• All data used in this manuscript are available as Supplementary Information.


The contribution of extra-pair paternity (EPP) to sexual selection has received considerable attention, particularly in socially monogamous species. However, the importance of EPP remains difficult to assess quantitatively, especially when many extra-pair young have unknown sires. Here, we combine measurements of the opportunity for selection (I), the opportunity for sexual selection (IS), and the strength of selection on mating success (Bateman gradient, βSS) with a novel simulation of random mating tailored to the specific mating system of the blue tit (Cyanistes caeruleus). In a population where social polygyny and EPP are common, the opportunity for sexual selection was significantly stronger and Bateman gradients significantly steeper for resident males than for females. In general, success with the social mate(s) contributed most to variation in male reproductive success. Effects of EPP were small, but significantly higher than expected under random mating. We used sibship analysis to estimate the number of unknown sires in our population. Under the assumption that the unknown sires are nonbreeding males, EPP reduced the variance in and the strength of selection on mating success, a possibility that hitherto has not been considered.

In sexually reproducing organisms, fitness fundamentally depends on achieving matings. This generates selection on mating success and in turn selection on traits linked to mating success: sexual selection. Sexual selection is a major force in the evolution of phenotypic differences between the sexes, and of mating systems and sex roles (Andersson 1994).

Pair bonding with (social) monogamy is the apparent mating system in a wide range of animal taxa (Lack 1968; Caldwell 1997; Kvarnemo et al. 2000; Baeza 2008). Monogamy constrains the potential for sexual selection, because mating success can only vary from zero to one and—assuming an unbiased sex ratio—reproductive and mating success are equal for both sexes. However, the realized mating system is often genetic promiscuity with extra-pair paternity (EPP; Griffith et al. 2002; Chapple 2003; Lodé and Lesbarrères 2004; Cohas and Allainé 2009), and extra-pair matings have the potential to dramatically alter the strength of sexual selection in one or both sexes.

The influence of EPP on the strength of sexual selection in males has been subject of extensive research effort (reviewed in Schlicht and Kempenaers 2010). Most studies are motivated by the idea that EPP increases the strength of sexual selection (Poesel et al. 2011), which is the case when EPP leads to a nonrandom reallocation of mating success from lower-ranked males to “top” males, resulting in highly skewed male mating success similar to that observed in lekking species (“hidden lek,” Wagner 1997). However, the strength of sexual selection could also remain unchanged by EPP, either if extra-pair mating is random, that is, when all males have an equal probability to gain or lose paternity (Schlicht and Kempenaers 2010), or if paternity gain and loss cancel each other out, for instance, as a consequence of a trade-off between protecting paternity with the social mate and pursuing extra-pair matings (Freeman-Gallant et al. 2005; Whittingham and Dunn 2005). Finally, EPP can even diminish the strength of sexual selection, if it reduces variation in mating success among males, for example, if the extra-pair sires are males that failed to obtain a territory or a social mate (Lebigre et al. 2012). The aim of this study is to analyze the effect of EPP on the potential for sexual selection in a population of blue tits (Cyanistes caeruleus). Because blue tits are facultatively polygynous (Kempenaers 1994), we assess effects of variation in both social and extra-pair mating success on sexual selection.

It remains a matter of debate how to quantify mating systems and sexual selection independent from specific traits that may be sexually selected (Klug et al. 2010; Krakauer et al. 2011). One approach is to use a combination of three indices: the opportunity for selection, I; the opportunity for sexual selection, IS; and the Bateman gradient βss (Wade and Arnold 1980; Arnold and Wade 1984). I and IS estimate the variation available to selection and are a measure of the upper limit of the response to selection (Crow 1958; O'Donald 1970). βss quantifies the link between mating success and fitness and is therefore a measure of the strength of selection on mating success. It is estimated as the slope of the (partial) least-squares regression of reproductive on mating success (Arnold and Duvall 1994). These three measurements have been proposed as adequate tools to quantify mating patterns and to characterize mating systems (Jones et al. 2004; Mills et al. 2007; Jones 2009; Croshaw 2010).

Here, we estimate I, IS, and βss, combined with novel approaches that specifically address two issues that have been raised about these estimates. First, random mating can cause variation in mating success (and as a consequence variation in reproductive success) that is independent of male traits and that will thus not lead to sexual selection (Hubbell and Johnson 1987; Gowaty and Hubbell 2005; Klug et al. 2010; Jennions et al. 2012). To argue that selection and not drift is at work, it is therefore necessary to determine the level of variation expected by chance alone. Ideally, under randomness measurements of the opportunity for sexual selection should be similar for different study systems (Kokko et al. 1999). However, when describing random mating via a Poisson, binomial, or multinomial distribution, it can be shown that I and IS increase with the number of individuals mating (randomly) and with the number of (randomly distributed) matings available, as determined for instance by clutch size (Downhower et al. 1987; Ruzzante et al. 1996; Fairbairn and Wilby 2001; Walsh and Lynch 2008). Hence, variance-based estimates reflect both trait-based and stochastic fitness variation. To solve this, various alternative indices have been derived that are standardized in relation to a given sampling distribution (e.g., Poisson, binomial), thus incorporating randomness (e.g., Morisita index, Iδ; monopolization index, Q; binomial skew index, B; Ruzzante et al. 1996, Kokko et al. 1999, Nonacs 2000, Fairbairn and Wilby 2001). With correct choice of a null model, the systematic effects are removed so that a comparison of selection opportunities becomes more meaningful (Jennions et al. 2012).

Similarly to the effect of clutch size, the rate of EPP may cause systematic effects on I and IS, making it difficult to determine effects of EPP on sexual selection, unless a null model of random mating is included (Schlicht and Kempenaers 2010). However, the above-mentioned null models based on simple sampling distributions probably do not correct for random mating in a way that is biologically relevant in a system with social polygyny and EPP, where mating takes place in two arenas: with social and with extra-pair mates. Here, we solve this problem by simulating random mating based on a model specifically derived for such a mating system.

The second issue is that sampling is often incomplete in studies on EPP, because (1) some young are sired by males that remain unsampled, leaving the paternity of these young unassigned, and (2) individuals included in the study may have sired offspring in unsampled broods. Comparisons based on opportunity measurements can be misleading due to such sampling limitations. A reduced number of assigned young increases estimates for the realized mating system (Møller and Ninni 1998; Freeman-Gallant et al. 2005) and the focal individuals may be a nonrandom subsample of the population (Webster et al. 1995; Jones et al. 2001). Our study provides no ultimate solution to this problem, but we (1) assess the number of unsampled sires via sibship analysis and (2) consider how sensitive estimates are to assumptions about the status of these unsampled individuals. We do this based on a scenario where unsampled individuals diverge strongly from the sampled population and effects are expected to be strong: we assume that unsampled individuals are unpaired males.

Neither opportunity estimates nor Bateman gradients are related to the strength of selection on an individual trait (Klug et al. 2010). However, here we seek to gain an understanding of the potential for sexual selection, without making prior assumptions about the traits under selection. I, IS, and βss—when corrected for randomness—provide information relevant in this context (Krakauer et al. 2011). Values of I and IS significantly above what is expected under random mating correspond to the inequality among individuals in their reproductive and mating success, unlikely to be generated by chance, but instead by the combination of all their traits. This allows a comprehensive quantification of sexual selection that can be compared among populations and is—assuming sufficient heritabilities—linked to overall phenotypic evolution.

Given a particular (sexual) selection potential among males, it is interesting to consider the sources of this reproductive skew. Variation between males may be mainly due to the contrast between those that successfully mate and reproduce and those that do not. Alternatively, most of the variation may lie within the class of successfully reproducing males. Further, variability in both extra- and within-pair reproductive success may arise through variation in mate number, in the number of offspring per mate, and in the proportion of these offspring sired (Webster et al. 1995). Calculating how much of the variation in male reproductive success can be assigned to each of these components then allows to assess the selection potential arising via extra- versus within-pair reproduction. Such a calculation can be done analytically (Webster et al. 1995), but in addition, we here implement a statistical method to inspect fitness components. We also construct confidence intervals (CIs) for these values, as well as for those obtained for I, IS, and βss. This allows to assess the uncertainty around values that are customarily presented as point estimates.



We studied a nest-box population of blue tits in a forest patch of high-quality habitat at Kolbeterberg, Vienna, Austria, from 1998 to 2003. We captured mature individuals, banded them with a metal ring and a unique combination of three plastic color bands, and aged them as yearlings or older (“adults”) following Svensson (1992). For birds with inconsistent aging between repeated captures (12 males and 20 females), age information was not used. Unless the hatch year is known from previous captures or breeding, the exact age of birds in adult plumage was unknown (43 males and 52 females). We visited nests regularly to monitor breeding activity. Identity of social pairs and socially polygynous males was determined via direct observation. Nestlings were banded with a metal ring 14–16 days after hatching. See online Supplementary Material for a more detailed description of the study site and procedures.

From all adults and nestlings, we collected a small (5–50 μl) blood sample for molecular sexing and parentage analysis. We also collected unhatched eggs or dead nestlings for genotyping. We determined parentage of offspring using five to eight highly polymorphic autosomal microsatellite markers (combined probability of exclusion P > 0.999) following standard procedures detailed in Foerster et al. (2003) and Delhey et al. (2007) (probability of false inclusion P ≤ 4.77×10−3 in all cases). For all young with unknown sires or unidentified social parents, sibship analysis was performed using Colony 2.0 (Wang 2008), as described in the Supplementary Material. Based on parentage and sibship analysis we constructed artificial IDs for unknown parents. No age variables were assigned to birds with artificial IDs.

Calculation of male and female reproductive success (RS) and mating success (MS) is based on a total of 4644 young (eggs, nestlings, or fledglings) from 473 breeding attempts, with a mean (±SD) brood size of 9.8 ± 2.8. Of all breeding events, 262 (55%) contained extra-pair offspring. The mean number (proportion) of extra-pair young (EPY) in such clutches was 2.9 ± 2.2 (0.31 ± 0.24). We assigned paternity to 96% of the young (N = 4476). Of all offspring, 747 (16%) were extra-pair, and of these 22% (168) were sired by an unknown male. This could be (1) an unrecognized breeder, that is, breeding in a natural cavity or in the low quality habitat surrounding the study site, (2) an unsuccessful breeder, that is, with a breeding attempt that failed before parents were identified, or (3) a nonbreeder, that is, a male without a territory or mate.

Of 498 annual male breeders (376 individual males) we recorded, 187 (38%) sired extra-pair offspring (154 individual males, 41%). Of all resident males, 29 (8%) were socially polygynous, two of them in 2 years (31 annual breeders, 6%). Of all 449 annual female breeders (314 individual females), 202 (45%) had EPY (156 individual females, 47%).


Initially, we calculated both annual and lifetime (summed up across all years an individual was observed breeding on the study site) RS and MS, but we focus on annual estimates here. Both males and females gain additional matings and additional offspring with additional breeding seasons. This leads to an association between mating and reproductive success that is unrelated to sexual selection (see also Gerlach et al. 2012), but reflects the well-known differences between one and multiple-year breeders (Dhondt 1989). Because covariance between EPP and survival was nonsignificant, EPP essentially operated within 1 year only. Our estimates of I and IS for males reflect the inequality among males breeding in the same year, and we are interested in how this is affected by reallocation of paternity via EPP. In this sense, the length of one breeding season is the relevant timescale, given the question we study and the life history of blue tits (Gerlach et al. 2012; Kokko et al. 2012). We do not present results for each year separately, because year-wise CIs were large and showed great overlap, despite substantial differences in point estimates (Schlicht and Kempenaers 2010).

RS is defined as the number of young in the nest at day 14–16 posthatch. We did not include information on unhatched eggs and dead nestlings, because sampling at this stage is often incomplete (e.g., due to predation). Breeding attempts that failed before the young were banded are thus included with RS set to zero. Based on the sibship analysis, we considered one scenario for the impact of unassigned EPY on the results; we assumed that all sires (N = 64, with artificial male IDs) were nonbreeders, so that they only reproduced via EPP. Known males that sired EPY without breeding in one of the monitored nests (28 individuals, 29 annual breeders) were also included only here. We repeated all calculations using the number of fledged young instead of nestlings, a measurement that may reflect fitness more closely. Results remained qualitatively unchanged. Thus, we only report results based on nestlings.

MS is defined as the total number of mates with whom an individual has genetic offspring. We included information from unhatched eggs and dead nestlings here, because we seek a measure for the number of successful matings. Because we are lacking information on copulation behavior, we make use of all available information from the parentage analysis. All nesting males were assigned one apparent and within-pair mate (two for polygynous males), even when they did not sire a single offspring, because mating is considered successful on a behavioral basis. Following the scenario described above, the 92 males that are assumed to have only sired EPY are given zero apparent (within-pair) mates.


We calculated I, IS, and βSS following the standard definitions (Jones 2009):

display math
display math
display math

The slope was taken from a generalized linear mixed-effect model (Gaussian-GLMM) as described below in Statistical Analysis.

For the partitioning of variance in male RS, males were separated into two classes according to their actual RS (males without versus males with sired offspring), and according to their MS (genetically monogamous versus genetically promiscuous males). We calculated the relative importance of variation within and between the two classes, using the fact that the variance of a variable X split into a class a with frequency pa and a class b with frequency pb can be written as:

display math

where the first two variance terms reflect the within-class variances, and the last term reflects the between-class variance (modified from Wade and Shuster, 2004).

The contribution of different fitness components to male RS was inspected analytically and statistically. Total genetic reproductive success (G) can be partitioned as:

display math

with the parameters M, N, and P representing the total mate number, average brood size, and total percentage sired, respectively. The subscripts W and E denote within- or extra-pair parameters. Terms for the contribution of each of these six parameters and their covariances to the variance in male RS are derived analytically in Webster et al. (1995). The contributions of NE and PE are based only on individuals with nonzero ME.

The statistical analysis of the contribution of the different fitness components to variance in male RS is based on R2-values from GLMMs (see below). The R2-value of the full model, including all relevant fitness components as explanatory variables, was used as reference. The reduction in R2 after removal of one of the variables is a measure of the variance explained by this variable (see Vedder et al. 2011 for a similar approach). Because maximum likelihood is the criterion of fit in GLMMs, pseudo-R2 values are used following Nagelkerke (1991). For comparison, models were reduced to linear models and the procedure was repeated with adjusted R2 values. Results were almost identical and only the contributions based on pseudo-R2 values are reported here. To compare these results with those derived analytically, both were rescaled to sum up to 1 for all components included in the model.


We estimated CIs for opportunity estimates using the fact that the square root of opportunity estimates is the coefficient of variation (CV). We calculated confidence boundaries of the CV based on an approximation by Kelley (2007; R-package “MBESS”: Kelley and Lai 2010) and squared them. For variance ratios, bootstrap CIs were constructed using the R-package “boot,” based on Davison and Hinkley (1997, ch. 5). Parameters were set to 10,000 replicates, simulation-type “ordinary,” “indices” resampling, and interval-type “basic.”


To compare estimates of I, Is and βss to values expected under random mating, we simulated random within- and extra-pair mating, based on the original data. For random within-pair mating, the observed brood sizes and values of PW were separated and randomly reallocated to each other. For random extra-pair mating, we used two approaches to assign EPY. In model A, each EPY was assigned a sire independently. Probabilities for siring young were initially equal for all potential sires, but decreased for a male with the number of young already sired by that male. In model B, the unit of assignment was not individual EPY, but instead the fraction of EPY in a brood sired by the same male. This takes into account that extra-pair fertilizations within the same brood may be nonindependent (Brommer et al. 2007). Details of the simulation are given in the Supplementary Material. Estimates of sexual selection were calculated for the simulated populations in the same way as for the original population. The simulation was repeated 10,000 times and the mean of the estimates from all simulations and their 95% CIs (inner range of 95% of simulated values) are reported.


All statistical analyses were performed with the software R 2.12.1 (R Development Core Team 2011). To account for annual differences and repeated measures from individuals breeding in several years, we used GLMMs (package “lme4”: Bates et al. 2011) with year and ID as random factors. Depending on the distribution of the response variable, we used models with a Gaussian (identity-link function), Poisson (log-link function), or binomial (logit-link function) error structure. All estimates are presented on the original scale. Thus, estimates from a model with Poisson error structure (Poisson–GLMM) represent a multiplicative effect (referred to in the Results as m-effect), that is, a difference by a factor given by the back-transformed estimate (1 corresponds to no difference). Estimates from a model with binomial error structure (binomial–GLMM) represent a probability effect (p-effect), that is, a difference in probability as given by the back-transformed estimate (0 corresponds to no difference). For models with a Gaussian error structure, P values and estimates were obtained by Markov chain Monte Carlo simulations (package “languageR”: Baayen 2010, 100,000 iterations). Credibility intervals are highest posterior density (HPD) intervals, from which the P values are calculated. For models with a Poisson or binomial error structure, 95% CIs were calculated by inference from the general linear hypothesis of the model (package “multcomp”: Hothorn et al. 2008). Ninety-five percent CI or HPD intervals are reported in parentheses behind effect sizes. We assessed effects of age (1) as a continuous variable, ranging from 1–6 years (mean for annual breeders: 1.5 ± 0.8 SD), (2) as the quadratic term of (1) to account for potential senescence in mating performance, and (3) as a categorical variable separating yearlings (477 annual breeders) from older birds (238 annual breeders). In all models, model fit was diminished when including (2) so that models were reduced to (1). Whenever age effects were solely due to differences between yearlings and older birds, we only report the effect of the categorical variable.



Of the 405 resident annual male breeders for which paternity loss could be determined, 70 both lost and gained paternity, whereas 56 gained paternity without loss and 130 lost paternity without gain. Reciprocal cuckoldry occurred rarely in three of the six study years (in total nine out of 347 male–male pairs).

Considering all males, there was no association between measures of paternity gain and loss; for instance, the probabilities to lose or gain paternity were unrelated (p-effect = 0.01 [−0.13 to 0.14], N = 364, z = 0.09, P = 0.93). However, considering only males that were involved in EPP, paternity gains and losses did not compensate each other (mean difference for males that gained paternity: 1.10 [0.49–1.69], N = 126, P = 0.0004; mean difference for males that lost paternity: −1.91 (−1.42 to −2.41), P = 0.0002; Fig. 1).

Figure 1.

Net paternity gain or loss for subgroups of male blue tits. Boxes indicate mean and standard error. Values at the bottom indicate sample size.

We expected that the probability of paternity loss would be higher for socially polygynous than for socially monogamous males, because their risk is twice as high (two broods vs. one) and because males may not be able to guard two females simultaneously. However, this was only the case for yearling and not for older polygynous males (Table 1A, Fig. 2). Similarly, the probability that a brood contained EPY was higher only when the owner was a yearling polygynous male (Table 1B). For polygynous males, paternity loss did not differ between primary and secondary broods (data not shown).

Table 1. Effects of male age and social polygyny on paternity loss in blue tits. Binomial–GLMMs with (A) male perspective: paternity loss in at least one brood (yes/no, N = 305 males) and (B) brood perspective: brood containing EPY (yes/no, N = 333 broods) as dependent variables, and with year (1998–2003) and male identity as random factors. All estimates are back-transformed to the original scale (p-effect)
Explanatory variableEffect (95% CI)zP
  1. EPY = extra-pair young; GLMM = generalized linear mixed-effect model.

(A) Probability of paternity loss for a male   
Male mating status (social polygyny)−0.04 (−0.34 to 0.29)−0.250.80
Male age (yearling)−0.03 (−0.18 to 0.13)−0.400.69
Mating status×age0.44 (−0.07 to 0.50)2.200.03
(B) Probability of containing EPY for a brood   
Male mating status (social polygyny)−0.24 (−0.41 to 0.04)−2.070.04
Male age (yearling)−0.03 (−0.18 to 0.13)−0.400.69
Mating status×age0.28 (−0.07 to 0.44)1.980.05
Figure 2.

Relationship between paternity loss and social polygyny for yearling and older (adult) male blue tits (see Table 1a for statistical details). Values below bars are sample sizes (total N = 305) and error bars indicate the standard error. Dashed lines show fp, the expected frequency of paternity loss for polygynous males, based on fm, the observed frequency of paternity loss in monogamous males of the respective age class (fp = 2 fmfm2).


Taking EPP into account led to a significant increase in selection opportunities (Table 2). For resident males, selection opportunities arising from the apparent mating system were systematically lower than the values obtained under the two simulations (Table 2). Regarding the realized mating system, the opportunity for selection I did not differ from the values obtained under the random mating simulations, but the opportunity for sexual selection Is was significantly larger than expected under random mating (the 95% CIs do not overlap; Table 2). In contrast, the Bateman gradient was higher for the apparent mating system than expected from the random mating simulations, whereas the realized Bateman gradient was similar to that obtained from simulations (Table 2).

Table 2. Measurements of sexual selection based on reproductive (RS) and mating success (MS) for male and female blue tits. For males, different categories of birds are used. Resident males are those known to have bred in the study area. “Realized” and “apparent” refer to the genetic and social reproductive or mating success, respectively. “Extra-pair” and “within-pair” refer to selection arising from extra-pair and within-pair siring success, separately. “Unknown males” refers to unidentified sires under the assumption that they were unpaired. See text for details
  Opportunity forOpportunity for sexualBateman gradient
  selection (RS)selection (MS)(MSRS)
CategoryNI95% CIx¯σ2IS95% CIx¯σ2βSS95% CIR2
  • 1

    Probability for I < 0.28: P = 0.16.

  • 2

    P < 0.0001.

  • 3

    Values are means across 10,000 runs.

  • 4

    Mean value, all P < 0.01.

  • 5

    Probability for I > 0.26: P = 0.18.

  • 6

    P = 0.80.

Resident males realized4050.3110.26–0.378.321.10.350.30–0.421.–2.440.182
Resident males apparent4050.220.18–0.268.917.10.060.05––6.690.112
Resident males simulation A34050.270.25–0.308.519.60.240.21––1.590.104
Resident males simulation B34050.320.29–0.358.523.00.230.20––3.120.184
Resident males extra-pair3874.462.99–7.380.93.33.352.34––1.730.682
Resident males within-pair3640.170.14–0.208.311.50.0630.05––4.990.092
Resident and unknown males realized4980.470.39–0.567.223.90.340.29–0.401.–2.540.162
Resident and unknown males apparent4980.500.42–0.607.225.90.310.26–0.400.880.27.56.87–8.170.512
Unknown males only931.130.72––0.391.50.61.480.87–2.020.222
Resident females4470.2450.21––−0.01−0.37 to 0.480.006

Assuming a nonbreeder status for unknown males increased I, but not Is or βss (Table 2). Among “non-breeding males,” βss was slightly flatter than among resident males (Table 2, Fig. 3B).

Figure 3.

Relationship between reproductive and mating success (Bateman gradient) for (A) resident males versus females, (B) resident males versus unknown sires, assuming the latter were unpaired, as well as for both groups of males combined, and (C) separately for extra- and within-pair reproduction of resident males (see Table 2 for details).

I, IS, and βss were higher for males than for females and CIs showed only minimal overlap (Table 2, combined probability for Imales < 0.28 and Ifemales > 0.26: P = 0.16 × 0.18 = 0.03). This was especially true for βss, which is significantly positive for all categories of males, but essentially zero for females (Table 2, Fig. 3A).

The frequency distributions of RS and MS showed similar levels of dispersion, asymmetry, and peakedness for males and females (Fig. 4A–D), and they were well described by a two-step (RS) or one-step (MS) Poisson distribution. The deviation from equality was also similar for both sexes (Fig. 4E, F).

Figure 4.

Distributions of reproductive and mating success for a population of blue tits. (A–D) Frequency distributions of reproductive success (A, B) and mating success (C, D) for males (A, C) and females (B, D). (E, F) Cumulative distributions for reproductive success (open circles, left and bottom axes) and mating success (open squares, right and top axes) for males (E) and females (F). Indication of inequality in (A–D) is given by dispersion (variance), symmetry (skewness), and peakedness (kurtosis) of distributions (calculations follow Zar 1984). Open circles refer to the actual data, filled circles show random distributions that were generated based on the observed frequencies by sampling from a Poisson distribution conditioned on an interval h of observed values >0 (A, B) or all observed values (C, D). The parameter, λ, was chosen such that the mean of this conditional distribution fitted the mean of the observed frequencies in h. Zero is excluded from h in (A, B) to account for zero-inflation in RS due to complete nest failures. In (E) and (F), inequality is indicated by the deviation from the straight black line.

Variation within the group of successful (RS > 0) males produced more variance in RS than the variation between successful and unsuccessful (RS = 0) males: fraction within = 60% (70% with inclusion of unknown males as nonbreeders). The opposite was the case for variance in male MS: variation between the groups of genetically monogamous versus promiscuous males contributed more than the variation within those groups (fraction between = 66%; 64% with inclusion of unknown males as nonbreeders).

Among resident males, the selection opportunities arising from EPP were much higher than those from within-pair paternity (Table 2). However, βss was much flatter for EPP than for within-pair paternity (Table 2, Fig. 3C), indicating that an additional social mate (social polygyny) led to a larger increase in RS than an additional extra-pair mate.


Overall, the effect of within-pair success on variation in RS dominated that of extra-pair success both in the analytical and statistical analysis (Tables 3, 4). Brood size of the social mate (NW) was the most important component of variation in male RS, followed by success at protecting paternity in the own brood (PW) and the number of social mates (MW). Most influential for variation in extra-pair success was the number of extra-pair mates (ME), whereas brood size of extra-pair mates (NE) or the amount of paternity gained in the extra-pair broods (PE) played a negligible role. Male extra-pair and within-pair success showed a small, but positive covariance. Results largely agreed between the analytical and statistical approach, although in the statistical approach the contribution of extra-pair success is more prominent (Tables 3, 4).

Table 3. Partitioning of the total variance in G (annual male genetic reproductive success in a population of blue tits) into its within-pair (W) and extra-pair (E) components due to mate number (M), brood size (N), and siring success (proportion of the brood sired, P). Contributions are given as percent of total variance (95% CI) and represent the relative value (and its bootstrap confidence interval) of the corresponding variance term when total variance is partitioned analytically (see Methods for details). [Correction added on April 2, 2013, after first online publication: In row 10, column 2, “0.9” was changed to “−0.9”.]
Component of RSAll males1Residents2Resident yearlings3Resident adults4
  • 1

    Unknown sires included under the assumption that they were unpaired (N = 498).

  • 2

    Unknown sires excluded (N = 405).

  • 3

    Only resident males in their first breeding season included (N = 239).

  • 4

    Only resident males after their first breeding season included (N = 153).

G100.0 (I=0.465)100.0 (I=0.305)100.0 (I=0.284)100.0 (I=0.253)
W92.4 (85.7–98.6)78.8 (72.9–84.5)88.9 (83.1–95.0)70.5 (60.2–79.0)
MW47.5 (38.2–55.9)16.3 (10.3–21.4)16.7 (7.9–23.9)22.4 (10.1–31.6)
NW30.6 (24.6–35.9)52.3 (43.6–60.0)57.8 (47.3–67.5)51.1 (35.2–63.9)
PW12.6 (9.0–15.8)21.6 (15.8–26.8)22.9 (15.0–29.9)19.7 (10.0–27.8)
E16.2 (11.8–20.1)15.1 (10.2–19.4)6.9 (2.9–10.1)24.9 (13.8–33.0)
ME9.8 (6.6–12.4)10.3 (5.8–13.7)3.8 (0.6–6.0)20.0 (8.6–27.8)
NE1.4 (0.9–1.8)0.9 (0.5–1.3)0.3 (0.0–0.4)2.8 (0.7–4.1)
PE2.8 (1.5–3.8)2.0 (0.7–2.9)0.6 (0.1–1.0)6.4 (0.4–10.3)
Covariance of W and E−8.5 (−15.2 to −0.9)6.1 (1.4–11.2)4.2 (0.0–8.4)4.6 (−4.9 to 17.1)
Table 4. Components of male total (G), within-pair (W) and extra-pair (E) genetic reproductive success in a population of blue tits, based on GLMMs with year (1998–2003) and male identity as random factors. Relative contribution is the reduction in the pseudo-R2 value when the component is removed from the full model, rescaled to sum up to 1 for all components included in the model. Analytical results are based on Table 3 (residents), with values rescaled to sum up to 1 for all components included in the statistical model
  Statistical results RelativeAnalytical results Relative
Dependent variableComponentEffect (95% CI)1χ2 2contributioncontribution (95% CI)
  • 1

    Highest posterior density intervals (G, W) or confidence intervals (E).

  • 2

    All df = 1, all P < 0.0001.

  • 3

    Gaussian error structure.

  • 4

    Poisson error structure, estimates back-transformed to original scale (m-effect).

  • GLMM = generalized linear mixed-effect model.

G (N=364)3W0.94 (0.88–0.99)5070.740.84 (0.78–0.90)
 E1.02 (0.93–1.11)2640.260.16 (0.11–0.21)
W (N=364)3Mw5.78 (5.42–6.14)4870.230.18 (0.11–0.24)
 Nw0.85 (0.81–0.88)6590.420.58 (0.48–0.67)
 Pw8.05 (7.66–8.47)6030.350.24 (0.18–0.30)
E (N=109)4ME1.67 (1.49–1.87)3340.820.78 (0.44–1.00)
 NE1.17 (1.09–1.24)1580.120.07 (0.03–0.10)
 PE22.97 (10.85–48.61)1000.060.15 (0.05–0.22)

The role of paternity gain for variance in male RS (as reflected in E) was enhanced for adult males compared to yearling males, whereas the contribution of paternity loss (measured by PW) as well as the covariance between E and W was similar (Table 3). The covariance between within-pair paternity (proportion of the brood sired) and the number of social mates contributed little to the total variance in male RS, but it was negative for yearlings (−6.6%) and positive for adults (3.8%).

Including unknown males in the analysis, under the assumption that they were nonbreeders, changes the conclusions. First, the overall contribution of extra-pair success to the total variance in annual male RS became smaller, and the covariance between extra-pair and within-pair RS turned negative. Second, the number of within-pair mates (MW) became the most important contributor to variance in male RS (Table 3).



The major aim of our study was to assess how EPP influences quantitative correlates of sexual selection on males. We found that the opportunity for sexual selection among resident male blue tits was higher than expected under random mating. Paternity gain and loss were overall uncorrelated, and the contribution of the covariation between extra-pair and within-pair success to total variation in RS was small (6.1%; Table 3). Nevertheless, males involved in EPP gained more offspring than they lost in their own brood and the CI for the covariance was nonoverlapping with zero (Table 3). The results therefore indicate that EPP enhances differences between resident males and elevates selection on mating success. However, the size of this effect is small. Reciprocal cuckoldry was rare but did occur and many males both lost and gained paternity. In both sexes, reproductive skew (inequality) was low. The contribution of EPP to variation in male RS (15%) was small in comparison to the contribution of within-pair success (79%). Thus, social success is the main arena for sexual selection among the resident males of this population.

Our results are similar to those reported in other studies that considered effects of EPP on estimates of sexual selection (Webster et al. 2001; Kraaijeveld et al. 2004; Freeman-Gallant et al. 2005; Whittingham and Dunn 2005; Westneat 2006). Often, the contribution of EPP to total variance in RS was low, or the covariance of extra-pair and within-pair success was close to zero. In almost all studies to date, within-pair paternity remained the most influential component of male fitness (Schlicht and Kempenaers 2010; see also While et al. 2011; Lebigre et al. 2012). In our population, this results from two factors. First, clutches of blue tits are large and the proportion of a mixed paternity brood not sired by the social male was generally low (∼30%). Second, social polygyny was important (measured by MW). As a consequence, the Bateman gradients show that the effect of mating on reproduction was much stronger for within- than for extra-pair reproduction.

The importance of social polygyny is probably reduced when offspring quality is included in measurements of RS, because offspring of secondary females were in worse condition (see online Supplementary Material). Despite a strong link to fitness (RS), social polygyny may also come at a cost, particularly in the extra-pair arena. In a recent study on a Dutch blue tit population, yearling males were less successful at protecting paternity when mated polygynously, whereas this was not the case for older males, suggesting that the trade-off between increased social mating success and avoiding paternity loss is not straightforward (Vedder et al. 2011). Our results are similar: for yearlings, the fitness increase via acquisition of a secondary female is smaller than for adult males due to age-dependent paternity loss.


Most previous studies have only considered the resident male population (but see Sardell et al. 2010; Gerlach et al. 2012). However, often a substantial proportion of EPY cannot be assigned to any of these males (22% in this study). We specifically focused on unknown sires and determined their number via sibship analysis. Our results indicate that a surprisingly high number of individuals are missed when restricting evaluation to the resident male population (Gerlach et al. 2012). Unknown males could either be breeding in nests that were unsampled (natural cavities, nests outside the study area, nests failed early on), or they could be males that failed to obtain a territory or a mate (nonbreeders). It seems unlikely that all unknown sires were unsampled breeders because (1) monitoring started before breeding behavior commenced and showed that early nest failures by unidentified individuals were rare, (2) intensive observations revealed only a low number of pairs breeding in natural cavities in the study site, and (3) the study area is surrounded by lower quality habitat without nest boxes, so that the breeding density in the neighborhood is low. The occurrence of social polygyny also suggests that some males do not breed, unless the adult sex ratio is female biased (Kempenaers 1994; Vedder et al. 2011).

The presence of nonbreeding males in a population can have substantial consequences (Penteriani et al. 2011; see also Courtiol et al. 2012). Among others, it may influence territorial strategies (Campioni et al. 2010), social organization (Smith 1987), movement–settlement patterns (Petit 1991; Delgado et al. 2009; Mannan 2010), or the timing of reproduction (Hogstad 1999). Nonbreeding males may either fail to reproduce (Sergio et al. 2009) or sire offspring via second broods or EPP. The latter could be a conditional male strategy when initial mating has failed (Smith 1987; Marra and Holmes 1997), or even a way to obtain RS without having to care for an own brood (Kempenaers et al. 2001), comparable to alternative mating strategies in other species (Taborsky and Hudde 1987; Jukema and Piersma 2006).

Nonbreeding males were observed in several studies on EPP (Gibbs et al. 1990; Ketterson et al. 1997; Weatherhead and Boag 1997; Whittingham and Dunn 2005; Woolfenden et al. 2005; O'Connor et al. 2006; Albrecht et al. 2007; Balenger et al. 2009) and sometimes EPY could be assigned to these males (Freeland et al. 1995; Kempenaers et al. 2001; Kleven et al. 2006; Pearson et al. 2006; Cooper et al. 2009; Sardell et al. 2010; Lebigre et al. 2012). Nonbreeding males could be present in many other populations where EPP is studied, but remain undetected.

Here, we ask how assumptions about the status of unknown sires affect our estimates of the potential for sexual selection. We examined this by considering the most extreme case, namely that all unknown sires were nonbreeders. Under this assumption there was a substantial change in the fitness components: even more of the variation in RS was due to variation in within-pair success. This implies that selection on “non-breeders” to find a breeding opportunity is strong: the potential for sexual selection via this pathway was increased (compare MW in Table 3). Importantly, variation in extra-pair and within-pair RS became negatively correlated. “Non-breeders” by definition had no social success while breeding males had a complete clutch: the apparent Bateman gradient is very steep (Table 2). This is partly compensated through EPP, leading to a negative covariance between within- and extra-pair success and a much lower realized βSS. Thus, if nonbreeding males father extra-pair offspring, EPP effectively lessens differences between males and leads to a reduction in the potential for sexual selection (Jones et al. 2001; Hauber and Lacey 2005; Singer et al. 2006; Webster et al. 2007; Lawler 2009; Collet et al. 2012; Lebigre et al. 2012).

Independent of the mechanisms of selection among unknown males, the estimates of the potential for sexual selection remained relatively stable, even under this anticonservative assumption (Fig. 3B, Table 2). Perhaps a more realistic assumption is that some of the unknown sires are breeders elsewhere. One would then expect results from the sampled resident males to fit the total population more closely.

An alternative hypothesis is that there are many more males without a social mate than the ones that sire the unassigned EPY, namely males that do not reproduce at all. We assessed the sensitivity of the estimates to this possibility and found that variance both in reproductive and mating success can increase dramatically, depending on the size of the nonreproducing male population (see online Supplementary Material; Supplementary Fig. S1). This highlights the importance in this type of study to collect and incorporate as much information about nonbreeding individuals as possible.


We found that the opportunity for selection and for sexual selection observed for resident male and female blue tits fell within the lower range of estimates from other studies on vertebrates (Pröhl and Hödl 1999; Jones et al. 2002; Woolfenden et al. 2002; Mobley and Jones 2007; Schlicht and Kempenaers 2010; Bergeron et al. 2012; Courtiol et al. 2012). However, most previous studies did not consider the influence of random mating (but see Baena and Macías-Ordóñez 2012; Byers and Dunn 2012; Garg et al. 2012). Here, we show that empirical frequency distributions of reproductive and mating success were similar to those from related random frequency distributions and the level of inequality (“reproductive skew”) was low for both resident males and females. Thus, the variation on which sexual selection can act appears to be small in this population, and may be largely caused by stochastic processes, unlinked to traits that could be selected. Based on this, one would predict only a minor impact of sexual selection on the evolution of behavior and morphology in this population of blue tits, at least in the period under study.

This may explain the lack of a straightforward link between male mating success and presumably sexually selected traits, such as body size (Foerster et al. 2003), dawn song characteristics (Poesel et al. 2001), and crown coloration (Delhey et al. 2007) in this and other (Krokene et al. 1998; Charmantier et al. 2004) blue tit populations. Often, it is only the comparison between specific groups of males (e.g., extra-pair sires and the males they cuckold) that reveals effects of these traits (Kempenaers et al. 1992, 1997; Delhey et al. 2003; Foerster et al. 2003; Poesel et al. 2006), in line with the idea that sexual selection on these traits is not particularly strong.

Nevertheless, the Bateman gradient for resident male blue tits revealed that each additional mate leads to two additional offspring. Despite low variation in MS, there is strong positive selection on individuals to acquire additional mates through social polygyny or EPP, because this leads to significantly higher RS. Accordingly, the difference between genetically monogamous versus promiscuous males generates most of the potential for sexual selection, whereas variance within the group of promiscuous males is less important. Our results therefore suggest that in this population sexual selection on males is mediated mainly via social polygyny. Future studies of sexual selection on particular traits could inspect this further by assessing correlations between the focal traits and the different components of fitness (Freeman-Gallant et al. 2009).

RS measured as the number of 14-day-old nestlings may not adequately reflect fitness variation when quality of young (e.g., condition) strongly influences their later survival and reproduction (López-Rull et al. 2011). We cannot exclude that the patterns we found become relatively unimportant when a better (more comprehensive) fitness estimate is used. At least, our results remained stable when fitness was measured as the number of fledged young (see also Dhondt 1989; Weatherhead and Dufour 2000). For several males, breeding attempts failed completely, leading to zero RS. Such failures may be largely stochastic, but may drive the relationship between RS and MS. However, the majority of the variance in RS among males was due to variance within the group of successful males.

Contrary to males, RS was uncorrelated to MS for resident females, as reflected by a Bateman gradient close to zero. Selection opportunities for females were also distinctly lower than those for males. In accordance with Bateman's principles (Arnold 1994), variation in RS and MS, constituting selection potential, as well as their direct link, were reduced in females compared to males. This suggests that in this population sexual selection is likely to be more important in males than in females.

Our results further indicate that higher estimates for males also emerged when the additional matings (e.g., arising from EPP) are randomly allocated to males. This means that the differences between males and females could at least partly be the result of a stochastic increase in mate number for some males, from which increased RS follows. On the other hand, there is no association between mate and offspring number for females, which would not occur if offspring from additional matings were randomly allocated to females (Gerlach et al. 2012). This implies that the sex differences in estimates arise not from enhancement in males, but from attenuation in females. Thus, it is the sex which shows smaller selection opportunities that shapes predictions about how sexual selection influences mating systems by nonrandom behavior (Shuster and Wade 2003; Jones et al. 2005; see also Krakauer et al. 2011).


The aim of this study is to inspect the effect of EPP on the intensity of sexual selection. Yet, we present estimates (I, IS, and βss) that do not directly measure the strength of sexual selection. These estimates capture both random and nonrandom variation and have no relation to any specified phenotypic trait (Jennions et al. 2012). Thus, in a hypothetical case where random processes have an important influence on mating allocation, inequality among individuals does not reflect the substrate for a selective response. Modeling random mating—in a biologically adequate way—should lead to similar inequality. If instead random processes play a minor role, the success of individuals should be predictable from a systematic factor that is a component of their identity, that is, a trait or a combination of traits. In other words, under this scenario, phenotypic variation is linked to variation in mating or reproductive success, and the phenotypic traits are then under (sexual) selection. The estimates do not allow to detect which specific traits are under selection and the strength of selection on them. In fact, selection on a specific trait may be weak despite high selection opportunity. Still, the size of estimates quantifies selection acting on the complete phenotype, that is, on all traits combined. In this interpretation, the presented estimates shed light on the strength of sexual selection, beyond the analysis of individual traits, for example, via selection differentials.

To put this in practice, it is necessary to show that an estimate is significantly higher than expected under randomness. This is done by simulating random mating and assessing the uncertainty for realized as well as simulated estimates (Jennions et al. 2012, see Baena and Macías-Ordóñez 2012; Byers and Dunn 2012; Garg et al. 2012 for recent implementations). Simulation of random mating can also correct for the inherent bias in the correlation between mating and reproductive success (as established via βss) that occurs because there is at least one offspring for every mate (Gerlach et al. 2012). This effect also applies to the estimate obtained in the simulation, which can therefore be used to take this issue into account.

It should be noted that the implemented estimates are corrected for random mating only in a statistical sense. There is always a chance that a particular pattern in a population is realized via purely random or purely directional processes. The simulation of random mating and the use of CIs can only be used to assess the likelihood that the observed variation in mating and reproductive success as well as their association are due to random mating alone. This is different from the use of selection differentials, where any link between trait and fitness will—assuming sufficient heritability of the focal trait—lead to a selective response, even if the trait-fitness correlation is a chance event.


Overall, the potential for sexual selection in our blue tit population showed no strong sensitivity to the incomplete sampling of sires. Estimates of sexual selection were higher for males than for females and mainly mediated by social success. In general, potential for sexual selection was low. However, the effect of EPP on sexual selection can either be positive or negative, depending on the presence of socially unsuccessful males in the population. In birds, these could commonly occur, either if populations contain (cryptic) nonbreeding individuals, or if auxiliary males can offset low social success via EPP in cooperative breeders (Webster et al. 2007). In summary, our results suggest that knowledge about the socially nonreproducing part of a population may be essential to assess the role of EPP in the process of sexual selection.


We are grateful to all the people that helped with field and laboratory work, in particular K. Delhey, K. Foerster, S. Kuhn, A. Peters, K. Teltscher, and A. Tuerk. We also thank H. Winkler, R.-T. Klumpp, and A. Fojt for logistic support, M. Valcu and L. Schlicht for help with the statistical analyses, and S. Nakagawa, B. Sheldon, and two anonymous reviewers for comments that improved an earlier version of the manuscript. This research was financially supported by the Austrian Academy of Sciences (BK) and by the Max Planck Society (ES, BK). We have no conflicts of interest to declare.