in environment
1 as EðWjz, N, 1Þ ¼ eMðz,N,1Þ , the function M(z, N, 1) is then the
Malthusian parameter of a hypothetical population of individuals
with phenotype z and population size N under constant environmental conditions 1. Averaging W over demographic as well
as environmental stochasticity using the notation E1 for the expectation, we define lðz, NÞ ¼ E1 ðWjz, N, 1Þ ¼ erðz;NÞ , where r(z, N)
is the deterministic growth rate of a hypothetical population of
individuals with phenotype z at density N. Averaging the conditional Malthusian parameter over the fluctuating environment
1 we obtain the mean Malthusian parameter mðz, NÞ ¼ E1 M
ðz, N, 1Þ for given z and N, which is the long-run growth
rate of a hypothetical population with parameters z and N. The
first-order approximation to the mean Malthusian parameter is
mðz, NÞ ¼ E1 lnðWjz, N, 1Þ rðz, NÞ 1
rðz, NÞ s2e ,
2
1
var1 [Mðz, N, 1Þ]
2l ðz, NÞ
2
ð2:1Þ
where the last term, which is generated by the common environmental noise, will depend slightly on z and N, but is here
approximated by its mean value s2e through time.
An important general result [21] is that expected evolution of
the mean phenotype z subject to density-dependent selection
always increases the function
sðzÞ
s2 ðzÞ
QðzÞ ¼
gðKðzÞÞ:
ð2:2Þ
¼ 1 e
ðzÞ
2rðzÞ
g
Here sðzÞ is the long-run growth rate of the population in the
absence of density regulation so that sðzÞ ¼ rðzÞ 1=2 s2e ðzÞ,
where rðzÞ is the deterministic growth rate of the mean phenotype in the average environment, s2e ðzÞ is the environmental
ðzÞ is the average strength of density dependence in
variance, g
the population growth rate and g(N ) is an increasing function
of N describing the density regulation (for theta-logistic density
regulation g(N ) ¼ Nu and for the logistic model g(N ) ¼ N ). The
(c) Estimation procedures
We perform the statistical analysis on the individual fitness
of females W using a mixed log-linear model with 2W ¼ 2I þ B
as dependent variables taking integer values 0, 1, 2,. . .. Then
ln Eð2Wjz, NÞ ¼ b01 þ b2 z þ b3 z2 þ b4 N þ b5 Nz þ 1, where b01 ¼
b1 þ ln 2 1=2 s2e and the temporal variance of e is the environmental variance s2e : Writing W for the vector of observed
individual fitness in a given year with population size N and
b ¼ ðb10 , b2 , b3 , b4 , b5 ÞT , where superscript T denotes matrix
transposition, the model takes the form ln Eð2WÞ ¼ Xb þ 1U,
where E denotes the expectation. The left side is here the
column vector with components Eln(2W ) defined for each
observed female with observed dependent variable 2W a given
year, the rows of X are the individual vectors ð1, z, z2 , N, NzÞ
of these individuals and U is a normal environmental noise variable with zero mean and variance s2e , assumed to be
independent among years.
(d) Ecological and evolutionary dynamics
Engen et al. [21] showed that the dynamics of total population size
N in this model is of the logistic type determined by the mean
value of the parameters across individuals. Let p(z) be the
normal phenotypic distribution of z with evolving mean z and variance P Ðassumed to be constant.Ð The mean parameters are then
r0 ðzÞ ¼ r0 ðzÞpðzÞdz and g
ðzÞ ¼ gðzÞpðzÞdz: Assuming that selection is weak so that N changes much faster than z, the infinitesimal
mean and variance of the diffusion approximation for ln N for a
z, NÞ ¼ sðzÞ g
ðzÞN
given z is the mean Malthusian fitness mð
and s2e , respectively, where sðzÞ ¼ r0 ðzÞ s2e =2 is the long-run
growth rate for densities close to zero. Then the selection differential is according to Lande & Arnold [39] and Lande et al. [20]
z, NÞ, where P is the phenotypic variance. With appropriPrmð
ately defined trade-offs preventing unlimited growth of z,
Engen et al. [21] showed that z will have stationary fluctuations
around the mean phenotype z*, maximizing the function
QðzÞ ¼ sðzÞ=
gðzÞ, where s2e appearing in sðzÞ in general also
may depend on the mean phenotype (see Engen et al. [21] for
details). Writing KðzÞ ¼ r0 ðzÞ=
gðzÞ for the carrying capacity
in the corresponding deterministic model, the function that
is maximized (equation (2.2)) can alternatively be written
3
Proc. R. Soc. B 283: 20152411
(b) Model
parameter KðzÞ is then the carrying capacity in the corresponding
deterministic model so that gðKðzÞÞ ¼ rðzÞ=
gðzÞ: The expected
evolution of the mean phenotype z under density-dependent
selection will be towards the value zopt maximizing QðzÞ,
which is the mean of g(N) for a given z [21]. The expected evolution of z thus corresponds to an increase of QðzÞ, but
environmental stochasticity always perturbs it back to values
slightly below the maximum so that z has temporarily stationary
fluctuations around the optimal phenotypic value zopt.
We adopt the model of Engen et al. [21] writing rðz, NÞ ¼
r0 ðzÞ gðzÞN defining a logistic dynamic model [17] for a
hypothetical population of individuals with phenotype z. Here
r0(z) is the deterministic growth rate at small population sizes,
while g(z) defines the strength of density regulation. Because
large variation in the deterministic growth rates at small densities
with variation in clutch size is known to occur [25,27], it is required
to use a second-degree approximation r0 ðzÞ ¼ b1 þ b2 z þ b3 z2 ,
also allowing for variation in the slopes. The deterministic
growth rate then has a maximum if b3 , 0. There is, on the other
hand, much less knowledge about the phenotypic variation in
the strength of density regulation. We, therefore, believe that the
best choice for achieving our main goal of detecting a decrease in
g(z) with increasing phenotype, which is required for densitydependent selection to occur, is to avoid over-parametrization by
using a simple linear relationship gðzÞ ¼ b4 b5 z to describe
how the strength of density dependence depends on phenotype z.
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combination of density-dependent effects as well as environmental
fluctuations especially caused by variation in beech crops and
winter temperatures [33– 35]. In our study populations, immigrants constitute an important part of the population and
strongly affect population dynamics [31].
We checked nest-boxes for nest building, number of eggs or
number of nestlings at least once a week from April onwards.
The parents were caught when the nestlings were 7–10 days old.
When already ringed they were identified, if unringed they were
given a metal ring with a unique number. Nestlings were ringed
on day 7. Female great tits can produce a second brood within
the same season (i.e. raising a new brood after successfully
fledging the first brood), although the frequency of this doublebrooding has declined in recent decades in this population [36].
Unringed females were not included in the analyses, as their survival to future breeding seasons could not be determined. The
probability of recapturing a female was very high (average ¼
98.7%) [37]. Manipulated broods (both parents and offspring)
were excluded from all analyses.
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ð2:3aÞ
and
ðzÞ ¼ b4 b5z,
g
ð2:3bÞ
mean Malthusian fitness
−0.2
N = 20
−0.4
N = 70
−0.6
−0.8
N = 125
−1.0
−1.2
N = 200
−1.4
5
10
15
20
mean total clutch size
25
5
10
15
20
mean total clutch size
25
(b)
1.5
selection gradient
s2e
2
4
0
1.0
0.5
0
−0.5
−1.0
which determines the function QðzÞ and the centre phenotype z*,
maximizing QðzÞ. The individual fitness will show a similar
pattern of variation with z as the mean Malthusian fitness, just
differing with a constant b3P. The estimate of the variance P
^ ¼ 20:05:
was P
−1.5
(e) Estimation of heritability
The heritability was estimated following procedures in Husby et al.
[40] using a residual maximum-likelihood mixed model (animal
model). Animal models are based on pairwise relatedness between
all individuals and partition phenotypic variance into its additive
genetic and environmental variance components [41].
(f ) Simulations of phenotypic evolution
The ecological and evolutionary process can be simulated
taking selection and random genetic drift as well as the estimated
heritability and stochastic environmental variation into account.
The dynamics of N are simulated by the mixed log-linear
model for individual fitness that was fitted to the data (equation
(2.2)), using the actual parameter estimates. The response to
zÞ ¼ h2 Pðb2 þ 2b3 z þ b5 NÞ, whereas the
selection is h2 Prmð
change in breeding value due to random genetic drift is
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
pffiffiffiffiffiffiffiffiffiffiffi
h2 V P=Ne ¼ h2 V s2d P=N , where Ne ¼ N=s2d is the effective
population size [42] and V is a random variable with expectation 0 and unit variance [38,43]. Following procedures in
Sæther et al. [44], the estimate of the demographic variance was
^d2 ¼ 0:42:
s
The simulations of the temporal variation in breeding values
assume that environmental stochasticity affects all phenotypes
similarly, that there is no phenotypic plasticity and that the
immigrants have the same z as natives.
3. Results
Our analyses reveal that mean Malthusian fitness (equation
(2.1)) as well as the selection differential (the gradient of
z, NÞ with regard to z) changed with phenotypic mean
Pmð
in a way that depends on population size (figure 1 and
table 1). The mean fitness decreased considerably with population size (figure 1a), confirming strong density regulation.
Malthusian fitness
(c)
0.4
CS
0.2
CS =
= 12
CS
=1
8
10
CS
0
CS = 5
−0.2
= 15
CS
=2
0
−0.4
CS
−0.6
=2
5
0
50
100
150
population size
200
Figure 1. Density-dependent selection on fitness. (a) The influence of total
number of eggs produced per breeding season on mean (solid lines) and
individual Malthusian fitness (dotted lines) of great tits for different population sizes N. (b) Selection differential on the total number of eggs
produced as function of mean total clutch size for different population
sizes N. The diamonds denote where the direction of selection changes.
(c) Influence of fluctuations in population size on density-dependent selection
on total clutch size in great tits. The mean Malthusian fitness s(z) is calculated at different population sizes for different total clutch sizes (i.e. the total
number of eggs produced per breeding season).
The maximum mean fitness fluctuated considerably with N
(figure 1a), producing selection for larger and smaller
clutch sizes at small and large population densities, respectively (figure 1b). As revealed by the gradient of the strength
ðzÞ (2b5 in equation (2.3b)), females
of density regulation g
producing a larger number of eggs at small population
sizes were those more strongly affected by variation in population density. The significant negative sign of b5 indicates
that when the mean clutch size was small, selection will
most of the time be towards large clutch sizes but in the
opposite direction at large clutch sizes. When clutches were
Proc. R. Soc. B 283: 20152411
sðzÞ ¼ b1 þ b2 z þ b3 ðz2 þ PÞ (a)
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as QðzÞ ¼ f1 s2e =½2rðzÞgKðzÞ, which has the same form as
the function found to be maximized in the haploid model of
Lande et al. [20].
So far, we have ignored migration, which constitutes an important component of the dynamics of this population [31]. This
includes treating emigrants as dead individuals, which makes
sðzÞ on average negative. To obtain a stationary model for using
the results of Engen et al. [21], we must assume an immigration
rate m replacing sðzÞ by sðzÞ þ m in the expression for QðzÞ: The
average growth rate at the log scale can be estimated as
ln W 1=2 s2e , giving the estimate of the immigration rate
^ ¼ ln W þ 1=2 s2e so that sðzÞ þ m on average equals zero. We
m
assume that immigration is independent of phenotype and that
the mean Malthusian parameter mðz, NÞ (equation (2.1)) does
not differ between immigrants and locally born females. Accordingly, the total clutch size did not differ significantly between
locally born females and immigrants (generalized linear mixed
model, P ¼ 0.223 including year as a random effect).
In the present parametric model, we find
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Q (−
z)
0
−50
size of
first clutch
size of
second clutch
−100
20.4761
0.1971
1.5480**
−150
0.1352***
20.0036***
0.0455
0.0002
20.1408*
0.0012**
20.0008
20.0028
20.0093*
20.0002*
0.2145
20.0001
0.2044
0.0006
0.1342
on average of intermediate sizes the direction of selection
may fluctuate considerably.
The optimal clutch size for a given population size, i.e. the
number of eggs produced that maximizes the fitness of a
female, decreased with increasing population size (figure 1a, see
also Both et al. [27]). This relationship was in particular owing to
low reproductive success of second clutches in our population
[27,36]. Accordingly, none of the bi for the first clutches were significantly different from zero, whereas significant stabilizing
selection was found for the second clutches (table 1).
Our estimates (table 1) imply that the strength of density
regulation gðzÞ ¼ b4 b5 z increases significantly with
increasing clutch size. Accordingly, at small population sizes
the Malthusian fitness was highest among females with large
clutch sizes, but the fitness of these females decreased rapidly
with increasing population size and was very low at large population sizes (figure 1c). By contrast, the Malthusian fitness of
females laying few eggs showed less variation with changes in
population size.
This pattern of density-dependent selection demonstrated
selection for high reproductive output at smaller population
sizes, but the fitness of these high-fecundity females was at the
same time more susceptible to fluctuations in population size
as revealed by the significant increase in the strength of density
dependence with increasing total clutch size (table 1). This tradeoff between r- and K-selection resulted in stabilizing, stochastic
phenotypic selection towards an intermediate clutch size z* ¼
15.97 in this population (figure 2), maximizing the function
QðzÞ (equation (2.1)) where we have inserted the average immigration rate m ¼ ðln W þ 1=2s2e Þ ensuring that that sðzÞ þ m
fluctuates around zero. The maximum value of QðzÞ at z* is of
an order of magnitude similar to the estimated carrying capacity
^ ¼ 125 (using a logistic model) in this population. Furthermore,
K
the mean value of z during the study period was 11.20, which is
close to z* considering the large stochasticity in the process as
well as the uncertainty in the function QðzÞ, mainly owing to
large standard errors in b3 and b5 (table 1). We also note that
the mean Malthusian fitness at z* is still quite small (figure 1a).
This illustrates that a large immigration rate m ¼ 0.34 is necessary
for long-term persistence of this population [31].
In this population, the heritability h 2 of the total number
of eggs produced per season is significantly larger than zero
5
10
15
20
total clutch size
25
30
Figure 2. Stabilizing selection on mean total number of eggs laid per breeding
season in great tits. The density-dependent selection is expressed as the effects
of varying the mean total number of eggs produced per seasonz on the function
g(z ) [21], where s(z ) ¼ r(z ) 1=2 s2e ðz Þ and m is the
Q(z ) ¼ [s(z ) þ m]=
estimated mean migration rate. The function Q(z ) governs the expected evolution of the mean phenotype in a density-dependent population, analogous
to the mean fitness when there is no density dependence [21]. Assuming
that z is heritable, fluctuating selection will cause z to fluctuate around z*
(dotted line), which is the value maximizing Q(z ):
18
16
14
12
10
8
0
50
year
100
150
Figure 3. Temporal variation of mean breeding values of the total number of
eggs laid per breeding season z simulated over a 150 year period. The parameters are given in table 1 and assuming heritability of total clutch size
^h2 ¼ 0:12: Blue lines are simulations using the estimated value b3 ¼ b^3
and red lines are simulated with b3 ¼ b^3 1:5 s:e:, where s.e. is the standard error of b^3 (table 1). The solid line indicates the intermediate clutch size
maximizing the function Q(z ) (equation (2.1)), which is the mean population
size for a given z :
(^h2 ¼ 0:12). As a consequence, density-dependent selection
results in the evolution of the mean breeding value that
will fluctuate slowly around z* (figure 3). Thus, r- and
K- selection can produce stabilizing selection around an intermediate phenotype even though there is directional selection
acting in a single year, environmental stochasticity is substantial (table 1) and demographic stochasticty induces genetic
drift that causes random variation in z [38].
4. Discussion
Our analyses reveal that in great tits the total number of eggs
produced per female during a breeding season is subject to
fluctuating r- and K-selection. This occurs because the selection
is density dependent (figure 1). When mean clutch size is
small, selection will most of the time be towards large clutch
Proc. R. Soc. B 283: 20152411
b1
b2
b3
b4
b5
s2
total number
of eggs laid
z*
50
mean, z
parameter
5
100
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Table 1. Analyses of variation in fitness Wz of breeding females of great tits.
(The effects of number of eggs laid per breeding season z is approximated
by a second-order polynomial b1 þ b2 z þ b3 z2 , representing stabilizing
selection if b3 , 0. The strength of density dependence on z is assumed
linear so the mixed model takes the form ln Eð2 WÞ ¼
b1 þ b2 z þ b3 z 2 þ b4 N þ b5 Nz þ 1, where N is population size, 1 is
the residual variation, E denotes the expectation and year is entered as a
random effect to account for environmental stochasticity (s 2).)
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Ethics. This study was carried out with the approval of the Animal
Experimentation Committee of the Royal Dutch Academy of Sciences
under licence NIOO 10-07.
Data accessibility. The data on which the analysis in this paper are based
are available from the data repository of the Netherlands Institute of
Ecology. This is a data repository which is managed by the Institute
and is available via http://data.nioo.knaw.nl/index.php.
Authors’ contributions. S.E. and B.-E.S. developed the model; S.E., B.-E.S.
and V.G. performed the statistical analyses; M.E.V. provided the data
and contributed to the biological interpretation of the results and all
authors contributed to the writing of the paper.
Competing interests. We declare we have no competing interests.
Funding. B.-E.S., S.E. and V.G. were supported by the European
Research Council (ERC-2010-AdG 268562) and the Research Council
of Norway (SFF-III 223257/F50) and MEV by the European Research
Council (ERC-2013-AdG 339092).
Acknowledgements. We are grateful to A. Husby for providing heritability estimates. We thank T. Reed for comments to a previous version of
the paper.
6
Proc. R. Soc. B 283: 20152411
eggs produced per breeding season, which is a precondition
for evolutionary responses to selection. In this case, densitydependent selection to maximize mean population size
(equation (2.2)) will result in a stationary distribution of the
breeding values of z. Simulations of sample paths from this
stationary distribution of breeding values show that the temporal variation in mean phenotype z will be small (figure 3)
because of the trade-off involving higher susceptibility of individuals with high growth rates at small densities to changes in
population size (table 1). However, the recorded values of z
was somewhat smaller than the predicted intermediate value
z* (figure 3), which is expected from the large uncertainties
in parameter estimates (table 1) as well as by our ignoring
of the effects of phenotypic plasticity and fluctuations in
age-distributions. Accordingly, the simulations (figure 3) can
only be used to characterize the general properties of the
stationary fluctuations in the mean breeding values.
A general problem in evolutionary biology has been to
explain the long periods typically seen in the fossil record of
small changes in morphology [10,50,51]. In general, this is
explained by stabilizing selection around an optimal phenotype
[10,52], which assumes stable fitness peaks, corresponding to
niches stable over time [50]. Our results indicate that ongoing
r- and K-selection may provide a general mechanism for such
stabilizing selection in environments that fluctuate over time
(figure 3) because it produces stabilizing selection around an
intermediate phenotype z* (figures 1a and 2). This implies
that characters may show variation over longer time periods,
still with no temporal trend in spite of directional selection on
heritable characters [14,50,53].
Evolutionary biology is currently experiencing a period of
great synthesis where several important contributions have
been made in our understanding of the evolutionary process
[10,54,55]. Our results suggest that the inclusion of specific
assumptions about the ecological dynamics involved can
produce precise predictions about expected patterns of phenotypic evolution. We have recently experienced several
advances in our understanding of eco-evolutionary dynamics
typically involving feedback processes in which the organism
modifies the effects of its environment through strong trophic
interactions [56 –58]. Here we have shown that feedback
loops are not a prerequisite for generating eco-evolutionary
dynamics, only density-dependent selection is necessary.
Such selection will then alter the evolutionary response to
changes in the environment [22,30].
rspb.royalsocietypublishing.org
sizes and in the opposite direction for large clutch sizes. The
significant negative interaction between total clutch size and
population size (table 1) indicates that the fitness of highfecundity females is most strongly affected by large population
sizes, causing the breeding value of total clutch size to fluctuate
around an intermediate value (figure 3). Thus, such densitydependent selection provides a reciprocal link between current
ecological dynamics and evolutionary processes operating at
longer time scales [30].
The Malthusian fitness, which is the growth rate on the logarithmic scale of a hypothetical population of individuals with
a given phenotype and population size (equation (2.1)) showed
a maximum at intermediate total clutch sizes that fluctuates
with the population size (figure 1a). This is supported by evidence from large-scale brood size manipulation experiments
in years which differed in density. They suggest that there
exists an intermediate clutch size that maximizes the offspring
production of a breeding female [25,27] and that this optimal
clutch size varies with density [27]. Furthermore, analyses of
the dynamics of populations of great tits have shown that
changes in population size between years are determined by
a balance between the number of new recruiting offspring produced, which is affected by density-independent factors such
as weather and beech mast [32], and density-dependent
losses of individuals during the non-breeding season [45].
In particular, variation in juvenile survival strongly affects
the fluctuations in population size [33] as well as the fitness
of individual females (i.e. the number of offspring produced
that recruit to the next generation) [46]. These effects operate
through a joint effect of environmental variation on the
demography of both local residents and immigrants [31,35].
These analyses are based on several simplifying assumptions. First, we assume that the effects of fluctuations in the
environment are independent of the phenotype so that there
are no stochastic components in the selection process except
what is governed by fluctuations in N (see Lande [47], Engen
& Sæther [38] and Chevin et al. [19] for other stochastic components). Second, there is no phenotypic plasticity with
regard to population size in total number of eggs produced
[27], which may affect the estimated response to selection
(figure 3). Third, we disregard age-dependency which is
known to cause transient fluctuations in selection differentials
even in short-lived passerines such as the great tit [48]. Fourth,
we consider only one phenotypic characteristic, ignoring the
influence on total clutch size of correlated selection on other
characters. For instance, in great tits variation among females
in reproductive success is also affected by the timing of breeding [37], which influences the number of broods that can be
produced per season [36]. Accordingly, the density-dependent
selection on total clutch size occurs mainly as an effect of population size on the breeding success via second clutches (table 1),
which has been shown to strongly affect the reproductive rate
of this population [36]. We also assume that the immigrants
have the same z as the native population. Still, in spite of
these assumptions, our model captures essential characteristics
of the dynamics of this population (figure 2), enabling us to
demonstrate that those females producing a large number of
clutches at small population sizes are also those that experience
the stronger density regulation as revealed by the significant
interaction between the total number of eggs produced and
population size (table 1).
As is the case for many reproductive traits of tits [49], there
was significant heritable variation in the total number of
Downloaded from http://rspb.royalsocietypublishing.org/ on June 15, 2017
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