Polyandry in coal tits Parus ater: fitness consequences of putting eggs into multiple genetic baskets

Abstract

Females of many species mate with multiple males within a single reproductive cycle. One hypothesis to explain polyandry postulates that females benefit from increasing within-brood genetic diversity. Two mechanisms may render sire genetic diversity beneficial for females, genetic bet-hedging vs. non-bet-hedging. We analysed whether females of the socially monogamous coal tit (Parus ater) benefit via either of these mechanisms when engaging in extra-pair (i.e. polyandrous) mating. To obtain a measure of within-brood genetic diversity as a function of paternal genetic contributions, we calculated a sire diversity index based on the established Shannon–Wiener Index. In 246 broods from two consecutive years, sire genetic diversity had no effect on either the mean or the variance in brood fitness measured as offspring recruitment within 4 years after birth. The hypothesis that benefits of increasing sire diversity contribute to selection for female extra-pair mating behaviour in P. ater was therefore not supported.

Introduction

Females of many animal species frequently mate with more than one male within a single reproductive cycle and, accordingly, multiply sired clutches are the rule rather than an exception in most animal mating systems (e.g. Birkhead, 1998; Jennions & Petrie, 2000). This also holds for species that maintain social pair bonds like many bird species (e.g. Griffith et al., 2002). Whenever females gain material benefits, such as access to various types of resources, any costs of polyandry may be easily compensated for and leave females with a net benefit of actively seeking or passively accepting matings with multiple males (e.g. Arnqvist & Nilsson, 2000; Møller & Jennions, 2001). If direct benefits are absent, various genetic benefits can outweigh potential costs of polyandry (reviewed in Jennions & Petrie, 2000; Neff & Pitcher, 2005).

One hypothesis based on genetic rewards postulates that females benefit from involving more than a single genetic sire for a given clutch because this increases the within-clutch genetic diversity (termed sire genetic diversity below) among their offspring (genetic diversity hypothesis, reviewed in Yasui, 1998; Jennions & Petrie, 2000, note that sire genetic diversity in this sense refers to genetically based differences between offspring with different sires within a clutch, not to genic diversity within individuals). According to this idea, sire genetic diversity is advantageous because genotype-by-environment interactions within clutches will render multiply sired clutches necessarily more rewarding compared with clutches sired by any single male. Within the genetic diversity framework, involving multiple sires for a given clutch may be beneficial because of two different mechanisms: non-bet-hedging as opposed to bet-hedging. It is important to clearly distinguish between these mechanisms, because they lead to different predictions with respect to the fitness consequences of polyandrous mating (Yasui, 1998, see also Table 1).

Table 1.   Predicted effects of sire genetic diversity on mean and variance in brood fitness under two different mechanisms of the ‘genetic diversity hypothesis’, non-bet-hedging and genetic bet-hedging.

Effects of sire genetic diversity on	Non-bet-hedging mechanism	Genetic bet-hedging mechanism
Both mechanisms may explain why within-brood genetic diversity is beneficial for polyandrously mating females (see text).
(a) arithmetic mean of within-generation brood fitness	Positive	No effect predicted
(b) variance of within-generation brood fitness	No effect predicted	Negative

The non-bet-hedging mechanism predicts a positive effect of sire genetic diversity on (within-generation, between-female) arithmetic mean fitness (Yasui, 1998). Such a fitness benefit may result because reduced competition among half-siblings when compared with full-siblings leads to more efficient resource utilization by multiply sired clutches. Another possibility is the opportunity for beneficial interactions among half-siblings as opposed to full-siblings. For example, genetically based differences in offspring parasite resistance could prevent infections from spreading efficiently within a clutch (Jennions & Petrie, 2000). Thus there is no single best sire for any given female in the non-bet-hedging scenario and diversity is per se advantageous.

In contrast, the genetic bet-hedging mechanism predicts a positive effect of sire genetic diversity on (between-generation, within-lineage) geometric mean fitness which is mediated by a decrease in between-generation fitness variation (Yasui, 1998). Such a fitness benefit may result when future environmental conditions experienced by offspring (such as resource abundance and quality or parasite abundance and virulence) vary in an unpredictable manner over time. Thus, a single best sire for any given female may well exist in the bet-hedging scenario, but cannot be identified and females therefore have to employ a risk-spreading, or bet-hedging, strategy to handle uncertainty. In this case, genetically diverse clutches will have an increased probability of at least some offspring being well adapted to the prevailing conditions. A polyandrous female mating strategy leading to high sire genetic diversity may then reduce between-generation fitness variation, thereby increase geometric mean fitness and will thus be selected for, even if this comes at a cost of within-generation arithmetic mean fitness (Jennions & Petrie, 2000). If between-generation variation in fitness is reduced through polyandry, however, we also expect that within-generation fitness variation is less pronounced compared with a monandrous mating strategy that would yield either comparatively low or comparatively high (i.e. in any case rather extreme) rewards (Jennions & Petrie, 2000).

Avian extra-pair mating systems (e.g. Griffith et al., 2002) offer an interesting model to assess the role of genetic benefits in the evolution of female multiple mating behaviour, as potentially confounding non-genetic benefits of extra-pair mate choice are considered to be of very limited importance (Jennions & Petrie, 2000; Griffith et al., 2002). We therefore studied the long-term fitness consequences of multiple matings in the socially monogamous coal tit (Parus ater), a passerine bird with a high frequency of extra-pair paternity (Lubjuhn et al., 1999a; Dietrich et al., 2004). Maternal half-sibling comparisons within broods have previously shown that female coal tits may gain genetic benefits from extra-pair fertilizations in terms of increased offspring viability (Schmoll et al., 2005). However, this seemed only to be the case under comparatively poor environmental conditions (i.e. within second brood periods when overall performance had significantly declined compared with first brood periods). As there was no evidence that females were rewarded with a genetic benefit from extra-pair fertilizations within first brood periods (in terms of offspring viability and/or fecundity), we reasoned that a further type of benefit could contribute to maintaining female extra-pair mating behaviour in the study population. In contrast to ‘good genes’ or ‘compatible genes’ hypotheses of extra-pair mating the genetic diversity hypothesis predicts that benefits of mating multiply will apply to all females irrespective of the genetic quality or genetic compatibility of their social mates. Thus, virtually all females should be expected to engage in extra-pair copulations and a comparatively high overall degree of polyandry may be expected. Accordingly, the coal tit provides a candidate species to test the genetic diversity hypothesis, because it is among the bird species with the highest frequencies of extra-pair paternity (Lubjuhn et al., 1999a; Dietrich et al., 2004). Indeed, Dietrich et al. (2004) were able to show that nearly all females in a coal tit population had engaged in extra-pair matings at least once when monitored over three successive brood periods. Furthermore, recent studies in other passerine birds provided experimental evidence that the frequency of extra-pair fertilizations detectable by means of molecular genetic tools may well underestimate the frequency of extra-pair copulations (Michl et al., 2002; Fossøy et al., 2006). This suggests that females of apparently less polyandrous species may also have a much stronger propensity to mate multiply than the genetic data reveal, and that a genetic diversity benefit may well be postulated also for such species.

Here we test whether females of the socially monogamous coal tit benefit from increasing within-brood genetic diversity through extra-pair (i.e. polyandrous) mating via either of the two suggested mechanisms (i.e. non-bet-hedging or bet-hedging). We first analyse the fitness consequences of sire genetic diversity and then examine the distribution of paternities among sires. More specifically, if benefits of producing genetically diverse broods contribute to selection for female extra-pair mating behaviour, we predict that increasing sire genetic diversity is associated with:

• (i)
  an increase in within-generation arithmetic mean brood fitness (non-bet-hedging mechanism, see also Table 1); and/or
• (ii)
  a decrease in within-generation variance in brood fitness (bet-hedging mechanism, see also Table 1), expected if sire diversity increases geometric mean fitness by lowering between-generation variation in fitness.

Furthermore, we would expect under both the mechanisms that females try to maximize diversity and thus that – for a given number of potentially costly (e.g. Lubjuhn et al., 1993; Valera et al., 2003) extra-pair fertilizations – they engage in copulations with many rather than few extra-pair sires (EPS) and that – for a given number of genetic sires – females distribute offspring evenly over sires such that males within multiply sired broods have a rather fair share in terms of paternity.

To obtain a suitable measure of within-brood genetic diversity as a function of paternal genetic contributions, we calculate a sire diversity index D using the established Shannon–Wiener Index. We then use Generalised Additive Models for Location, Scale and Shape (GAMLSS, Rigby & Stasinopoulos, 2005) to simultaneously test for effects of sire diversity on the mean and the variance of local recruitment success.

Materials and methods

Study species, study population and general field methods

Coal tits are small, territorial, altricial, cavity-nesting passerine birds with biparental care (Glutz von Blotzheim & Bauer, 1993). They are socially monogamous (Glutz von Blotzheim & Bauer, 1993), but show comparatively high rates of extra-pair paternity (cf. appendix in Griffith et al., 2002). Within the well-investigated genus Parus (chickadees and titmice) these are the highest rates recorded so far (Lubjuhn et al., 1999a; Dietrich et al., 2004).

We studied an established nest-box population of coal tits in a mixed coniferous forest near Lingen/Emsland (Lower Saxony, Germany, 52°27′N, 7°15′E) in 2000 and 2001. In addition, recapture data from 2001 to 2005 were used. The 325-ha study area contained about 560 nest-boxes, harbouring 132 coal tit breeding pairs in 2000 and 184 pairs in 2001. During the breeding seasons (April–July) all nest-boxes were monitored at least weekly to record breeding phenology (laying and hatching date), parameters of reproductive performance (clutch and brood size, hatching, fledging and recruitment success) and the identity of adult birds. Adults captured while feeding nestlings 10–14 days old were regarded the social (i.e. putative) parents of the respective broods. Both adults and nestlings were banded with uniquely numbered metal rings of the Institute of Avian Research ‘Vogelwarte Helgoland’ (Wilhelmshaven, Germany). In the years 2000 and 2001, blood samples (∼50 μL) were taken from the ulnar vein under license (No. 509f-42502-46), diluted in 250 μL of APS buffer (Arctander, 1988) and stored at −20 °C until further use.

Assignment of genetic parentage

We used a combination of multilocus DNA fingerprinting and microsatellite analysis to: (i) exclude genetic parentage for the putative (i.e. social) parents; and (ii) assign extra-pair offspring (EPO) to their genetic fathers (extra-pair sirer, EPS). Existing multilocus data on parentage exclusion (see Dietrich, 2001) as well as assignment of EPO to EPS based on a multilocus procedure (Schmoll et al., 2003) were cross-checked and complemented using four polymorphic microsatellite markers. The resulting parentage assignments were thus supported by two independent sets of molecular genetic markers for > 99% of offspring analysed (a few samples failed to be genotyped by one of the methods).

Multilocus DNA fingerprinting

Details of the basic DNA fingerprinting procedures used for parentage exclusion have been described elsewhere (Lubjuhn et al., 1999a; Dietrich, 2001); hence the fundamental method is outlined only briefly. DNA was isolated according to a modified standard protocol (Lubjuhn & Sauer, 1999) and digested with the restriction enzyme Hae III. After separation by horizontal agarose gel electrophoresis, gels were dried followed by in gel hybridization using the ³²P-labelled oligonucleotide (CA)₈. The banding patterns were visualized by scanning with a phospho-imager (Storm 860, Amersham, Biosciences, Freiburg, Germany). Parentage exclusion gels always contained a brood's nestlings along with its social (i.e. putative) parents. Banding patterns were highly informative and analysed according to Westneat (1990) using the image-editing software Adobe® Photoshop® 5.5. The putative (i.e. social) fathers were excluded from genetic parentage if ≥ 2 novel fragments (i.e. distinct fragments neither attributable to the social mother's nor to the social father's banding pattern) were present in the banding pattern of the focal nestling (Dietrich, 2001). The probability of falsely assigning one putative parent to an offspring was as low as 1.1 × 10⁻⁵ (Dietrich, 2001).

We assigned EPO to EPS by means of standardized across-gel comparisons of multilocus DNA fingerprints using scanned gels and standard image-editing software. As the procedures are described in detail elsewhere (Schmoll et al., 2003), only the fundamental principle of the method is outlined here. In brief, in addition to the DNA fingerprint gels prepared for parentage exclusion (see above) we ran and processed – under identical conditions – five and eight gels containing DNA samples of all potential EPS (referred to as PEPS gels) representing all 107 and 174 territorial males that were blood-sampled in the study population in 2000 and 2001 respectively. Meanwhile, patterns of diagnostic paternal fragments within an EPO's banding pattern (i.e. novel fragments that must have been inherited from an EPS; see above) had been marked by symbols within parentage exclusion gel files. These symbol patterns were first copied onto the DNA fingerprint banding pattern of the respective brood's social father using the software's ‘copy’ option. Then the pattern of symbol marks was pasted – combined with the underlying social father's banding pattern itself – into the PEPS gel file that contained a copy of the social father's banding pattern. The crucial point in the procedure is that now the social father's DNA fingerprint could be aligned along a copy of itself that had been run on another gel (the PEPS gel). It could therefore be adjusted to the specific running conditions of the respective PEPS gel by using the software's ‘distort’ option. Together with the social father's banding pattern, the pattern of symbol marks representing diagnostic paternal fragments to be matched by a potential EPS had thus also been adjusted to the specific conditions of the PEPS gel. This procedure leaves the symbol marks in the same gel-specific positions in which fragments of the true genetic father must be expected. PEPS gels were then screened for potential EPS males by shuttling the pattern of symbol marks over them. Backed up by conventional DNA fingerprinting in cases of doubt, this procedure allows the screening and identification of EPS (see Schmoll et al., 2003).

Microsatellite analysis

We used four polymorphic microsatellite loci (see Table 2) to cross-check and complement the results obtained from multilocus DNA fingerprinting analysis. DNA was isolated according to the same modified standard protocol (see above) and loci were amplified by polymerase chain reaction (PCR) according to optimized standard protocols (for details on PCR conditions see Stiels, 2004; Mund, 2005). PCR products were separated on an ABI PRISM® 377 DNA sequencer (Applied Biosystems, Foster City, CA, USA) and allele sizes were scored using GENESCAN 2.1 (Applied Biosystems). We used CERVUS 2.0 (Marshall et al., 1998) to calculate population genetic parameters and exclusion probabilities for these loci. Variability and informativity of the markers used are shown in Table 2 based on a sample of 211 successfully genotyped territorial adults from the year 2000. The combined exclusion probability of the four loci (i.e. the probability that a randomly chosen male will not possess an offspring's paternal alleles given the genotype of the mother is known, Jamieson, 1994) amounted to > 0.999. The probability of chance inclusion (i.e. the probability of a male matching an offspring's genotype purely by chance given the genotype of the mother is known, Jeffreys et al., 1992) was low (mean ± SD: 1.5 × 10⁻³± 2.5 × 10⁻³, range: 1.8 × 10⁻² to 1.0 × 10⁻⁶ based on 773 nestling-mother dyads). Nestlings were regarded within-pair offspring if there was a complete match with their putative parents’ genotypes. Only a single nestling in 2001 did not match the putative mother's genotype and exclusion of genetic maternity was also supported by the multilocus approach in this case (this brood was excluded from further analysis). For all remaining offspring social maternity was thus assumed to reflect genetic maternity and this was also backed-up by the multilocus approach in all cases. Accordingly, nestlings were regarded EPO if their genotypes did not match that of the putative father at one or more loci. An EPO was assigned to an EPS if there was a complete match of their respective genotypes and also the multilocus procedure (see above) supported the respective assignment.

Table 2.   Variability and informativity of four microsatellite markers used to assign genetic parentage in the coal tit.

Marker	Isolated from	n	Number of alleles	Observed heterozygosity*	Expected heterozygosity†	Exclusion probability (1st parent)‡	Exclusion probability (2nd parent)§	Reference
Calculations are based on all successfully genotyped adult birds that were territorial in 2000. *We found evidence for the presence of a null-allele in a single case only (locus Pocc6) with a female being apparently homozygote whereas five confirmed genetic offspring being apparently homozygote for the paternal allele. †There were no significant deviations from Hardy–Weinberg equilibrium (all P ≥ 0.28). ‡Probability that an individual chosen at random will not have the offspring's alleles (and will thus be excluded from genetic parentage). §Probability that a male chosen at random will not have the offspring's paternal alleles (and will thus be excluded from genetic paternity) given the genotype of the mother is known (genetic maternity was confirmed for all but a single nestling in 2001, see text).
Patmp43	Poecile atricapillus	211	22	0.938	0.914	0.703	0.825	Otter et al. (1998)
Pdom5	Passer domesticus	208	37	0.904	0.918	0.720	0.836	Griffith et al. (1999)
Pocc6	Phylloscopus occidentalis	210	21	0.919	0.910	0.689	0.816	Bensch et al. (1997)
Mcyu4	Malurus cyaneus	206	20	0.888	0.872	0.596	0.747	Double et al. (1997)

Number of genetic sires per brood

The number of genetic sires involved was exactly determinable for 87% of 246 broods analysed (see also Table 3). This included broods for which paternity had been assigned to all nestlings as well as broods within which (extra-pair) paternity had not been assigned to a single EPO. For all remaining broods a minimum number of sires was estimated by combining information obtained from microsatellite and multilocus genotyping. For broods with only two EPO remaining unassigned (four cases in 2000 and 10 in 2001), microsatellite data are of no use and we capitalized on information from multilocus DNA fingerprint banding patterns instead. A pair of EPO qualified as full-siblings (i.e. only a single EPS was involved) if their DNA fingerprints shared at least two novel fragments (for information on multilocus fingerprint informativity see above). A pair of EPO qualified as half-siblings (i.e. two EPS were involved), if their DNA fingerprints shared no novel fragments at all. One brood in 2001 within which a pair of EPO shared only a single novel fragment was excluded from analysis. For broods with more than two EPO remaining unassigned (11 cases in 2000 and 16 in 2001), microsatellite data were used to propose putative full-sibships in a parsimonious manner by assigning offspring alleles to the lowest possible number of different EPS. Note that this procedure represents a conservative approach with respect to the goal to establish a minimum number of genetic sires per brood. Putative full-sibships were then cross-checked with multilocus DNA fingerprint banding patterns. We accepted proposed full-sibships only if every pair-wise comparison of EPO banding patterns within proposed full-sibships revealed at least two shared novel fragments and if every pair-wise comparison of EPO banding patterns between proposed full-sibships revealed no shared novel fragments at all (see above). A few broods (three in 2000 and five in 2001) where microsatellite vs. multilocus-based results led to inconsistent conclusions were excluded from further analysis.

Table 3.   Frequency of broods with a single, two or three genetic sires in relation to the number of extra-pair offspring (EPO) present.

Year	No. of genetic sires	No. of EPO per brood										Total
		0	1	2	3	4	5	6	7	8	9
Figures in brackets refer to sub-samples from the respective category for which the number of sires was not exactly known but had to be estimated (see text for details).
2000	1	30	0 (0)	0 (0)	0 (0)	0 (0)	0 (0)	1 (0)	0 (0)	1 (0)	0 (0)	32 (0)
	2	–	15	13 (4)	7 (1)	4 (1)	3 (0)	3 (1)	1 (0)	1 (0)	2 (1)	49 (8)
	3	–	–	2 (0)	1 (0)	1 (1)	2 (1)	2 (1)	1 (1)	0 (0)	0 (0)	9 (4)
	∑	30	15	15 (6)	8 (1)	5 (2)	5 (1)	6 (2)	2 (1)	2 (0)	2 (1)	90 (12)
2001	1	52	0 (0)	0 (0)	1 (0)	0 (0)	1 (0)	0 (0)	1 (0)	1 (0)	0 (0)	56 (0)
	2	–	29	22 (8)	10 (2)	11 (4)	8 (1)	8 (1)	1 (0)	1 (1)	0 (0)	90 (17)
	3	–	–	3 (1)	3 (0)	1 (1)	2 (1)	1 (0)	0 (0)	0 (0)	0 (0)	10 (3)
	∑	52	29	25 (9)	14 (2)	12 (5)	11 (2)	9 (1)	2 (0)	2 (1)	0 (0)	156 (20)

Sire diversity index, maximum possible sire diversity and sire evenness

To obtain a measure of within-brood genetic diversity as a function of paternal genetic contributions, we calculated a sire diversity index D based on the Shannon–Wiener Index rooted in information theory and widely used in community ecology to quantify diversity (Begon et al., 2005). The sire diversity index D takes into account the number of genetic sires represented within a given brood as well as the proportion (and thus the degree of equipartition) of offspring assigned to different sires. Sire diversity indices D were calculated for each brood as

• 

where S is the number of genetic sires represented in the respective brood and p_i is the proportion of offspring sired by the ith sire in the respective brood.

Two additional indices were derived from the diversity index D. First, for broods with at least one EPO, we calculated the maximum possible sire diversity given the number of EPO in the brood as a hypothetical diversity score D_Hyp that would have resulted if each EPO had been sired by a different extra-pair male. The ratio D/D_Hyp will then reflect to which degree a female has exploited the potential to produce a diverse clutch if constrained to a fixed number of successful extra-pair fertilizations. Second, for broods with multiple paternity, we calculated the maximum possible sire diversity given the number of genetic sires involved as a hypothetical diversity score D_max = ln S that would have resulted if offspring had been evenly distributed over sires. The ratio D/D_max will then reflect to which degree a female has exploited the potential to produce a diverse clutch if constrained to a fixed number of sires and is identical with sire evenness E as

• 

Nestling local recruitment

Recruitment success was defined as the proportion of offspring recruiting from a given brood. We regarded individuals as locally recruited if they were found breeding in the study area within 4 years after birth (i.e. between 2001 and 2004 for nestlings born in 2000 and between 2002 and 2005 for nestlings born in 2001). A total of 14.6% of 748 nestlings born in 2000 and 8.1% of 1104 nestlings born in 2001 had locally recruited into the breeding population within 4 years after nestling birth. This included a total of 23 and 21 nestlings from the 2 years that had not been found breeding for the first time in the year subsequent to their year of birth but in the second-next (15 and 14 recruits), third-next (five and six recruits) or fourth-next year (three and one recruits respectively). Blood sampling had no detectable effect on nestling local recruitment probability into the study population (Schmoll et al., 2004).

Statistical analysis

To simultaneously test for effects of sire diversity on the mean and the variance of recruitment success, we used Generalised Additive Models for Location, Scale and Shape (GAMLSS, Rigby & Stasinopoulos, 2005). By means of GAMLSS, we fitted a model for recruitment success and used sire diversity as explanatory variable and included hatching date and year of nestling birth as covariates because these had been shown to affect local recruitment in previous analyses (see Schmoll et al., 2005). We assumed a beta-binomial error distribution, i.e. a statistical distribution for proportional data that has two parameters: the mean μ and the dispersion σ. The variance of a beta-binomial distribution increases monotonously with σ, and is given by

• 

where n is the ‘binomial denominator’ (the number of analysed nestlings per brood) and var_bin (μ, n) is the variance of a binomial distribution with mean μ and denominator n. In GAMLSS analyses, we used the canonical link functions for response variables with beta-binomial error distribution, i.e. a logit link for the mean μ and a log link for the dispersion parameter σ (for details see Rigby & Stasinopoulos, 2005). The significance of effects of explanatory variables on mean and dispersion was assessed by means of likelihood-ratio tests (Rigby & Stasinopoulos, 2005). Confidence intervals (95% CI) of GAMLSS parameter estimates obtained were estimated by non-parametric bootstrapping (1000 replicates). GAMLSS models were fitted in R 2.2.1 (R Development Core Team, 2005), whereas some further analyses were conducted in SPSS 12.0 (SPSS Inc., Chicago, IL, USA). All statistical tests were two-tailed and the null hypothesis was rejected at P < 0.05.

Sample size and frequency of extra-pair paternity

Analyses were based on 246 first broods, comprised a total of 1852 offspring and involved 203 different females, 204 different males and 224 different, uniquely composed breeding pairs. Detailed information on the basic patterns of extra-pair paternity in the study population has been published elsewhere (Dietrich et al., 2004) and the global sample used by Dietrich et al. (2004) included the sub-sample used in this study. For the subsample used here, the percentage of broods containing at least one EPO amounted to 66.6% of 90 and 66.6% of 156 broods in 2000 and 2001 respectively. The percentage of offspring sired through extra-pair copulations was 26.5% of 748 and 27.8% of 1104 nestlings and these proportions did not differ significantly between years (likelihood ratio test: χ² = 0.40, d.f. = 1, P = 0.56).

Results

Number of genetic sires per brood and sire diversity index

The number of genetic sires per brood ranged from one to three and the respective frequency distributions did not differ between years (likelihood ratio test: χ² = 1.03, d.f. = 1, P = 0.63, see also Table 3). The number of sires did not covary with progressing season within either of the two first brood periods (Spearman rank correlations with hatching date: both P > 0.92). Sire diversity indices D ranged from zero to 1.06 and 1.00 with medians of 0.38 and 0.41 in 2000 and 2001 respectively. The frequency distributions of diversity indices were statistically indistinguishable between years (Kolmogorov–Smirnov two-sample test: z = 0.52, P = 0.75, see Fig. 1). Sire diversity did not covary with progressing season within either of the two first brood periods (Spearman rank correlations with hatching date: both P > 0.33).

Figure 1.  Frequency distributions of sire diversity indices D for coal tit first broods in (a) 2000 (n = 90) and (b) 2001 (n = 156).

Sire diversity and arithmetic mean of recruitment success

Neither sire diversity (see Fig. 2) nor hatching date or their two-way interactions with year had a significant effect on mean recruitment success (GAMLSS analysis: P > 0.45 for all model terms, see Table 4a). Only year of nestling birth was a significant predictor of recruitment success with recruitment from 2000 being 1.8 times higher than recruitment from 2001 (P < 0.001, see Table 4a). The logit-scale parameter estimate for the effect of sire diversity was 0.03 (95% confidence interval: −0.52 to 0.54) and the respective estimate for the difference between nestlings born in 2001 and 2000 was −0.66 (95% confidence interval: −0.99 to −0.34). Essentially, the same results were obtained when analyses were based on the sub-sample of broods for which the number of EPS was exactly known (data not shown).

Figure 2.  Recruitment success (proportion of offspring locally recruited within 4 years after nestling birth) in relation to sire diversity for coal tit first broods in (a) 2000 (n = 90) and (b) 2001 (n = 156). Bubble sizes indicate the number of multiple data points and lines visualize predictions of Generalised Additive Models for Location, Scale and Shape (GAMLSS, see text). Solid lines: predicted means; dashed lines: predicted 5% and 95% quantiles. Quantiles are predicted for the median brood size in each year (nine and seven nestlings in 2000 and 2001 respectively).

Table 4.   Results of stepwise backward simplification of GAMLSS models for local recruitment success.

Step	Change in d.f.	Change in deviance	Residual d.f.	Residual deviance	AIC	P-value
AIC, Akaike Information Criterion. Models assumed a beta-binomial error distribution with a logit link for the mean recruitment probability μ and a log link for the dispersion parameter σ. The initial model for both μ and σ included the main effects of sire diversity, year and hatching date as well as the two-way interactions between the factor year and the two continuous variables. (A) Simplification of the model for mean recruitment, μ. (B) Simplification of the model for the dispersion parameter, σ (mean recruitment is modelled as a function of year here).
(A)
Initial model	–	–	239	565.63	579.63	–
Year by hatching date	1	0.03	240	565.66	577.66	0.87
Year by sire diversity index	1	0.11	241	565.78	575.78	0.73
Sire diversity index	1	0.01	242	565.79	573.79	0.92
Hatching date	1	0.53	243	566.31	572.31	0.47
Year	1	15.48	244	581.79	585.79	< 0.001
(B)
Initial model	–	–	238	563.15	579.15	–
Year by sire diversity index	1	0.62	239	563.77	577.77	0.43
Sire diversity index	1	0.11	240	563.88	575.88	0.74
Year by hatching date	1	1.75	241	565.62	575.62	0.19
Hatching date	1	0.25	242	565.88	573.88	0.62
Year	1	0.44	243	566.31	572.31	0.51

Sire diversity and variance in recruitment success

The proportion of offspring recruited from a given brood ranged from 0 to 0.56 and from 0 to 0.43 in 2000 and 2001 respectively. Neither sire diversity (see Fig. 2), nor hatching date, any two-way interactions with year of nestling birth or the main effect of year of nestling birth had a significant effect on the dispersion parameter, σ, of a beta-binomial distribution for local recruitment success (P > 0.18 for all model terms, see Table 4b). The log-scale parameter estimate for the effect of sire diversity was 0.64 (95% confidence interval: −3.55 to 6.94). As sire diversity also did not affect mean local recruitment μ (see above) it had no detectable effect on the variance in local recruitment success (see formula for variance of a beta-binomial distribution in the methods section). The same results were obtained when analyses were based on the sub-sample of broods for which the number of EPS was exactly known (data not shown).

Sire diversity and natal dispersal

If sire diversity affects offspring natal dispersal, the use of local recruitment success as a fitness proxy might be unreliable. We therefore checked for such potentially confounding effects by analysing the relationship between sire diversity and the mean and variance in average dispersal distance of offspring recruited from a given brood. However, neither sire diversity nor hatching date, any two-way interactions with year of nestling birth or the main effect of year of nestling birth had a significant effect on the mean or variance in natal dispersal distances (GAMLSS analysis: P > 0.14 for all model terms).

Maximum possible sire diversity and sire evenness

Assuming that increasing sire genetic diversity is advantageous, females may maximize diversity in two different ways. First, by involving as many different EPS as possible for the given number of extra-pair fertilizations attained; second, by allocating paternity as evenly as possible to the genetic sires involved. Thus, could broods containing a given number of EPO or involving a given number of EPS have been more diverse? When plotting the ratio of D and D_Hyp (i.e. realized diversity divided by maximum possible diversity given the number of EPO) against the number of EPO present (Fig. 3), we found that maximum possible sire diversity D_Hyp was only rarely realized and mostly when this was inevitable (i.e. in cases of just a single EPO present, Fig. 3). Likewise, when plotting the ratio of D and D_max (i.e. sire evenness E) against the number of EPO present, we found that paternity was only rarely allocated as evenly as possible (Fig. 4).

Figure 3.  Realized sire diversity D divided by maximum possible diversity D_Hyp for a given number of extra-pair offspring (EPO) in relation to the number of EPO present per brood for the first brood periods in (a) 2000 (n = 60) and (b) 2001 (n = 104). Only broods with extra-pair paternity are included in this figure because maximum possible sire diversity D_Hyp is zero for broods without extra-pair paternity. Bubble sizes indicate the number of multiple data points and numerals refer to the numbers of broods with only a single EPO present. Note that for these broods realized divided by maximum possible sire diversity is necessarily = 1 as referred to by a quadratic instead of circle plot symbol.

Figure 4.  Sire evenness E in relation to the number of extra-pair offspring (EPO) present per brood for the first brood periods in (a) 2000 (n = 58) and (b) 2001 (n = 100). Only broods with multiple paternity are included in this figure because sire evenness is not defined for broods with a single sire. Bubble sizes indicate the number of multiple data points.

Discussion

In this study, we tested the hypothesis that increasing within-brood genetic diversity by involving EPS is advantageous to females of the socially monogamous coal tit. To quantify within-brood genetic diversity as a function of paternal genetic contributions, we calculated a sire diversity index D based on the established Shannon–Wiener Index. This index provides a gradual measure of sire genetic diversity and thereby differs from the simple dichotomy between singly and multiply sired broods examined in earlier studies that addressed fitness consequences of extra-pair mating (e.g. Lubjuhn et al., 1999b; Charmantier et al., 2004). We suggest that application of the sire diversity index may be useful for any study aiming to quantify genetic diversity as a function of polyandry, because it reflects the actual degree of promiscuity within a genetic mating system more accurately than other measures (like the number of sires involved per clutch or the proportion of multiply sired clutches). The diversity index may then be used to test for correlations with further variables of interest within as well as across species.

When analysing the fitness consequences of sire genetic diversity, we found neither the predicted positive relation to mean recruitment success nor the predicted negative relation to variance in recruitment success (see Table 1 and Fig. 2). Thus, there was no evidence that sire diversity had a beneficial effect on female fitness, neither through a genetic bet-hedging mechanism nor through a non-bet-hedging mechanism. Differential dispersal with respect to sire genetic diversity was absent and can thus not have confounded these results. The lack of statistically significant associations could result because effects of sire diversity were non-existent or because they were too small to be detected with the sample sizes analysed here. Although we used one of the largest data sets available for birds, the latter could potentially be the case for benefits that were to be realized via the genetic bet-hedging mechanism, because here theory predicts that a low population size as well as low costs of polyandry for females are required to yield a non-trivial net benefit (Yasui, 1998, 2001). However, we showed that the 95% confidence interval for the parameter estimate for dispersion in recruitment success, σ, included zero and was substantially shifted towards positive values. Thus if anything, sire diversity showed a tendency to increase rather than decrease variation in recruitment success. Furthermore, we also found that the 95% confidence interval for the parameter estimate for the effect of sire diversity on arithmetic mean recruitment success μ well included zero. This suggests that diversity effects were probably non-existent for the sample analysed here and the fitness surrogate used. We conclude that the hypothesis that benefits of increasing sire diversity contribute to selection for polyandrous (i.e. extra-pair) mating behaviour in the study population was not supported.

This view is sustained by the observed distribution of paternities among sires. Females only rarely realized the maximum possible sire diversity D_Hyp for a given number of EPO (Fig. 3). This is not in line with the expectation that females should involve rather many than few different EPS for a given number of potentially costly (e.g. Dixon et al., 1994; Valera et al., 2003) extra-pair fertilizations. If constrained to a given number of sires, females could still increase diversity by allocating paternity as evenly as possible for the number of sires actually involved. However, females also rarely realized the maximum possible sire diversity for a given number of sires so that most broods had sire evenness E < 1 (Fig. 4). This is not in line with the expectation that females should distribute offspring as evenly as possible over a given number of sires. However, the argumentation building on the distribution of paternities relies on the assumptions that: (i) every extra-pair fertilization requires a separate, costly extra-pair copulation; and that (ii) females have a high degree of behavioural and/or physiological control over the allocation of paternity to specific sires. The first assumption seems plausible as last male sperm precedence is thought to be the rule in birds (Birkhead, 1998) and as there is pronounced sperm competition in the study population (Dietrich et al., 2004). However, the degree of female control over paternity allocation is unknown and if male fertilization success is mainly determined by male–male competition (potentially also including post-copulatory mechanisms) rather than by female choice, females may well lack sufficient control to properly exert choice of specific EPS and/or to allocate paternity evenly. Furthermore, females may be constrained in their choice of multiple extra-pair mates through the spatial and/or temporal availability of potential extra-pair mating partners, possibly mediated through mate-guarding skills of their social males.

Finally, the lack of a significant association between the sire diversity index and brood fitness does not preclude the possibility that within-brood genetic diversity is important. For example, females will produce broods that differ substantially in genetic diversity even when being faithful depending on the interaction between their own genotype and that of the social mate. More generally, the marginal value of within-brood genetic diversity as a function of polyandry is likely to differ between females and they may individually optimize their extra-pair mating behaviour accordingly: some females will have to be more polyandrous than others to achieve the same degree of within-brood genetic diversity and this is not captured by the sire diversity index as used here. This idea could be tested in future studies using a within-brood genetic diversity measure that is based on offspring genotypes at a large number of marker loci. Furthermore, experimental approaches that increase within-brood genetic diversity (e.g. through a balanced cross-foster design) and measure the long-term fitness consequences of this treatment could overcome this problem.

In conclusion, although virtually all females of the coal tit study population engage in extra-pair matings (Dietrich et al., 2004), the lack of any relationships between sire genetic diversity and brood fitness and the distribution of paternities among sires do not support the idea that females mate with multiple males to increase within-brood genetic diversity. The hypothesis that benefits of increasing sire diversity may contribute to selection for female extra-pair (i.e. polyandrous) mating behaviour in our study species was therefore not supported. The methodological approach presented here can be used to test the generality of our results in studies in other (highly) polyandrous species.

Acknowledgments

We thank Sabrina Bleidissel, Verena Dietrich-Bischoff, Anke Kalt, Maria Orland and Christiane Wallnisch for their help in the laboratory, Julia Delingat, Julia Eggert, Jorg Welcker and especially Verena Dietrich-Bischoff, Volker Janzon and Doris Winkel for support in the field and Karin and Herbert Körner for their hospitality during field work. Katharina Förster kindly assayed microsatellite markers for their cross-amplificability in coal tits. We thank Ben Sheldon and an anonymous reviewer for useful comments. This project was supported by the Deutsche Forschungsgemeinschaft (Lu 572/2–4).