1
Double decomposition: decomposing the variance in subcomponents of male
2
extra-pair reproductive success
3
4
5
6
Sylvain Losdat*a, Peter Arceseb, Jane M. Reida
7
8
a
9
Zoology Building, University of Aberdeen, Tillydrone Avenue, Aberdeen AB24 2TZ,
10
Institute of Biological and Environmental Sciences, School of Biological Sciences,
Scotland.
11
12
b
13
British Columbia, Vancouver BC V6T 1Z4, Canada.
Department of Forest and Conservation Sciences, 2424 Main Mall, University of
14
15
*
Corresponding author: [email protected]
16
17
Running headline: decomposition of extra-pair paternity
18
1
1
Summary
2
1.
3
socially monogamous systems, and could cause selection on female extra-pair
4
reproduction if extra-pair offspring (EPO) inherit high value for EPRS from their
5
successful extra-pair fathers. However, EPRS is itself a composite trait that can be fully
6
decomposed into subcomponents of variation, each of which can be further
7
decomposed into genetic and environmental variances. However, such decompositions
8
have not been implemented in wild populations, impeding evolutionary inference.
9
2.
Extra-pair reproductive success (EPRS) is a key component of male fitness in
We first show that EPRS can be decomposed into the product of three life-
10
history subcomponents: the number of broods available to a focal male to sire EPO, the
11
male’s probability of siring an EPO in an available brood, and the number of offspring
12
in available broods. This decomposition of EPRS facilitates estimation from field data
13
because all subcomponents can be quantified from paternity data without need to
14
quantify extra-pair matings. Our decomposition also highlights that the number of
15
available broods, and hence population structure and demography, might contribute
16
substantially to variance in male EPRS and fitness.
17
3.
18
wild song sparrows (Melospiza melodia) to partition variance in each of the three
19
subcomponents of EPRS, and thereby estimate their additive genetic variance and
20
heritability conditioned on effects of male coefficient of inbreeding, age and social
21
status.
22
4.
23
repeatability, reflecting combined permanent environmental and genetic effects.
24
Number of available broods and offspring per brood showed low additive genetic
25
variances. The estimated additive genetic variance in extra-pair siring probability was
We then used 20 years of complete genetic paternity and pedigree data from
All three subcomponents of EPRS showed some degree of within-male
2
1
larger, although the 95% credible interval still converged towards zero. Siring
2
probability also showed inbreeding depression and increased with male age, while the
3
numbers of available broods and offspring per brood did not.
4
5.
5
offspring in an available brood is the primary source of genetic variation in male EPRS,
6
implying that the evolution of female extra-pair reproduction could be facilitated by
7
genetic covariance with this subcomponent of EPRS.
Our results indicate that the probability that a male will sire an extra-pair
8
9
10
Key-words: Bayesian animal model, fertilisation success, multiple mating, paternity
success, polyandry, quantitative genetics, sexual selection, population structure
3
1
Introduction
2
Despite decades of research the evolutionary causes of extra-pair reproduction in
3
socially monogamous systems are still widely debated (Arnqvist & Kirkpatrick 2005;
4
Evans & Simmons 2008; Schlicht & Kempenaers 2011; Slatyer et al. 2012; Parker &
5
Birkhead 2013). Socially-paired males have the potential to increase their total
6
reproductive success and hence fitness through extra-pair reproductive success (EPRS),
7
defined as the total number of extra-pair offspring sired (Webster et al. 1995; Westneat
8
& Stewart 2003; Whittingham & Dunn 2005; Parker & Birkhead 2013). Selection for
9
female extra-pair reproduction could then operate if extra-pair sons, which are by
10
definition sired by successful extra-pair sires, become successful extra-pair sires
11
themselves (Evans & Simmons 2008; Forstmeier et al. 2011; Slatyer et al. 2012).
12
However, this mechanism requires heritability in EPRS, such that extra-pair offspring
13
(EPO) inherit high genetic value for EPRS (i.e. the sexy-son hypothesis, Weatherhead
14
& Robertson 1979; Tschirren et al. 2012).
15
Testing the above hypothesis, and hence understanding the evolution of extra-
16
pair reproduction, requires estimation of additive genetic variance in EPRS (Arnqvist
17
& Kirkpatrick 2005; Reid et al. 2011; Reid 2014). However, male EPRS is a composite
18
trait that is the outcome of multiple lower level life-history components, and variation
19
in these components creates opportunity for pre- or post-copulatory sexual selection
20
(Schlicht & Kempenaers, 2011). Decomposing EPRS into its subcomponent parts
21
rather than treating it as a single composite trait, and then further partitioning variance
22
in each subcomponent, could therefore identify the sources of additive genetic variance
23
in EPRS and hence help identify the subcomponents of EPRS that might cause indirect
24
selection on female extra-pair reproduction (Arnqvist & Kirkpatrick 2005; Evans &
4
1
Simmons 2008). This approach could also allow genetic covariances among
2
subcomponents and hence potential genetic trade-offs or synergies, to be estimated.
3
4
Decompositions of EPRS have previously been proposed and utilized. For
instance, Webster et al. (1995) decomposed EPRS as
5
EPRS = Nmates × Ppat × Noffspring
(1)
6
where Nmates is the number of extra-pair females with whom a male mated, Ppat is the
7
probability of siring an extra-pair offspring given mating and Noffspring is the total
8
number of offspring produced by extra-pair females with whom a male mated (Fig. 1a,
9
Table 1). However, this decomposition does not explicitly consider that Nmates is itself
10
a composite term that comprises the product of two components: the number of females
11
that were available to a male for extra-pair mating and the probability that a male will
12
mate with such a female. The number of ‘available’ females refers to females that are
13
socially, spatially or temporally available as potential extra-pair mates to a given male.
14
In nature, extra-pair reproduction can be constrained by social structure or breeding
15
synchrony (Stewart, Westneat & Ritchison 2010; Canal, Jovani & Potti 2012; Wang &
16
Lu 2014), or spatial structure (Canal, Jovani & Potti 2012; Taff et al. 2013). For
17
instance, adjacent (i.e. neighbouring) males often sire most EPO in passerine birds
18
(Freeman-Gallant et al. 2005; Suter et al. 2007; Sardell et al. 2010; Kingma, Hall &
19
Peters 2013; Taff et al. 2013). Furthermore, the number of broods might also vary
20
among available females, further increasing variation among males in their opportunity
21
to sire EPO.
22
The term Nmates in equation 1 can therefore be replaced by the product of the
23
number of broods produced by females that are available to any focal male for potential
24
extra-pair matings (Nbroods) and the probability of mating with a female that has an
25
available brood (Pmating, Fig. 1b), so that
5
1
EPRS = Nbroods × Pmating × Ppat × offspring
(2)
2
where offspring is the mean number of offspring produced in available broods (Table 1).
3
This new decomposition explicitly incorporates among-male variation in the number of
4
broods available for potential extra-pair reproduction and in a male’s probability of
5
mating with a female for each of her broods.
6
Variation in any of the four components in equation 2 will cause variation in
7
male EPRS and fitness (Webster et al. 1995; Lebigre et al. 2012). Indeed, variation in
8
Pmating and Ppat will create opportunity for pre-and post-copulatory sexual selection
9
(Anderson 1994; Schlicht & Kempenaers 2011). In contrast, Nbroods, the number of
10
broods produced by females available for potential extra-pair matings has been less
11
emphasised as a determinant of any male’s EPRS. offspring may also affect a male’s
12
EPRS because the opportunity to sire EPO increases with the number of offspring
13
produced by available females (Webster et al. 1995). Therefore, while male EPRS is
14
generally viewed as a male-only trait, equation 2 shows that it incorporates variation in
15
the number of available females and their reproductive rate (Fig. 1).
16
Decomposing EPRS into its subcomponents parts, either as previously defined
17
(equation 1) or using our new formulation (equation 2, Table 1), allows the specific
18
subcomponents that might underlie the evolution of extra-pair reproduction to be
19
identified. However, EPRS and its subcomponents are difficult to measure in wild
20
populations. Measuring EPRS ideally requires complete paternity assignment of all
21
offspring across all potential sires in a population (Freeman-Gallant et al. 2005; Lebigre
22
et al. 2012). Measuring Nbroods requires comprehensive knowledge of a population’s
23
social structure, and of corresponding social or spatial constraints on extra-pair
24
reproduction (Canal, Jovani & Potti 2012; Taff et al. 2013; García-Navas et al. 2014).
25
Estimating Pmating requires all extra-pair matings to be documented (rather than solely
6
1
matings that result in observed EPO), which is virtually impossible in nature. Ppat
2
cannot be readily estimated either as it requires both complete paternity data to assign
3
EPO to their extra-pair sire and observation of all matings. These difficulties have led
4
empirical decompositions of the variance in male EPRS to assume that all extra-pair
5
matings result in at least one EPO (e.g. Stutchbury et al. 1997; Woolfenden, Gibbs &
6
Sealy 2002; Freeman-Gallant et al. 2005; Whittingham & Dunn 2005; Dolan et al.
7
2007), which is unlikely given that observed matings commonly lead to zero paternity
8
(Birkhead & Møller 1998). In such cases, neither Nmates and Ppat (Fig. 1a), nor Ppat and
9
Pmating (Fig. 1b) can be truly distinguished.
10
One way to partially overcome the difficulties of estimating Pmating and Ppat is
11
to consider their product, which equals the probability that an offspring within an
12
available brood will be sired as an EPO by a focal male (Psire, Fig. 1b, Table 1) allowing
13
equation (2) to be rewritten as
14
EPRS = Nbroods × Psire × offspring
(3)
15
The combined probability Psire has the advantage that it can be estimated in systems
16
with genetic paternity assignments, and where broods available to any male (Nbroods)
17
can be identified, thus alleviating the need to observe all extra-pair matings.
18
However, since Psire amalgamates both pre- and post-copulatory episodes of
19
selection (Fig. 1, Table 1), an informative additional parameter to estimate is Ppat.success,
20
the probability that an offspring within an available brood will be sired as an additional
21
EPO by a focal male given that he sired one EPO in that brood, thereby approximating
22
the probability of siring an extra-pair offspring given mating (Ppat, equation 2).
23
Ppat.success (unlike Psire) is limited to describing post-mating paternity success (i.e. any
24
unsuccessful and hence undetected matings are excluded, see Discussion).
7
1
All subcomponents of total variance in EPRS (equations 2 and 3) could be
2
influenced by numerous underlying traits. For example, Pmating likely depends on
3
secondary sexual characters, while Ppat likely depends on sperm performance and/or
4
mating rate. Identifying and measuring such underlying traits would therefore allow
5
some proportion of variation in the subcomponents of variance in EPRS to be
6
explained. However, equation 2 and 3 provide complete and general decompositions of
7
the total phenotypic variance in EPRS at the level of life-history components. Our
8
decomposition therefore serves to partition total variance in EPRS rather than
9
attributing variance to any underlying traits, and can potentially be fully parameterised
10
using field data.
11
Having decomposed EPRS into its underlying subcomponents, understanding
12
the evolution of extra-pair reproduction requires each of these subcomponents to be
13
further decomposed into additive genetic and environmental variances, conditioned on
14
individual male effects of interest. Specifically, reproductive success and fitness
15
commonly decrease with individual coefficient of inbreeding (f) constituting inbreeding
16
depression (Crnokrak & Roff 1999; Keller & Waller 2002). Inbreeding depression
17
commonly affects male reproductive traits such as sperm performance and competitive
18
fertilization success (e.g. Simmons 2011, Losdat, Chang & Reid 2014). Inbreeding
19
depression can also reduce male EPRS (Reid et al. 2011; Reid, Arcese & Losdat 2014),
20
potentially imposing selection for females to outbreed and hence produce outbred sons
21
with high EPRS.
22
Male reproductive success can also depend on age (Mauck, Huntington &
23
Grubb 2004; Benowitz et al. 2013), as can sperm performance (Møller et al. 2009;
24
Gasparini et al. 2010), reproductive tactics (Rasmussen et al. 2008), territory defence
25
(Arcese 1987) and the number of EPO sired (Wetton et al. 1995; Cleasby & Nakagawa
8
1
2012). Subcomponents of male EPRS may therefore also depend on male age, which
2
could reflect differential investment among subcomponents of EPRS, and/or age-
3
dependent reproductive strategies.
4
In socially monogamous species, a male’s social status, specifically whether he
5
is socially-paired or unpaired, may also affect subcomponents of EPRS. Socially-paired
6
males engaging in extra-pair reproduction may face a trade-off between within-pair and
7
extra-pair paternity success (Westneat & Stewart 2003; Reid, Arcese & Losdat 2014).
8
Conversely EPRS can be higher in socially-paired males (Freeman-Gallant et al. 2005;
9
Whittingham & Dunn 2005; Sardell et al. 2010), suggesting that social status may
10
influence any subcomponent of EPRS.
11
To date, additive genetic variance and effects of inbreeding, age and social
12
status on individual subcomponents of EPRS have not been estimated in free-living
13
animals. Here, we used 20 years of complete genetic pedigree and paternity data from
14
socially monogamous but genetically polygynandrous song sparrows (Melospiza
15
melodia) to quantify additive genetic variance and estimate effects of inbreeding, age
16
and social status on Nbroods, Psire, offspring and Ppat.success. We thereby decompose
17
variance in each subcomponent of male EPRS, and hence in key life-history
18
components of variation that could shape evolution of extra-pair reproduction.
19
20
Material and methods
21
22
Study system
23
A resident socially monogamous population of song sparrows Melospiza melodia
24
inhabiting Mandarte Island (ca. 6 hectares, British Columbia, Canada) has been
25
intensively monitored since 1975 (e.g. Smith et al. 2006; Lebigre et al. 2012), and
9
1
recently numbered ca. 10-50 breeding pairs. Song sparrows of both sexes can first breed
2
aged one year (median reproductive lifespan: 2 years). Social pairs typically rear 2-3
3
broods during April-July. Each year, all nests on Mandarte were monitored and all
4
offspring surviving to six days post-hatch were uniquely colour-ringed to allow
5
subsequent identification (Smith et al. 2006). Brood size at ringing averaged 2.8
6
offspring (standard deviation 1, median 3, range 1-4). Adult immigrants (on average
7
1.1 per year) were mist-netted and colour-ringed soon after arriving. Every year, all
8
territories were mapped and all adults were identified with high resighting probability
9
(ca. 0.99, Wilson et al. 2007). We therefore had complete data describing reproductive
10
success, survival, and identity of all social parents of all offspring.
11
Males actively prospect for and defend breeding territories annually,
12
particularly in early spring, including perching prominently, singing, and engaging in
13
aggressive display with surrounding males (Arcese 1987; 1989). Each year, territorial
14
behaviour including song posts and boundary disputes was observed for about one hour
15
at least every 5 days before the onset of incubation. Following these repeated
16
observations, each male’s territory was mapped when social pairs were formed for their
17
first brood (i.e. by April 30th, Arcese 1989; Smith et al. 2006). Since adult sex ratio is
18
male-biased in most years, some males remained as socially unpaired territorial males,
19
or as non-territorial floater males (Smith et al. 2006; Sardell et al. 2010).
20
21
Paternity analysis
22
From 1993 to 2012, 99.6% of ringed offspring and adults were blood sampled and
23
genotyped at 13 polymorphic microsatellite loci to assign paternity (Sardell et al. 2010;
24
Reid et al. 2014). Bayesian models that included genetic and spatial information
25
assigned genetic sires to 99.7% of sampled offspring with >95% confidence (Sardell et
10
1
al. 2010) using MasterBayes package in R software (Hadfield, Richardson & Burke
2
2006). 99% of offspring paternities were subsequently verified using up to 170
3
polymorphic microsatellite loci (Nietlisbach et al. 2015). Overall, 28% (range: 20%-
4
48% across years) of offspring were assigned to extra-pair males and hence classified
5
as extra-pair offspring (EPO) rather than within-pair offspring (WPO).
6
Paternity assignment indicated that extra-pair paternity is biased towards
7
neighbouring males with 88% of EPO sired by neighbours, 11% by non-neighbour
8
territorial males, and 1% by non-territorial floater males (Sardell et al. 2010). Since
9
most EPO were sired by neighbours, we assumed that each male could potentially have
10
sired EPO in all broods produced in its neighbouring territories (thereafter ‘available
11
broods’) but could not necessarily sire EPO in broods produced in non-neighbouring
12
territories.
13
14
Measurement of subcomponents of EPRS
15
We considered annual EPRS rather than lifetime EPRS because variance in the latter
16
includes variance in male lifespan, which was not the focus of our study.
17
Males were classified annually as territorial, or as non-territorial floaters. Each
18
territorial male was in turn classified with respect to every brood from which ≥1
19
offspring survived to colour-ringing as ‘neighbour’ if he shared a territory boundary
20
with the focal brood’s natal territory, or as ‘non-neighbour’ if he did not share any
21
boundary. Territorial males were further classified annually as ‘socially-paired’ if they
22
were paired with a female on April 30th and subsequently produced ≥1 offspring, or as
23
‘socially-unpaired’ if not.
24
Using the above conventions, Nbroods was measured as the total number of
25
broods produced across all of each focal male’s neighbouring territories in each year
11
1
(Table 1). Psire was measured for each male as the number of EPO sired out of the total
2
number of offspring within each of the available neighbouring broods (one value per
3
male per available brood, hereafter ‘male-brood’). Since offspring sired as EPO by one
4
male cannot be sired as EPO by another male, one male’s Psire will depend on Psire of
5
other neighbour males. However, this conceptual non-independence does not impede
6
current analyses or interpretations because observed EPRS is by definition the outcome
7
of competition for paternity. offspring is defined as the mean number of offspring across
8
broods produced in a male’s neighbouring territories (Fig. 1, equation 2). However, we
9
modelled the number of offspring per neighbouring brood rather than the mean across
10
broods because modelling mean values artificially reduces phenotypic variance. In
11
practice, a model fitted to offspring itself provided similar conclusions (data not shown).
12
Finally, Ppat.success was measured for each male that sired ≥1 EPO in any brood as the
13
number of further EPO sired out of the total number of remaining offspring in the brood
14
(i.e. excluding one EPO). All males included in this analysis had therefore definitely
15
mated with the female that produced the focal brood. Ppat.success was therefore measured
16
for males that sired ≥1 EPO in broods where ≥2 offspring survived to paternity
17
assignment.
18
19
Analysis implementation
20
Using phenotypic data spanning 1993 to 2012, we fitted univariate animal models to
21
each subcomponent of EPRS (Figs. 1b and 1c, Table 1) using Bayesian methods
22
implemented in package MCMCglmm 2.14 in R version 3.0.1 (Hadfield 2010; R Core
23
Team 2013), assigning observed phenotypes to focal males. For phenotypes that might
24
be expected to be primarily under female control (i.e. Nbroods and brood sizes), models
25
can be interpreted as estimating ‘indirect’ or ‘associative’ genetic and environmental
12
1
effects attributable to focal males (Bijma 2010). Nbroods was assumed to follow an over-
2
dispersed Poisson distribution, with log link function. Posterior predictive checking
3
showed no zero-inflation of Nbroods compared to expectation given estimated
4
overdispersion (e.g. Hadfield 2010). Psire and Ppat.success were assumed to follow
5
binomial distributions, with logit link functions, thereby quantifying a male’s liabilities
6
to sire EPO in a neighbouring brood and to sire additional EPO given one EPO,
7
respectively. The number of offspring produced across available broods was assumed
8
to follow a Gaussian distribution, with identity link function.
9
Because non-territorial floater males have a value of zero for Nbroods (having
10
zero neighbours), they have undefined values for subsequent subcomponents of EPRS
11
and were therefore excluded from the analyses. However, excluding them from the
12
analysis of Nbroods could bias estimates of variance components by reducing variance
13
in Nbroods. We therefore re-ran the analysis of Nbroods including values of zero for
14
floaters (Appendix S1).
15
Animal models included a variance-covariance matrix of random additive
16
genetic effects derived from pairwise kinship coefficients k calculated from pedigree
17
data, allowing estimation of additive genetic variance (VA, Kruuk 2004; Reid et al.
18
2011). Genetic parentage data spanning 1993-2012 were used to compile a complete
19
genetic pedigree for this period, with all adults assigned to their genetic mother and
20
most probable genetic sire (Reid et al. 2011, 2014). Related and unrelated males are
21
distributed over years and territories, precluding substantial bias in estimates of VA due
22
to male relatives solely competing with each other for paternity success (e.g. Garcia-
23
Gonzalez & Evans 2011). Since datasets often included multiple observations per male,
24
random male effects were fitted to account for correlations among observations of the
25
same male within and/or across years, thereby estimating permanent individual
13
1
variance
2
environmental variance stemming from permanent or consistent environmental effects
3
on individual phenotype, and non-additive genetic variance (Kruuk 2004). Models also
4
included random year effects and therefore estimated among-year variance (VY), and
5
also estimated residual variance (VR), thereby encompassing remaining within-male
6
variance (Kruuk 2004).
(VPI).
Permanent
individual
variance
comprises
both
permanent
7
We used standard algorithms to compute the inverse relationship matrices and
8
individual f values from the pedigree pruned to males who contributed phenotypic data
9
and all their known ancestors. Kinship (k) measures the relatedness between individuals
10
and it equals the f value of hypothetical offspring produced by those individuals.
11
Kinship between immigrants and Mandarte-hatched natives was defined as zero relative
12
to the pedigree baseline (Reid, Arcese & Keller 2006). Phenotypic data for seven
13
immigrant males, whose f values were undefined relative to the pedigree baseline, were
14
excluded from analyses.
15
Models included a fixed regression on male f and fixed effects of male social
16
status (socially-paired or unpaired, modelled as a two-level factor) and age modelled as
17
a three-level factor comprising males aged 1 year, 2 to 5 years and 6 to 9 years based
18
on previously reported differences in EPRS among these three ages classes (Reid,
19
Arcese & Losdat 2014). Fixed effect priors were normally distributed with mean zero
20
and large variance (108). Analyses used parameter-expanded priors for variance
21
components with working parameter prior mean and variance of 0 and 1000,
22
respectively, and location effect priors with degree of belief 1 and variance 1 (Hadfield
23
2010). Analyses used 1,005,000 iterations, burn-in 5000 and thinning interval 1000,
24
ensuring low autocorrelation among thinned samples (<0.05). Analyses were re-run
14
1
using inverse Wishart priors on the variance components with variance 1 and degree of
2
belief of 0.002. Posterior distributions were robust to these prior specifications.
3
Posterior mean heritabilities were calculated as h2 = VA/(VP + log(1/exp(xp)+1))
4
from the Poisson model (Nbroods), as h2 = VA/(VP + π2/3) from the binomial models (Psire
5
and Ppat.success), and as h2 = VA/VP from the Gaussian model (number of offspring per
6
brood), where VP is the total phenotypic variance (i.e. sum of all estimated variance
7
components) and exp(xp) was taken as the raw trait mean. Repeatabilities were
8
calculated by adding VPI to the numerator of these expressions (Nakagawa & Schielzeth
9
2010). Heritabilities were calculated conditional on fixed effects, thereby controlling
10
for possible variation among age classes and social status categories, and ensuring that
11
estimates of VA were not biased by un-modelled inbreeding depression (Reid & Keller
12
2010). All models were re-run including random maternal and social paternal effects
13
(i.e. the male that reared each focal male) to verify that estimates of VA were not
14
confounded by parental effects (Appendix S2). Because estimated VA in all
15
subcomponents was relatively small (see Results), genetic covariances among
16
subcomponents were not estimated. Raw means are presented ± 1SD and posterior
17
means are presented with 95% credible intervals (CI). The percentage of phenotypic
18
variance in each subcomponent explained by each fixed effect (i.e. male f, age and
19
social status) was calculated by running two additional mixed models for each
20
subcomponent that solely estimated individual, year and residual variances., and that
21
did and did not include each fixed effect. The percentage of variance was calculated as
22
the difference between VP estimated from the models without and with each fixed effect
23
divided by the former.
24
Previous quantitative genetic analyses of EPRS treated as a single trait
25
estimated non-zero VA and moderate heritability in our study population (h2=0.14,
15
1
Reid, Arcese & Losdat 2014). This updates an earlier estimate of low and non-
2
significant VA and h2 due to four additional years of phenotypic data (Reid et al. 2011).
3
The existence of low or moderate heritability in a composite life-history component
4
(such as EPRS) does not necessarily imply that all underlying subcomponents will have
5
low heritability. In general, the product of a moderately heritable trait and a trait with
6
high environmental variance could create a composite trait with low heritability. In such
7
cases, the heritable underlying trait could be usefully identified as the primary route
8
through which the composite trait could respond to selection. Our current analyses
9
demonstrate a statistical route to decomposing EPRS into its subcomponents and to
10
partitioning variance in these, hence identifying the key life-history components
11
through which genetic variation in EPRS is exhibited (see also Appendix S3).
12
13
Results
14
Nbroods
15
Nbroods was measured for 327 individual males and 786 male-years (mean 2.4±1.7 years
16
per male, median 2, range 1-8), including 558 socially-paired and 228 socially-unpaired
17
male-years. Nbroods averaged 5.2±2.8 (range 1-22, median 5.0, Fig. 2a). Descriptive
18
statistics of the pedigree data for these 327 males are provided in Table 2.
19
Posterior mean VA in Nbroods was ca. 0.01 with 95%CI that converged towards
20
zero (Table 3a). Posterior mean VPI was 0.03 with 95%CI that did not converge towards
21
zero (Table 3a). Within-male repeatability was therefore ca. 0.12 (95%CI 0.06-0.18)
22
but the estimated heritability was ca. 0.03 with 95%CI that converged towards zero
23
(Table 3a). Nbroods did not vary significantly with male f, age or social status (Table 3a),
24
all of which explained <1% of the total phenotypic variance. Conclusions remained
16
1
similar when models were re-run including 109 additional observations of Nbroods for
2
44 floater males (Appendix S1).
3
4
Psire
5
Psire was measured for the 327 males (Table 2) across 4083 male-broods (mean number
6
of available broods per male 12.5±9.6, range 1-50, median 10). Mean Psire was
7
0.06±0.20 (range 0-1, median 0, 3680 zeros (90.1%), Fig. 2b). The value of 0.06 differs
8
from the population-wide proportion of offspring that were EPO (0.28) because many
9
offspring were available as potential EPO to multiple males.
10
Posterior mean VA was ca. 0.78 but the 95%CI was wide and converged towards
11
zero. VPI was ca. 1.5 with 95%CI that did not converge towards zero (Table 3b). Within-
12
male repeatability was ca. 0.13 (95%CI 0.06-0.18) and estimated heritability was ca.
13
0.04 with 95%CI that converged towards zero (Table 3b). Psire decreased with male f,
14
increased with age and did not vary with social status (Table 3b). Male f, age and social
15
status explained approximately 1%, 8% and 7% of total phenotypic variance in Psire,
16
respectively.
17
18
Number of offspring per available brood
19
The number of offspring per available brood was measured for the 327 males and
20
averaged 2.8±0.8 (range 1-4, median 2.8, n=1016 broods, Fig. 2c). Posterior mean
21
estimates of VA and VPI were ca. 0.003 and ca. 0.008 respectively with 95%CI that
22
converged towards zero (Table 3c). Within-male repeatability and heritability were ca.
23
0.12 and 0.03 with 95%CI that converged towards zero (Table 3c). The number of
24
offspring produced across available broods decreased slightly with increasing male f
17
1
(ca. 89% of the posterior density was negative) but did not vary with age or social status
2
(Table 3c). All three fixed effects explained <1% of the total phenotypic variance.
3
4
Ppat.success
5
Ppat.success was measured for 167 males spanning 405 broods in which ≥1 EPO was sired,
6
averaging 2.6±2.0 broods per male (range 1-11, median 2). After excluding one EPO,
7
a mean of 2.1±0.7 remaining offspring were available as potential EPO per brood (range
8
1-3, median 2). Focal males actually sired 0.7±0.9 additional EPO on average (range 0-
9
3, median 0) and sired zero additional EPO in 223 (55%) of the 405 male-broods. Mean
10
Ppat.success was 0.34±0.40 (range 0-1, median 0). Pedigree data is described in Table 2.
11
Posterior mean estimates of VA and VPI were ca. 0.44 and ca. 0.19 with wide
12
95%CI that converged towards zero (Table 3d). Within-male repeatability and
13
heritability were ca. 0.08 and ca. 0.06 but the 95%CIs converged towards zero (Table
14
3d). Ppat.success did not vary with male f, age or social status (Table 3d), all of which
15
explained <1% of the total phenotypic variance.
16
17
Discussion
18
In socially monogamous but genetically polygynandrous systems, extra-pair
19
reproduction can allow a male to increase his total reproductive success (Webster et al.
20
1995; Westneat & Stewart 2003; Whittingham & Dunn 2005; Parker & Birkhead 2013).
21
Furthermore, if extra-pair sons were to inherit high value for extra-pair reproductive
22
success (EPRS), evolution of female extra-pair reproduction could be facilitated by
23
indirect selection. However, EPRS is a composite trait that encompasses multiple male,
24
and also female, components of life-history variation. Fully decomposing EPRS into its
25
subcomponents and then quantifying genetic and environmental variance in each of
18
1
these subcomponents could therefore facilitate understanding of mating system
2
evolution. We formulated a full decomposition of EPRS that allows key subcomponents
3
of variance to be estimated from observed paternity (equation 2). We then decomposed
4
these subcomponents using 20 years of genetic pedigree and paternity data from song
5
sparrows. Similar decompositions could potentially be applied to other composite
6
fitness components, such as male within-pair reproductive success. Although key
7
components can be challenging to estimate, full decompositions such as equation 2 are
8
valuable in highlighting life-history components that field studies should aim to
9
measure. Indeed, field studies could still usefully estimate and decompose variance in
10
individual subcomponents of EPRS, and of other composite traits, even if sufficient
11
data to partition variance in all subcomponents are not available.
12
13
Number of available broods and offspring
14
Our decomposition of EPRS highlights that a previously implicit component of
15
variance, Nbroods, the number of broods available to a male to potentially sire EPO,
16
could potentially cause substantial variation in EPRS. Indeed, numerical decomposition
17
showed that variance in Nbroods contributed substantially to the total phenotypic
18
variance in EPRS in song sparrows (Appendix S3). The number of available mates is
19
widely acknowledged to cause variation in EPRS and total reproductive success
20
(Anderson 1994; Webster et al. 1995). However, the role of Nbroods in causing variation
21
in EPRS has not been emphasised, perhaps because variation in EPRS is often assumed
22
to primarily reflect variation in mating or siring successes (Birkhead & Møller 1995;
23
Webster et al. 2007). In song sparrows, Nbroods varied substantially among male-years
24
(Fig. 2a), probably because Nbroods varies with the number of neighbouring females and
25
the number of broods each female produces per year. Both of these quantities depend
19
1
on population density, which varies among years on Mandarte (Smith et al. 2006).
2
Recent studies on other species also indicate that ecological and spatio-temporal factors
3
such as inter-nest distance (pied flycatcher, Ficedula hypoleuca, Canal, Jovani & Potti
4
2012), breeding density (common yellowthroat, Geothlypis trichas, Taff et al. 2013) or
5
population size (blue tit, Cyanistes caeruleus, García-Navas et al. 2014) influence
6
access to extra-pair mates and thus might contribute to variation in EPRS. Our
7
decomposition highlights that the number and reproductive rate of females available to
8
each male could potentially cause substantial variation in male EPRS.
9
In contrast, studies that use captive or experimental populations to explore the
10
evolution of polyandry and/or extra-pair reproduction typically control, constrain, or
11
remove variation in the number of available females, litters or broods and might
12
therefore artificially exclude a key component of variation in male EPRS (e.g.
13
Forstmeier et al. 2011). Likewise, field studies that have decomposed phenotypic
14
variance in EPRS without explicitly considering variation in the number of available
15
mates or broods, while perfectly valid, might have under-emphasized the role of this
16
component (e.g. Stutchbury et al. 1997; Woolfenden, Gibbs & Sealy 2002; Freeman-
17
Gallant et al. 2005; Whittingham & Dunn 2005; Dolan et al. 2007).
18
Our quantitative genetic analysis of Nbroods showed non-zero VPI and hence non-
19
zero within-male repeatability in Nbroods, attributable to permanent environmental
20
and/or non-additive genetic effects. Individual males therefore consistently occupied
21
territories that provided more or fewer opportunities for extra-pair reproduction,
22
potentially reflecting repeatability in behavioural traits linked to territory defense (e.g.
23
Bell, Hankison & Laskowski 2009; Duckworth & Sockman 2012) and/or male breeding
24
site fidelity across years (Winkler et al. 2004; Johnson & Walters 2008). Meanwhile,
25
estimates of VA and h2 in Nbroods were small, indicating limited potential for evolution
20
1
of Nbroods via selection on males. Our result suggests that the observed non-zero
2
heritability of EPRS (Reid, Arcese & Losdat 2014) does not stem primarily from
3
heritability of Nbroods.
4
For the number of offspring within a male’s available broods, repeatability, VA
5
and VPI were small and we detected no effect of male age, coefficient of inbreeding or
6
social status. This is perhaps not surprising because brood size is likely to be primarily
7
a female trait. Furthermore, numerical decomposition showed that variance in brood
8
size contributes little to total phenotypic variance in male EPRS in song sparrows
9
(Appendix S3), as observed in other species (Webster et al. 1995; Collet et al. 2012).
10
Our analyses assumed that neighbouring females and their broods were
11
available to any focal male for potential extra-pair paternity while non-neighbouring
12
females and their broods were not. This assumption broadly matches the observed
13
spatial pattern of male extra-pair paternity in song sparrows (Sardell et al. 2010) and
14
other species (Suter et al. 2007; Kingma, Hall & Peters 2013; Taff et al. 2013). In other
15
systems however, availability of extra-pair mates and broods may depend on other
16
factors that might constrain EPRS, such as breeding synchrony. Future analyses of other
17
systems should therefore incorporate such constraints.
18
19
Probability of paternity
20
Psire, the probability that an offspring within an available brood was sired as an EPO by
21
a focal male, varied substantially among male-broods (Fig. 2b) and numerical
22
decomposition showed that Psire contributed most of the total phenotypic variance in
23
male EPRS (Appendix S3). There is therefore substantial opportunity for selection on
24
male Psire, and also for selection on underlying traits.
21
1
Repeatability of Psire was ca. 0.13 and differed from zero, suggesting that
2
among-male variation in EPRS partly reflects among-male variation in Psire. Indeed,
3
significant repeatability has been shown in male traits predicting post-mating paternity
4
success in other species such as sperm performance (Evans & Simmons 2008; Lüpold
5
et al. 2012) and fertilization success itself (Tregenza, Attia & Bushaiba 2009; Evans et
6
al. 2013).
7
Our metrics of paternity success, Psire and Ppat.success, had posterior mean
8
estimates of 0.78 and 0.44 for VA, and 0.04 and 0.06 for h2, respectively, suggesting
9
that VA in Psire and Ppat.success may partly explain the non-zero VA in EPRS in song
10
sparrows (Reid, Arcese & Losdat 2014). Male paternity success therefore seems to be
11
the primary source of genetic variation in male EPRS (see also Forstmeier et al. 2011).
12
However, the posterior means had wide 95%CIs with lower limits that tended towards
13
zero, meaning that estimates were uncertain (Table 3). Likewise, heritability of male
14
fertilization success estimated in experimental systems is also low (Simmons 2003;
15
Konior, Keller & Radwan 2005).
16
17
Variation with inbreeding
18
Psire decreased substantially with increasing male f. Previously reported inbreeding
19
depression in male EPRS (Reid et al. 2011; Reid, Arcese & Losdat 2014) therefore
20
largely reflects inbreeding depression in Psire. Nbroods and the number of offspring
21
produced also tended to decrease with increasing male f, but estimated effects were
22
small with 95% credible intervals that overlapped zero (Table 3). Females that mate
23
with relatively less closely related within-pair or extra-pair males could therefore
24
produce relatively outbred sons that would achieve higher EPRS via higher Psire.
22
1
Since Psire is the product of the probability that a male will mate with a female
2
that has an available brood (Pmating) and the probability of siring an extra-pair offspring
3
given mating (Ppat, equation 2), future studies could usefully quantify inbreeding
4
depression in these two traits separately. Most wild population studies including ours
5
do not readily allow these two fitness components to be measured independently.
6
However, we did not detect inbreeding depression in Ppat.success, a fitness component
7
that reflects a male’s post-mating paternity success (i.e. an approximation of Ppat).
8
Inbreeding depression might therefore predominantly affect male mating success rather
9
than post-mating paternity success in song sparrows. Indeed, inbreeding depression in
10
mating success, and in secondary sexual traits that influence mating success, has been
11
reported in song sparrows (Reid et al. 2005) and other species (Ala-Honkola et al. 2009;
12
Valtonen, Roff & Rantala 2014).
13
The occurrence of inbreeding depression in Pmating but not in Ppat may explain
14
why inbreeding substantially decreases male EPRS but does not affect male within-pair
15
paternity success (WPPS, Reid et al. 2011, 2014; Reid, Arcese & Losdat 2014). Males
16
generally mate frequently with their socially paired female prior to laying, and within-
17
pair mating frequency can increase male WPPS (i.e. the paternity assurance/confidence
18
hypothesis, Møller 1987; Crowe et al. 2009). Conversely, extra-pair matings may
19
happen less frequently (Griffith, Owens & Thuman 2002; Westneat & Stewart 2003).
20
Variation in Pmating might consequently cause more variation in EPRS than in WPPS,
21
and inbreeding depression in Pmating might be expected to affect EPRS more than
22
WPPS. Inbreeding depression in Psire therefore suggests a proximate mechanism
23
explaining the observed differential inbreeding depression among different routes to
24
male reproductive success (i.e. WPPS and EPRS).
23
1
However, this conclusion should be interpreted cautiously because our metric
2
of post-mating paternity success Ppat.success does not incorporate unsuccessful matings
3
(i.e. matings that did not lead to EPO). Specifically, males with low value for Ppat might
4
rarely or never sire EPO even given extra-pair matings, meaning that these males would
5
not enter our analysis of Ppat.success. In practice, 49% of all focal males were excluded
6
from this analysis but mean f did not differ from the full set of males (Table 2). Still,
7
we cannot exclude the possibility that some degree of inbreeding depression occurs in
8
paternity success given mating.
9
10
Variation with age and social status
11
Psire decreased substantially with increasing male age but the same pattern was not
12
evident in other components of EPRS. Other cross-sectional studies have demonstrated
13
that male total reproductive success (e.g. Møller & Ninni 1998; Lifjeld et al. 2011) and
14
EPRS (Wetton et al. 1995; Cleasby & Nakagawa 2012) can vary with age. Interestingly,
15
although EPRS often varies with age, male WPPS often does not (Wetton et al. 1995;
16
Cleasby & Nakagawa 2012), as in Mandarte’s song sparrows (Reid, Arcese & Losdat
17
2014). Because we detected an age effect on Psire but not on Ppat.success (as for inbreeding
18
depression, see above), our data suggest that the higher Psire of older males most
19
probably stems from higher extra-pair mating success for older males.
20
No subcomponents of EPRS varied with a male’s social status, suggesting that
21
social status is not a primary determinant of EPRS in song sparrows. However, as
22
expected, socially-unpaired males had fewer available broods for potential extra-pair
23
reproduction when floater males were also considered (Appendix S1), emphasizing a
24
reduced opportunity for extra-pair reproduction for socially-unpaired individuals that
25
may be following alternative lifetime reproductive strategies.
24
1
2
Acknowledgements
3
4
We thank the Tsawout and Tseycum first nations bands for allowing access to Mandarte,
5
everyone who contributed to long-term field data collection, Matthew Wolak, Pirmin
6
Nietlisbach, Ryan Germain, Brad Duthie, Greta Bocedi for constructive comments on
7
manuscript drafts, and the European Research Council, Marie Curie Actions, UK Royal
8
Society, Swiss National Science Foundation and Natural Sciences and Engineering
9
Research Council of Canada for funding.
10
11
Data accessibility
12
Data have been archived in the Dryad Digital Repository doi:10.5061/dryd.1j25j
13
14
15
25
1
References
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
Ala-Honkola, O., Uddström, A., Pauli, B.D. & Lindström, K. (2009) Strong inbreeding
depression in male mating behaviour in a poeciliid fish. Journal of Evolutionary
Biology, 22, 1396-1406.
Anderson, M.J. (1994) Sexual selection. Princeton University Press, Princeton.
Arcese, P. (1987) Age, intrusion pressure and defence against floaters by territorial male song
sparrows. Animal Behaviour, 35, 773-784.
Arcese, P. (1989) Territory acquisition and loss in male song sparrows. Animal Behaviour, 37,
45-55.
Arnqvist, G. & Kirkpatrick, M. (2005) The evolution of infidelity in socially monogamous
passerines: the strength of direct and indirect selection on extrapair copulation behavior
in females. American Naturalist, 165, 26-37.
Bell, A.M., Hankison, S.J. & Laskowski, K.L. (2009) The repeatability of behaviour: a metaanalysis. Animal Behaviour, 77, 771-783.
Benowitz, K.M., Head, M.L., Williams, C.A., Moore, A.J. & Royle, N.J. (2013) Male age
mediates reproductive investment and response to paternity assurance. Proceedings of
the Royal Society B, 280, 20131124.
Bijma, P. (2010) Estimating indirect genetic effects: precision of estimates and optimum
designs. Genetics, 186, 1013-1028.
Birkhead, T.R. & Møller, A.P. (1995) Extra-pair copulation and extra-pair paternity in birds.
Animal Behaviour, 49, 843-848.
Birkhead, T.R. & Møller, A.P. (1998) Sperm competition and sexual selection. Academic Press,
San Diego
Canal, D., Jovani, R. & Potti, J. (2012) Male decisions or female accessibility? Spatiotemporal
patterns of extra pair paternity in a songbird. Behavioral Ecology, 23, 1146-1153.
Cleasby, I.R. & Nakagawa, S. (2012) The influence of male age on within-pair and extra-pair
paternity in passerines. Ibis, 154, 318-324.
Collet, J., Richardson, D.S., Worley, K. & Pizzari, T. (2012) Sexual selection and the
differential effect of polyandry. Proceedings of the National Academy of Sciences of
the United States of America, 109, 8641-8645.
Crnokrak, P. & Roff, D.A. (1999) Inbreeding depression in the wild. Heredity, 83, 260-270.
Crowe, S.A., Kleven, O., Delmore, K.E., Laskemoen, T., Nocera, J.J., Lifjeld, J.T. &
Robertson, R.J. (2009) Paternity assurance through frequent copulations in a wild
passerine with intense sperm competition. Animal Behaviour, 77, 183-187.
Dolan, A.C., Murphy, M.T., Redmond, L.J., Sexton, K. & Duffield, D. (2007) Extrapair
paternity and the opportunity for sexual selection in a socially monogamous passerine.
Behavioral Ecology, 18, 985-993.
Duckworth, R.A. & Sockman, K.W. (2012) Proximate mechanisms of behavioural inflexibility:
implications for the evolution of personality traits. Functional Ecology, 26, 559-566.
Evans, J. & Simmons, L. (2008) The genetic basis of traits regulating sperm competition and
polyandry: can selection favour the evolution of good- and sexy-sperm? Genetica, 134,
5-19.
Evans, J.P., Rosengrave, P., Gasparini, C. & Gemmell, N.J. (2013) Delineating the roles of
males and females in sperm competition. Proceedings of the Royal Society B, 280,
20132047.
Forstmeier, W., Martin, K., Bolund, E., Schielzeth, H. & Kempenaers, B. (2011) Female
extrapair mating behavior can evolve via indirect selection on males. Proceedings of
the National Academy of Sciences of the United States of America, 108, 10608-10613.
Freeman-Gallant, C.R., Wheelwright, N.T., Meiklejohn, K.E., States, S.L., Sollecito, S.V. &
Webster, M. (2005) Little effect of extrapair paternity on the opportunity for sexual
selection in savannah sparrows (Passerculus sandwichensis). Evolution, 59, 422-430.
26
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
Garcia-Gonzalez, F. & Evans, J.P. (2011) Fertilization success and the estimation of genetic
variance in sperm competitiveness. Evolution, 65, 746-756.
García-Navas, V., Ferrer, E.S., Bueno-Enciso, J., Barrientos, R., Sanz, J.J. & Ortego, J. (2014)
Extrapair paternity in Mediterranean blue tits: socioecological factors and the
opportunity for sexual selection. Behavioral Ecology, 25, 228-238.
Gasparini, C., Marino, I., Boschetto, C. & Pilastro, A. (2010) Effect of male age on sperm traits
and sperm competition success in the guppy (Poecilia reticulata). Journal of
Evolutionary Biology, 23, 124-135.
Griffith, S.C., Owens, I.P.F. & Thuman, K. (2002) Extra pair paternity in birds: a review of
interspecific variation and adaptive function. Molecular Ecology, 11, 2195-2212.
Hadfield, J.D. (2010) MCMC methods for multi-response generalized linear mixed models: the
MCMCglmm R package. Journal of Statistical Software, 33, 1-22.
Hadfield, J.D., Richardson, D.S. & Burke, T. (2006) Towards unbiased parentage assignment:
combining genetic, behavioural and spatial data in a Bayesian framework. Molecular
Ecology, 15, 3715-3730.
Johnson, M. & Walters, J.R. (2008) Effects of mate and site fidelity on nest survival of Western
Sandpipers (Calidris mauri). The Auk, 125, 76-86.
Keller, L.F. & Waller, D.M. (2002) Inbreeding effects in wild populations. Trends in Ecology
& Evolution, 17, 230-241.
Kingma, S.A., Hall, M.L. & Peters, A. (2013) Breeding synchronization facilitates extrapair
mating for inbreeding avoidance. Behavioral Ecology, 24, 1390-1397.
Konior, M., Keller, L. & Radwan, J. (2005) Effect of inbreeding and heritability of sperm
competition success in the bulb mite Rhizoglyphus robini. Heredity, 94, 577-581.
Kruuk, L.E.B. (2004) Estimating genetic parameters in natural populations using the animal
model. Philosophical Transactions of the Royal Society B: Biological Sciences, 359,
873-890.
Lebigre, C., Arcese, P., Sardell, R.J., Keller, L.F. & Reid, J.M. (2012) Extra-pair paternity and
the variance in male fitness in song sparrows (Melospiza melodia). Evolution, 66, 31113129.
Lifjeld, J., Kleven, O., Jacobsen, F., McGraw, K., Safran, R. & Robertson, R. (2011) Age before
beauty? Relationships between fertilization success and age-dependent ornaments in
barn swallows. Behavioral Ecology and Sociobiology, 65, 1687-1697.
Losdat, S., Chang, S.M. & Reid, J.M. (2014) Inbreeding depression in male gametic
performance. Journal of Evolutionary Biology, 27, 992-1011.
Lüpold, S., Manier, M.K., Berben, K.S., Smith, K.J., Daley, B.D., Buckley, S.H., Belote, J.M.
& Pitnick, S. (2012) How multivariate ejaculate traits determine competitive
fertilization success in Drosophila melanogaster. Current Biology, 22, 1667-1672.
Mauck, R., Huntington, C. & Grubb, T. (2004) Age-specific reproductive success: evidence for
the selection hypothesis. Evolution, 58, 880-885.
Møller, A.P. (1987) Copulation behaviour in the goshawk, Accipiter gentilis. Animal
Behaviour, 35, 755-763.
Møller, A.P., Mousseau, T.A., Rudolfsen, G., BalbontíN, J., Marzal, A., Hermosell, I. & De
Lope, F. (2009) Senescent sperm performance in old male birds. Journal of
Evolutionary Biology, 22, 334-344.
Møller, A.P. & Ninni, P. (1998) Sperm competition and sexual selection: a meta-analysis of
paternity studies of birds. Behavioral Ecology and Sociobiology, 43, 345-358.
Nakagawa, S. & Schielzeth, H. (2010) Repeatability for Gaussian and non-Gaussian data: a
practical guide for biologists. Biological Reviews, 85, 935-956.
Nietlisbach, P., Camenisch, G., Bucher, T., Slate, J., Keller, L.F. & Postma, E. (2015) A
microsatellite-based linkage map for song sparrows (Melospiza melodia). Molecular
Ecology Resources, In press.
Parker, G.A. & Birkhead, T.R. (2013) Polyandry: the history of a revolution. Philosophical
Transactions of the Royal Society B: Biological Sciences, 368, 20120335.
R Core Team (2013) R: a language and environment for statistical computing. Vienna, Austria.
27
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
Rasmussen, H.B., Okello, J., Wittemyer, G., Siegismund, H.R., Arctander, P., Vollrath, F. &
Douglas-Hamilton, I. (2008) Age-and tactic-related paternity success in male African
elephants. Behavioral Ecology, 19, 9-15.
Reid, J., Arcese, P., Cassidy, A.E., Marr, A., Smith, J.M. & Keller, L. (2005) Hamilton and Zuk
meet heterozygosity? Song repertoire size indicates inbreeding and immunity in song
sparrows (Melospiza melodia). Proceedings of the Royal Society B, 272, 481-487.
Reid, J.M. (2014) Quantitative genetic approaches to understanding sexual selection and mating
system evolution in the wild. Quantitative Genetics in the Wild (eds A. Charmantier,
D. Garant & L.E.B. Kruuk), pp. 34-53. Oxford University Press, Oxford.
Reid, J.M., Arcese, P. & Keller, L.F. (2006) Intrinsic parent-offspring correlation in inbreeding
level in a song sparrow (Melospiza melodia) population open to immigration. American
Naturalist, 168, 1-13.
Reid, J.M., Arcese, P., Keller, L.F. & Losdat, S. (2014) Female and male genetic effects on
offspring paternity: additive genetic (co)variances in female extra-pair reproduction
and male paternity success in song sparrows (Melospiza melodia). Evolution, 68, 23572370.
Reid, J.M., Arcese, P. & Losdat, S. (2014) Genetic covariance between male reproductive
tactics: within-pair paternity success and extra-pair reproductive success in song
sparrows. Journal of Evolutionary Biology, 27, 2046-2056.
Reid, J.M., Arcese, P., Sardell, R.J. & Keller, L.F. (2011) Additive genetic variance,
heritability, and inbreeding depression in male extra-pair reproductive success.
American Naturalist, 177, 177-187.
Reid, J.M. & Keller, L.F. (2010) Correlated inbreeding among relatives: occurrence,
magnitude, and implications. Evolution, 64, 973-985.
Sardell, R.J., Keller, L.F., Arcese, P., Bucher, T. & Reid, J.M. (2010) Comprehensive paternity
assignment: genotype, spatial location and social status in song sparrows, Melospiza
melodia. Molecular Ecology, 19, 4352-4364.
Schlicht, E. & Kempenaers, B. (2011) Extra-pair paternity and sexual selection. From Genes
to Animal Behavior (eds M. Inoue-Murayama, S. Kawamura & A. Weiss), pp. 35-65.
Springer Japan, Tokyo.
Simmons, L.W. (2003) The evolution of polyandry: patterns of genotypic variation in female
mating frequency, male fertilization success and a test of the sexy-sperm hypothesis.
Journal of Evolutionary Biology, 16, 624-634.
Simmons, L.W. (2011) Inbreeding depression in the competitive fertilization success of male
crickets. Journal of Evolutionary Biology, 24, 415-421.
Slatyer, R.A., Mautz, B.S., Backwell, P.R. & Jennions, M.D. (2012) Estimating genetic benefits
of polyandry from experimental studies: a meta-analysis. Biological Reviews, 87, 1-33.
Smith, J.N.M., Keller, L., Marr, A.B. & Arcese, P. (2006) Conservation and biology of small
populations: the song sparrows of Mandarte Island. Oxford University Press, New
York.
Stewart, S.L., Westneat, D.F. & Ritchison, G. (2010) Extra-pair paternity in eastern bluebirds:
effects of manipulated density and natural patterns of breeding synchrony. Behavioral
Ecology and Sociobiology, 64, 463-473.
Stutchbury, B.J.M., Piper, W.H., Neudorf, D.L., Tarof, S.A., Rhymer, J.M., Fuller, G. &
Fleischer, R.C. (1997) Correlates of extra-pair fertilization success in hooded warblers.
Behavioral Ecology and Sociobiology, 40, 119-126.
Suter, S.M., Keiser, M., Feignoux, R. & Meyer, D.R. (2007) Reed bunting females increase
fitness through extra-pair mating with genetically dissimilar males. Proceedings of the
Royal Society B, 274, 2865-2871.
Taff, C.C., Freeman-Gallant, C.R., Dunn, P.O. & Whittingham, L.A. (2013) Spatial distribution
of nests constrains the strength of sexual selection in a warbler. Journal of Evolutionary
Biology, 26, 1392-1405.
Tregenza, T., Attia, F. & Bushaiba, S.S. (2009) Repeatability and heritability of sperm
competition outcomes in males and females of Tribolium castaneum. Behavioral
Ecology and Sociobiology, 63, 817-823.
28
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
Tschirren, B., Postma, E., Rutstein, A.N. & Griffith, S.C. (2012) When mothers make sons
sexy: maternal effects contribute to the increased sexual attractiveness of extra-pair
offspring. Proceedings of the Royal Society B, 279, 1233-1240.
Valtonen, T.M., Roff, D.A. & Rantala, M.J. (2014) The deleterious effects of high inbreeding
on male attractiveness are observed under competitive but not under non-competitive
conditions. Behavior Genetics, 44, 144-154.
Wang, C. & Lu, X. (2014) Extra-pair paternity in relation to breeding synchrony in ground tits:
an individual-based approach. Journal of Avian Biology, 045, 1-5.
Weatherhead, P.J. & Robertson, R.J. (1979) Offspring quality and the polygyny threshold: "the
sexy son hypothesis". American Naturalist, 113, 201-208.
Webster, M.S., Pruett-Jones, S., Westneat, D.F. & Arnold, S.J. (1995) Measuring the effects of
pairing success, extra-pair copulations and mate quality on the opportunity for sexual
selection. Evolution, 49, 1147-1157.
Webster, M.S., Tarvin, K.A., Tuttle, E.M. & Pruett-Jones, S. (2007) Promiscuity drives sexual
selection in a socially monogamous bird. Evolution, 61, 2205 - 2211.
Westneat, D.F. & Stewart, I.R.K. (2003) Extra-pair paternity in birds: causes, correlates, and
conflict. Annual Review of Ecology, Evolution, and Systematics, 34, 365-396.
Wetton, J.H., Burke, T., Parkin, D.T. & Cairns, E. (1995) Single-locus DNA fingerprinting
reveals that male reproductive success increases with age through extra-pair paternity
in the house sparrow (Passer domesticus). Proceedings of the Royal Society B, 260,
91-98.
Whittingham, L.A. & Dunn, P.O. (2005) Effects of extra-pair and within-pair reproductive
success on the opportunity for selection in birds. Behavioral Ecology, 16, 138-144.
Wilson, S., Norris, D.R., Wilson, A.G. & Arcese, P. (2007) Breeding experience and population
density affect the ability of a songbird to respond to future climate variation.
Proceedings of the Royal Society B, 274, 2539-2545.
Winkler, D.W., Wrege, P.H., Allen, P.E., Kast, T.L., Senesac, P., Wasson, M.F., Llambías,
P.E., Ferretti, V. & Sullivan, P.J. (2004) Breeding dispersal and philopatry in the tree
swallow. The Condor, 106, 768-776.
Woolfenden, B.E., Gibbs, L.H. & Sealy, S.G. (2002) High opportunity for sexual selection in
both sexes of an obligate brood parasitic bird, the brown-headed cowbird (Molothrus
ater). Behavioral Ecology and Sociobiology, 52, 417-425.
33
34
Supporting Information
35
36
The following Supporting Information is available for this article online:
37
38
39
Appendix S1. Quantitative genetic analysis of the number of available broods
40
including non-territorial floater males
41
42
Appendix S2. Quantitative genetic analyses including parental effects
43
29
1
Appendix S3. Analytical decomposition of the phenotypic variance in male extra-
2
pair reproductive success
3
30
1
Figure legends
2
3
4
Figure 1. Schematic overview of the decomposition of male extra-pair reproductive
5
success. Extra-pair reproductive success is the product of (a) Nmates, Ppat and Noffspring
6
(Table 1) following Webster et al. (1995) and (b) Nbroods, Pmating, Ppat and offspring
7
(Table 1) following our new decomposition. (c) depicts Ppat.success (Table 1). Extra-pair
8
offspring sired by the focal male are shown in black while within-pair offspring are
9
shown in grey. Solid and dotted black arrows show that the focal male did and did not
10
mate with each female, respectively.
11
12
Figure 2. Distributions of four subcomponents of male extra-pair reproductive success.
13
Panels show the number of (a) available broods per male-year (Nbroods), (b) extra-pair
14
offspring (EPO) sired out of the total number of available offspring per male-brood, (c)
15
number of offspring per available broods and (d) additional EPO sired out of the total
16
additional offspring available per male-brood. Dashed and solid lines demarcate means
17
and medians respectively. In (b), bottom and top panels show male-broods where ≥1
18
EPO and zero EPO were sired, respectively. In (b) and (d), black, dark grey, light grey
19
and white bars represent broods with 1, 2, 3, or 4 offspring available as potential EPO,
20
respectively.
21
31
1
Table 1. Definitions of components of male extra-pair reproductive success.
2
Component
Nmates
Definition
Number of extra-pair females with whom a male mated (Me in Webster et al. 1995)
Total number of offspring produced by extra-pair females with whom a male mated
Noffspring
(Ne in Webster et al. 1995)
Ppat
Probability of siring an extra-pair offspring (EPO) given mating (Pe in Webster et al.
1995)
Nbroods
Number of broods (or litters) available to a focal male for potential extra-pair
paternity
Pmating
Male’s probability of mating with a female that has an available brood (or litter)
offspring
Mean number of offspring in available broods (or litters)
Psire
Probability that an offspring within an available brood (or litter) will be sired as an
EPO by a focal male. Psire = Pmating × Ppat.
Ppat.success
Probability that an offspring within an available brood (or litter) will be sired as an
additional EPO by a focal male given that he sired one EPO in that brood
32
Table 2. Statistics describing the pedigree data used for analyses of (a) Nbroods, Psire and µoffspring and (b) Ppat.success. ‘Individuals’ and ‘Focal males’
denote the numbers of individuals included in the pedigree and that contributed phenotypic data, respectively. ‘k (all individuals)’ and ‘k (focal
males)’ denote pairwise k across all individuals included in the pedigree and males that contributed phenotypic data, respectively. f is the
coefficient of inbreeding of these males. sd is the standard deviation.
k (all individuals)
k (focal males)
f
Individuals
Focal males
mean ± sd
median (range)
mean ± sd
median (range)
mean ± sd
median (range)
a)
625
327
0.057 ±
0.044
0.054 (0.0000.471)
0.071 ±
0.038
0.060 (0.000.471)
0.064 ±
0.051
0.058 (0.0000.308)
b)
466
167
0.053 ±
0.047
0.049 (0.0000.471)
0.072 ±
0.039
0.064 (0.0050.389)
0.055 ±
0.046
0.048 (0.0000.264)
33
Table 3. Posterior means (and 95% credible intervals) for additive genetic, permanent individual, year, and residual variances (VA, VPI, VY and
VR), inbreeding depression (f), social status and age effects, heritability (h2) and repeatability (R) in a) Nbroods, b) Psire, c) Number of offspring per
available brood, and d) Ppat.success. Estimates highlighted in bold have 95% credible intervals that did not converge to zero (variance components)
or overlap zero (fixed effects). ‘Obs.’ denotes the number of observations and ‘focal males’ denotes the number of individual males that
contributed phenotypic data.
Variance components
Sample sizes
Model
Obs.
a) Nbroods
786
b) Psire
4083
c) Number of
offspring
d) Ppat.success
a
4083
466
Fixed effects
Focal
males
VA
VPI
VY
VR
f
Social status
327
0.01
(<0.0001 –
0.03)
0.03
(0.008 –
0.05)
0.12 (0.05
– 0.20)
0.003
(0.002 –
0.009)
-0.31
(-1.07 –
0.49)
0.08 (-0.06 –
0.23)a
327
0.78
(<0.001 –
2.03)
1.50
(<0.001
– 2.71)
0.07
(<0.001 –
0.22)
12.8 (9.72
– 15.71)
-11.18
(-18.34 –
-4.54)
0.28 (-0.38 –
0.81)a
327
0.003
(<0.0001 –
0.01)
0.008
(<0.001
– 0.02)
0.09 (0.03
– 0.15)
0.88 (0.84
– 0.91)
-0.47
(-1.18 –
0.14)
0.003 (-0.12 –
0.12)a
167
0.44 (<
0.001 –
1.25)
0.19 (<
0.001 –
0.67)
0.13
(<0.001 –
0.46)
3.35 (1.80
– 5.21)
-3.91 (11.7 –
3.56)
0.10 (-1.70 –
2.11)a
Heritability Repeatability
Age
h2
R
0.02 (-0.06 – 0.08)b
-0.08 (-0.21 – 0.06)c
0.03
(<0.001 –
0.09)
0.12 (0.06–
0.18)
-2.63 (-3.27 – -2.01)b
-1.19 (-2.10 – -0.33)c
0.04
(<0.001 –
0.11)
0.03 (-0.05 – 0.09)
-0.10 (-0.22 – 0.03)c
b
-0.69 (-1.48 – 0.08)b
-0.75 (-1.79 – 0.33)c
estimate for socially-paired males relative to socially-unpaired males; bestimate for age 1 relative to age ≥ 6; cestimate for age 2 to 5 relative to age ≥ 6
34
0.13
(0.06 – 0.18)
0.03
(<0.001 –
0.11)
0.12 (0.001 –
0.26)
0.06
(<0.001 –
0.16)
0.08 (<0.001
– 0.18)
1
Figure 1
2
35
1
Figure 2.
(c)
400
(a)
140
Frequency of male-broods
Frequency of male-years
120
100
80
60
40
300
200
100
20
0
0
0
5
10
15
20
25
1.0
Number of available broods (Nbroods)
1.5
2.0
2.5
3.0
3.5
4.0
Number of offspring in available broods
220
(b)
(d)
200
1000
Frequency of male-broods
Frequency of male-broods
180
500
0
90
60
160
140
120
100
80
60
40
30
20
0
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0
Proportion of available offspring sired as EPO
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Proportion of additional EPO sired given paternity of 1 EPO
36