Introduction

Sex ratios in the Hymenoptera often deviate strongly from 1:1. This has been explained by two different factors: local mate competition (LMC), when related males compete for access to female sexuals (Hamilton 1967) or, in social species, worker manipulation of sex allocation in response to the asymmetric relatedness to their sexual brothers and sisters (Trivers and Hare 1976; Nonacs 1986; Boomsma 1989; Bourke and Franks 1995; Crozier and Pamilo 1996). In many parasitoid wasps and fig wasps, daughters and sons of one mother mate in a single, confined patch, such as the carcass of a host insect or a fig. In such a situation, mothers benefit most from producing just enough males to guarantee the insemination of all their daughters and produce progeny with a highly female-biased sex ratio (Werren 1987; Herre et al. 1997). In contrast, LMC appears to be of limited importance in the social Hymenoptera. Though it was soon brought up as an alternative cause of female bias (Alexander and Sherman 1977), the necessary preconditions of LMC are rarely met in ants, bees, and wasps. Instead, sib-mating appears to be typically avoided, perhaps because it leads to the production of diploid males owing to single locus complementary sex determination (Bull 1983; Cook 1993). Fertilized eggs, which are heterozygous at this sex determination locus, give rise to diploid females, while unfertilized eggs with a single sex allele and also fertilized eggs with two identical sex alleles develop to haploid and diploid males, respectively (Whiting 1967; Cook 1993; Bourke and Franks 1995; Cook and Crozier 1995; Beye et al. 2003). Haploid males are the normal male sexuals in Hymenoptera, but diploid males are often sterile and constitute additional costs in the social Hymenoptera because they do not work (Bull 1983; Ross and Fletcher 1985). In ants with reduced genetic variability, diploid male load is indeed a significant factor for the failure of colony founding (Ross and Fletcher 1986; but see Pamilo et al. 1994).

Several traits in the morphology and the behavior of sexuals and, on the colony-level, in the pattern of reproduction reduce the probability of mating among close relatives. For example, even in ants, where the workers are always wingless, sexuals are typically winged and disperse from their maternal nests before mating in large mating populations. Male or female wingless sexuals are known from many ant species, but exclusive winglessness of both sexes of a species has never been observed (Starr 1984; Heinze and Tsuji 1995; Heinze and Keller 2000). In some species, mating occurs in the nest (intranidal mating), but here too, the probability of mating among related individuals is typically reduced through pre-mating dispersal of the winged males, the adoption of alien males and/or the presence of multiple fertile queens (Starr 1984; Hölldobler and Bartz 1985; Peeters and Crewe 1986; Hölldobler and Wilson 1990; Passera and Keller 1994; Boomsma et al. 2005). Furthermore, in many species, colonies produce exclusively either male or female sexuals (split sex ratios; Boomsma and Grafen 1990) and the males leave their maternal nests earlier than female sexuals.

Significant deviations from random mating and presumed local mate competition have been described for a couple of species. However, they usually result from limited dispersal, strong population sub-structuring and highly localized nuptial swarms with random mating among sexuals from only a couple of colonies and not from regular sib-mating as in parasitoid wasps or fig wasps (Hasegawa and Yamaguchi 1995; Chapuisat et al. 1997; Cole and Wiernasz 1997; Pedersen and Boomsma 1998; Foitzik and Heinze 2001; Sundström et al. 2003).

Cardiocondyla batesii Forel, 1894 appears to be a very unusual ant in all the above-mentioned respects, because males are always wingless (“ergatoid”) and mate with winged female sexuals in their maternal nests in autumn. Young, inseminated queens shed their wings after hibernation and disperse on foot to found their own colonies independently, i.e., without the help of workers. Histological analyses of the wing muscles and the regular occurrence of short-winged female sexuals in some populations confirm that female sexuals cannot fly (A. Schrempf and J. Heinze, unpublished results; Heinze et al. 2002). Furthermore, all excavated colonies contained only a single fertile queen (monogyny), and workers never tolerated the presence of more than one fertile queen per laboratory nest (A. Schrempf and J. Heinze, unpublished results).

Due to this unique combination of life-history traits, C. batesii provides an exciting system for investigating the effects of possible brother-sister mating and strong local mate competition on the social and genetic structure of its colonies. Here we describe the genetic structure of colonies and populations of C. batesii and, in particular, address the following questions: whether local mate competition is associated with extremely female-biased sex ratios in this ant, whether diploid males are reared, and how strongly inbreeding affects nestmate relatedness.

Methods

Field collection and sampling

Colonies of C. batesii are relatively small (10–120 workers) and nest in cavities in the soil down to a depth of more than 1 m. In spring, many adults and brood can be found in the uppermost nest chambers, which makes the collection of complete or nearly complete colonies much easier during this season. Colonies were excavated and the positions of their nests were recorded at four different sites in the vicinity of Granada, Spain (Baza 37°31′N, 02°04′E; Padul 37°02′N, 03°40′E; Sierra Elvira 37°15′N, 03°45’E; Guadix 37°23′N, 03°08′E) in April 2001, October 2001, and June/July 2002. Each collecting site measured about 1,500 m2 and distances between the sites ranged between 30 and 100 km. Colony density was high, with up to one nest per square meter. Both in spring and autumn, winged female sexuals were found in the upper nest chambers of some colonies (mean 15.1±SD 15.5; min 2, max 53), together with workers and a single, fertile, dealate queen. In autumn, several colonies contained ergatoid males. Additionally, we collected founding queens that dispersed on foot in spring.

Colonies and founding queens were transferred into standard artificial nests in the laboratory (Heinze and Ortius 1991) and reared under temperature conditions simulating the natural seasons (winter: 12 h 8°C/12 h 12°C; summer: 12 h 24°C/12 h 27°C; 6–13 h light). For genetic analyses, 10–20 workers each (total: 379 workers) from 34 summer colonies (8, 14, 5, and 7 colonies from the 4 populations) and 12 males collected in autumn were frozen at −20°C shortly after collection. After polyandry had been detected (see below), an additional 10 young workers each and a total of 24 males from 9 laboratory-reared single-queen colonies were genotyped. Young workers in these colonies were definitely offspring of a single mother.

Microsatellite and allozyme analyses

For allozyme electrophoresis, the gasters of all frozen individuals were homogenized in 20 µl buffer (0.1 m TRIS, 0.002 m EDTA, 0.05 mm NADP; pH 7.0). We applied 12 µl of the homogenate to 7.5% vertical polyacrylamide gels (gel buffer: 0.5 m TRIS/HCl; pH 8.0; running buffer: 0.2 m glycine, 0.025 m TRIS; pH 8.3). Proteins were separated by electrophoresis at 10 V/cm for 120 min, and enzymes were stained following standard methods (Harris and Hopkinson 1978). Glucose phosphate isomerase (GPI) was slightly variable (3 alleles), but other enzymes (malate dehydrogenase, esterase) showed no consistent variability in 40 individuals from different colonies.

Following a method based on selective hybridization (Tenzer et al. 1999; Gautschi et al. 2000), eight microsatellite loci were isolated from ants from summer colonies. Two loci showed some variability with 4 (card 8) and 11 (card 21) alleles, respectively. The other loci did not reveal any variation in our sample (Table 1).

Table 1 Primer sequences, number of alleles (N A ), size range, repeat motif, and primer pair-specific annealing temperature (T A ) of eight microsatellite loci developed for the ant Cardiocondyla batesii. EMBL accession numbers were obtained only for the first two microsatellite loci, which showed considerable variability
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DNA for microsatellite analysis was isolated from heads and thoraces of all 469 frozen workers, 36 males, and 14 queens using a Puregene DNA Isolation Kit (Gentra Systems, Minneapolis, Minn.), as described by Foitzik and Herbers (2001). Standard PCR reactions were carried out in 20-µl reaction volumes. The amplified PCR-products (primers labeled with Tet and Fam dyes) were visualized on an ABI Prism 310 Genetic Analyzer. For 438 workers, the genotypes of both microsatellite loci were available. For 406 workers, all queens and all males, the genotypes at all 3 loci (microsatellites and GPI) were available.

In many summer colonies, queens could not be collected because of the depth of their nests, and in others they were kept alive for further behavioral investigations. In these cases, the genotypes of queens and their mates were reconstructed from the genotypes of their offspring. Subsequent genotyping of 14 queens confirmed that we had correctly reconstructed their genotypes from those of their workers.

Population genetic analysis

Regression relatedness (Queller and Goodnight 1989) among workers and between queens and their presumed mates was calculated using the program RELATEDNESS 4.2 (Goodnight and Queller 1994). Groups were weighted equally and standard errors were estimated by jackknifing over colonies. Coefficients of population subdivision and inbreeding were estimated from worker genotypes in a three-level analysis with the program Genetic Data Analysis (GDA) 1.1 (Lewis and Zaykin 2001), based on the algorithms by Weir and Cockerham (1984). In this analysis, the lowest level represents individuals within colonies (however, as workers in colonies are related, they do not represent independent samples), the next level colonies within subpopulations, and the highest level subpopulations within populations. The values obtained by GDA are Weir’s f (correlation between pairs of genes within individuals, compared to random genes within the colony), Weir’s F (correlation between pairs of genes within the individual, compared to random genes within the subpopulation), θS (correlation between pairs of genes within colonies, compared to random genes within the subpopulation) and θP (correlation between pairs of genes within subpopulations, compared to random genes within the population). For population analysis, F gives information about the amount of inbreeding due to non-random mating within subpopulations, and θP about allele frequency differences between subpopulations, taking variable population sizes into account (see also Sundström et al. 2003). Confidence intervals were obtained by bootstrapping 5,000 times over loci. The frequency of sib-mating α was estimated from F=α/(4–3α) (Suzuki and Iwasa 1980; Pamilo 1985).

Mating frequencies of queens were inferred by directly comparing queen and worker genotypes. In eight cases, in which it was not clear from the worker genotypes whether a heterozygous queen had mated once or a homozygous queen had mated twice, we assumed the former scenario. The mating frequency calculated by hand may therefore be underestimated.

In general, the effective mating frequency can be given by the harmonic mean of the number of mates per queen over all queens in the sample, assuming equal paternity among males (e.g., Pamilo 1993; Ross 1993; Pedersen and Boomsma 1999). A more accurate estimate of the pedigree-effective mate number is me,p=1/∑pi2, where pi is the proportional paternity contribution of the ith male (Starr 1984; Boomsma and Ratnieks 1996). The unbiased estimation of ∑pi2 corrected for sampling error after Pamilo (1993) with the observed male contributions yi is given by ∑pi2=(N∑yi2−1)/(N−1) (yi=number of detected fathers, N=number of analyzed offspring). The probability of missing a double-mated queen because two unrelated males have an identical multilocus genotype is

$$ d = {\prod\limits_{j = 1}^k {{\left( {{\sum\limits_{i = 1}^{aj} {{\mathop p\nolimits_{ij}^2 }} }} \right)}} }, $$

where p ij denotes the frequencies of a j alleles at each of k loci (Boomsma and Ratnieks 1996). With inbreeding, the non-detection error because of identical male genotypes at all loci can be calculated by

$$ m_{{{\text{e}}{\text{,p}}}} = {\left( {\bar{\pi }{\left( {1 - {\prod\limits_{k = 1}^l {{\left( {F + {\left( {1 - F} \right)}{\left( {1 - H_{{{\text{exp}}{\text{,}}k}} } \right)}} \right)}} }} \right)}} \right)}^{{ - 1}} , $$

where \(\ifmmode\expandafter\bar\else\expandafter\=\fi{\pi }\) is the sum of squared paternity contributions corrected for non-sampling error, F is the inbreeding coefficient, and Hexp,k is the expected heterozygosity at the kth locus in the absence of inbreeding (J.S. Pedersen, personal communication).

In addition, we estimated the mating frequency of queens from their female offspring with the program MateSoft 1.0 (Moilanen et al. 2004), using the broad deduction option for maternal genotypes, as multiple mating appeared to be common. The estimated pedigree-effective mate number (me,p) was subsequently corrected for non-detection error from identical male genotypes taking inbreeding into account (see equation above).

As null alleles may also cause heterozygote deficiency, we estimated the maximum frequency of potential null alleles as r0=D/(2−D), where D=(Hexp—Hobs)/Hexp (Chakraborty et al. 1992; Brookfield 1996). The number of individuals, which are expected to be homozygote for the null allele and therefore do not yield amplification products in PCR, is r02.

Results

Population structure and heterozygote deficiency

The value of θP (0.12; 95% confidence interval 0.01–0.23) suggested a moderately high genetic differentiation among the different populations. The inbreeding coefficients F, both averaged over all populations (0.55; 95% CI 0.45–0.65) and estimated separately for each population (Table 2), revealed a considerable heterozygote deficiency. They did not differ significantly among the four populations (ANOVA; F=0.99, df=3, P=0.45). Exclusion of GPI genotypes, which did not vary in populations 1 and 3, gave a similar result (F=1.17, P=0.42). The high inbreeding coefficient corresponds to 83.0% brother-sister matings (CI 76.6%–88.1%).

Table 2 Inbreeding coefficients in the ant Cardiocondyla batesii, estimated by microsatellite analysis and enzyme electrophoresis on workers. The notation follows that given by the program GDA, based on Weir and Cockerham (1984). F describes the amount of inbreeding due to non-random mating in the parental generation; θP shows differences between subpopulations. Values for f (individual in the colony) are expected to be zero or negative; those for θS (colony within subpopulation) are positive, when individuals are related
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Heterozygote deficiency may result from non-amplifying null alleles. However, explaining the high inbreeding coefficients in C. batesii from the occurrence of null alleles alone would require null allele frequencies of 38% and 36% at the two microsatellite loci card 8 and card 21, respectively. Null alleles have normally much lower frequencies of below 15% (Jarne and Lagoda 1996). Furthermore, with such high null allele frequencies, at least 13 of the genotyped 36 males and 61 of the 469 genotyped workers are expected to give no PCR product. In contrast, microsatellite DNA could be amplified in all males, and card 8 could not be amplified only in three workers. Card 21, which is very sensitive to low DNA quality, gave no amplification product (or a product, which could not be evaluated) in 28 workers. Assuming that all these workers were homozygous for null alleles gives null-allele frequencies of 0.08 (card 8) and 0.24 (card 21), respectively. Correcting the expected heterozygosity by including hypothetical null allele homozygotes as an additional class of genotypes still gives positive inbreeding coefficients (F=0.48 and 0.23, corresponding to 78.7 and 54.4% sib-mating). However, as all loci are similarly affected by inbreeding, and the F-values differ more strongly after correction for hypothetical null alleles, it appears that null alleles do not contribute considerably to the heterozygote deficiency.

Queen mating frequency

The worker genotypes matched the assumptions of monogyny and monandry in 19 of 34 colonies (55.9%; excluding 2 presumably “alien” workers from 1 colony, see below), monogyny and double paternity in 12 (35.3%; excluding 3 “alien” workers from 1 colony), and monogyny and triple paternity in 3 colonies (8.8%). Double mating was also found in three of nine single-queen laboratory colonies (33.3%), supporting the view that genetic heterogeneity in field colonies is usually not due to serial or simultaneous reproduction by multiple queens. Combined for all populations, the mean number of fathers detected per colony was 1.49±SD 0.63 (uncorrected pedigree-effective mate number, me,p=1.35; corrected for sampling error 1.48). The likelihood of missing a double-mated queen because of the probability that two unrelated males share the same multilocus genotype was d=0.12 when estimated from the overall allele frequencies at all three loci and 0.03 when calculating for each queen separately. However, this non-detection probability is considerably increased through regular inbreeding, resulting in 43% of the males being identical at all loci. Therefore, the corrected mating frequency (based on the mean number of fathers) was me,p=2.63.

The average estimated and corrected mating frequency over all groups obtained from MateSoft was me,p=3.42 (average pi over all groups=0.52). The average number of matings detected based on the frequency distribution of the number of patrilines per group was k=1.83 (corrected for inbreeding=3.23) and only slightly higher than the minimum average number of matings estimated from the smallest number of matings found per group (kmin=1.80; corrected for inbreeding=3.18). The power to correctly deduce the queen genotypes was >0.95 for all offspring groups except for one group, which was therefore left out from the analysis. As more than one queen genotype may occasionally be compatible with offspring data, MateSoft calculates the probabilities of the alternative genotypes from allele frequencies and/or the allele segregation among the offspring. In case any of the queen alternatives implies a segregation of the alleles among the offspring with very low probability (less than 0.2), we deleted these genotypes from the dataset. Furthermore, we excluded queen alternatives of 14 queens, for which the actual genotypes were known. The mating frequency calculated by hand is less than that calculated by MateSoft, because, in the first case, queens were always assumed to be heterozygous and single-mated rather than homozygous and double-mated.

The effective mating frequencies as estimated by MateSoft did not differ among populations (ANOVA: F=1.51, df=39, P>0.23). Nevertheless, the four populations appeared to differ significantly in the frequency of multiply mated queens. Queens from Sierra Elvira were more often multiply mated (87.5%: 7 of 8 colonies) than queens from Padul (35.7%: 5 of 14 colonies, Fisher’s exact test: P=0.03; including the laboratory colonies: 34.8%: 8 of 15 colonies, P=0.01) and Baza (16.7%: 1 of 6 colonies, P=0.01). Two of five queens (40.0%) from Guadix were also multiply mated (Fig. 1). Overall, populations, colonies with singly, doubly, and triply mated queens did not differ in worker number (ANOVA: F=0.87, df=2, P>0.43; Scheffé test: P>0.44, 0.80, and 0.99; Fig. 2).

Fig. 1
figure 1

Frequency of multiple paternity in four different populations of the ant Cardiocondyla batesii (including laboratory colonies).

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Fig. 2
figure 2

Frequency of multiple paternity in different size classes of C. batesii summer colonies (34 colonies).

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Colony structure and relatedness

Worker genotypes were consistent with monogyny in 32 of 34 colonies (94.1%). In 2 colonies, several workers (2 out of 10 and 3 out of 12; 22.5%) did not share a single allele with the queen but obviously belonged to a different matriline. As our laboratory observations indicate that it is unlikely that several fertile queens can coexist within a single nest (polygyny) (A. Schrempf and J. Heinze, unpublished results), the occurrence of multiple matrilines might be explained by queen replacement or the accidental adoption of stray foragers from neighboring colonies. However, the latter is not likely, since all foreign workers in each colony belonged to a single matriline. Furthermore, the genotypes of the alien workers did not fit to genotypes of neighboring colonies. In contrast, laboratory experiments suggested that founding queens may occasionally take over alien colonies (A. Schrempf and J. Heinze, unpublished results).

The overall relatedness among nestmate workers was bww=0.66±SE 0.07 (excluding the “alien workers” from two colonies 0.68±0.05). Relatedness was not significantly different between the four populations (ANOVA: F=1.07, df=3, P=0.38; Table 2). The regression relatedness of the genotyped queens (n=14) to their presumed mates was rqm=0.70±0.27, and that of the presumed mates to the queens was rmq=0.29±0.17. Including reconstructed queen genotypes in the analysis and thereby increasing the sample size (n=43) leads to an rqm=0.76±0.12 and rmq=0.26±0.09. These values are significantly different from zero (t-test, t=6.33, P<0.001 and t=2.89, P<0.001). The estimated rqm is slightly higher than the regression relatedness of sisters to brothers (0.5; t=2.17, P<0.05), while rmq is not significantly different from that of brothers to sisters (0.25; t=0.11, P>0.5). In 9 of 43 cases (20.9%), the alleles of one mate differed from those of the queen (2 single, 4 double, 3 triple matings), suggesting that the mating partners occasionally came from different colonies.

Sex ratios

Numerical sex ratios (relative proportion of female sexuals among all reproductives) were always highly female-biased (field-colonies in autumn: 0.94±0.04; laboratory-reared colonies: 0.87±0.09, Table 3). For field colonies, the coefficients of variability V (s/mean) were 43% for males and 65% for female sexuals. Laboratory colonies give similar values, when one colony with an extraordinarily large number of males is excluded (males: V=56%, female sexuals: V=79%).

Table 3 Sexuals present in field and laboratory colonies of the ant Cardiocondyla batesii and numerical sex ratio (relative proportion of female sexuals among all reproductives) in autumn. Mating is presumed to occur in autumn and female sexuals disperse after hibernation in spring
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In all laboratory colonies, one or two males emerged a few days before the first female pupae eclosed. In some colonies, one or a few additional males emerged some days later, together with the first female sexuals (the total number of males is given in Table 3). The rarity of adult males is in accordance with local mate competition theory, and also suggests that inbreeding does not lead to a substantial production of large numbers of adult diploid males. Furthermore, genotyping did not reveal any adult diploid males. Based on the frequency of heterozygosity among nestmate workers, 23 of 36 investigated males would have been heterozygous at 1 of the 3 loci had they all been diploid.

Discussion

Our data show that a considerable percentage of female sexuals of the ant C. batesii mate multiply and that more than 80% of all matings are between brothers and sisters. The inbreeding coefficient is the highest as yet reported from social Hymenoptera. Though DNA could be amplified in all haploid males, we cannot rule out that the inbreeding coefficient is inflated to some extent by null alleles. Nevertheless, the F-values remained significantly positive even after a correction for null alleles. As expected from local mate competition theory (Hamilton 1967), sex ratios were highly female biased. All three phenomena—local mate competition, inbreeding, and multiple mating—are remarkable in themselves, but their combination within a single ant species makes C. batesii truly exceptional.

Inbreeding with local mate competition and strongly female-biased sex ratios are common in solitary haplodiploid animals. Female ambrosia beetles, parasitoid wasps, and fig wasps adaptively adjust the sex ratio in their progeny by rearing more sons in the presence of reproducing conspecific females than when alone (e.g., Herre 1985; King 1986; Peer and Taborsky 2004). In ants, evidence for local mate competition affecting sex ratios is rare, owing to the prevalence of pre-mating dispersal (Hölldobler and Bartz 1985; Boomsma et al. 2005). Local mate competition in small, localized mating swarms may promote female-biased sex allocation in Messor aciculatus (Hasegawa and Yamaguchi 1995). Sex ratios are also more female biased than predicted from relatedness asymmetries alone in Technomyrmex albipes, an ant with locally mating, wingless replacement reproductives (Yamauchi et al. 1991), and several socially parasitic ants with intranidal mating, such as Myrmoxenus kraussei (Winter and Buschinger 1983; Bourke 1989). Of particular interest is the situation in C. obscurior, a facultatively polygynous relative of our study species. C. obscurior queens produce only very few ergatoid males, as long as they are the only reproductives in a colony, but strongly increase the production of such fighter males when other fertile queens are present in their nests (Cremer and Heinze 2002; De Menten et al. 2005).

Ergatoid males of C. obscurior always engage in deadly fighting, even in monogynous societies. In contrast, about one-third of the sampled C. batesii colonies contained several mutually tolerant males, and male fighting appeared to be very rare (unpublished results). It appears that queens produce just enough males to ensure the insemination of all their daughters. Ergatoid Cardiocondyla males differ from other Hymenopteran males in that their spermatogenesis continues throughout their lives (Heinze and Hölldobler 1993; Heinze et al. 1998). Very few males are therefore sufficient to inseminate all female sexuals produced in a colony. The number of males varied considerably less than the number of female sexuals, which is in accordance with the assumption that colonies invest first in a few males and, depending on resource availability, in a varying number of female offspring (constant male hypothesis, Frank 1987). Though queen mating frequency varied considerably between colonies, it is quite unlikely that this variation alone explains our sex-ratio data. According to split sex-ratio theory (Boomsma and Grafen 1990), workers from monandrous colonies produce a highly female-biased sex ratio, whereas workers from polyandrous colonies invest mostly in males, because the relatedness asymmetry of workers to female and male sexuals decreases. This results in bimodally distributed colony-level sex ratios, but sex ratios in C. batesii were always highly female biased. The number of colonies for which colony size, mating frequency, and sex ratio are exactly known is too small, however, to investigate whether sex ratios meet predictions about the variation of sex ratios under inbreeding with varying mating frequency.

The genetic data match conclusions based on the morphology and behavior of sexuals. Female sexuals apparently mate in their maternal nests before dispersing on foot, and all young queens that were collected outside their nests in spring were inseminated (Heinze et al. 2002). It is, therefore, quite surprising that approximately one-fifth of all matings involve unrelated partners. Though the wingless, small-eyed ergatoid males are obviously not well adapted for dispersal, they (and/or the winged female sexuals) might easily cross the short distance between neighboring nests to outbreed. Such behavior has as yet not been observed in the field, though Marikovsky and Yakushkin (1974) incorrectly cite Morley (1954) for ergatoid male dispersal in Cardiocondyla. However, Morley (1954) mentions neither ergatoid males nor Cardiocondyla. LMC should nevertheless be strong, as males apparently first mate inside the nest before dispersal.

In spite of the high inbreeding coefficient, we did not detect any diploid males. Even if our result is based on only a small number of analyzed males, the female-biased sex ratio supports the assumption that adult diploid males are absent or rare. Diploid males might either be detected and eliminated at a very early stage of development, as in honeybees (Woyke 1963), or are not produced at all. In a system with regular inbreeding, however, it seems more likely that a sex-determination mechanism has evolved, which is not susceptible to inbreeding. Such mechanisms, e.g., genomic imprinting, have previously been suggested for parasitoid wasps and socially parasitic ants with regular sib-mating (Buschinger 1989; Dobson and Tanouye 1998; Beukeboom et al. 2000; but see Stahlhut and Cowan 2004).

Even with the rather low resolution of our genetic markers, we were able to detect multiple mating in about one-third of all queens from both natural and definitively monogynous laboratory colonies. The correspondence between field and laboratory data indicates that queen replacement, though it might occasionally occur in the field, does not strongly affect the genetic colony structure. The effective frequency of multiple mating, both calculated by hand and with the program MateSoft, indicates that queens mate on average with more than two males. Laboratory observations of males indicate that all males copulate with all female sexuals, since they almost continuously show sexual behavior. Field colonies contained mostly single males, but the high frequency of multiply mated queens and our laboratory results suggest that not all males are produced at the same time. In laboratory colonies, one or two males were produced before the young queens eclosed, and several males eclosed later. Some of them might leave the colony after mating with their sisters and enter alien colonies to mate with unrelated queens, as well.

Although frequent multiple mating has been reported in several species of ants with large colony sizes (e.g., Formica, Pamilo 1993; Sundström 1993; Chapuisat 1998; Acromyrmex, Bekkevold et al. 1999; Boomsma et al. 1999; Pogonomyrmex, Cole and Wiernasz 1999; Gadau et al. 2003), female sexuals of related genera of Cardiocondyla with small colonies typically mate only once (e.g. Harpagoxenus, Bourke et al. 1988; Temnothorax, Foitzik et al. 1997; Leptothorax, Hammond et al. 2001; Protomognathus, Foitzik and Herbers 2001). Multiple mating in C. batesii lowers nestmate relatedness to 0.68 and thus counteracts the effects of inbreeding on relatedness. The frequency of multiple mating appeared to differ slightly between populations, but more data are needed to corroborate this result and investigate the consequences of varying mating frequency.

Hypotheses that explain polyandry through benefits from higher genetic variability are not easily applicable in C. batesii, because they have only a small colony size, simple division of labor, and live in a uniform habitat. Cardiocondyla workers are sterile (Heinze et al. 1993) and, due to inbreeding and local mate competition, their interests converge with those of the queen towards a highly female-biased sex ratio. The sperm-limitation hypothesis (Cole 1983) is also not supported because of the small colony size of C. batesii. Furthermore, our results show that single-mated queens produce similar worker numbers as multiply-mated queens. Polyandry may be a strategy for reducing diploid male load in species with complementary sex determination (Page and Metcalf 1982; Pamilo et al. 1994), but as suggested above, C. batesii might have evolved a sex determination mechanism, which is not sensitive to inbreeding.

Finally, multiple mating is typically considered to be selected against because it is costly to queens due to increased energy expenditure, time loss, and higher risks of predation and parasite transmission (Sherman et al. 1988; Keller and Reeve 1994; Bourke and Franks 1995; Boomsma and van der Have 1998). In C. batesii, these risks are probably negligible, because female sexuals mate in the safety of the nest. Because there are nearly no costs of multiple mating, it might simply not be selected against even if it were not associated with any particular fitness benefits.