Non Social Hymenoptera
Table 1 summarizes the non-social Hymenoptera in which sl-CSD is proposed to be the sex determining mechanism. Since many different methods have been used to infer the presence of sl-CSD we have graded all the species according to the five categories of increasing confidence level of evidence that were distinguished in the previous section. Apart from parent-offspring matings, which are probably extremely rare in nature, the highest risk of producing diploid males is in sib matings. Mating in gregarious parasitoid species (i.e. two or more offspring emerging from one host) generally occurs among individuals emerging from a single host before the females disperse . Gregariousness may therefore be in conflict with sl-CSD. The three Bracon species in Table 1 seem to violate this prediction. In B. hebetor sex ratios have been reported to be female-biased [21, 43]. Nevertheless, sib mating in B. hebetor is rare for a number of reasons. Females exhibit a pre-mating refractory period during which dispersal takes place [44–46], they have a mating preference for males that emerged from a different host , and males aggregate in leks that attract sperm-depleted females. A pre-mating refractory period of 4 to 5 hours after emergence has also been found in B. brevicornis . In the only other gregarious species in Table 1, Cotesia glomerata, 50 to 100 per cent of the females and, approximately, 30 per cent of the males disperse immediately after emergence from their natal patch. This results in only a minority of 25 per cent of females mating with sib males in the field . Clearly, these behaviours promote an outcrossing mating system.
In solitary parasitoid species (i.e. only one offspring emerging from a host) and sawflies the probability of sibs meeting each other in the field will depend on their temporal and spatial distribution. Oviposition in solitary species is a sequential process, where the searching time for oviposition sites or hosts causes a time delay between successive ovipositions. Additionally, differences in quality of sites and hosts and differences in microclimate induce further desynchronisation of development and emergence time. This, together with the fact that all solitary species in Table 1 are good dispersers with both sexes fully winged, may contribute considerably to an outbreeding mating structure. However, apart from these general mechanisms inherent to the solitary life cycle, there may be other aspects that further reduce the probability of sib mating.
Some species in Table 1 like Athalia rosae and Microplitis croceiceps initially produce female biased sex ratios, but lay male biased sex ratios later on in life [48, 49], causing a further temporal segregation of female and male sibs. A similar effect results from the tendency of Diadegma species to lay male eggs in young, small hosts and female eggs in older and larger hosts [50, 51]. Other species in Table 1 divide their total egg complement over many host patches thereby creating a spatial segregation of offspring. In Neodiprion nigroscutum, Bathyplectes curculionis and Diadromus pulchellus, for example, this results from the fact that their hosts occur in low numbers per patch [52–54]. Comparing the behaviour of thelytokous and arrhenotokous forms of V. canescens Thiel et. al.  recently found strong indications that the oviposition behaviour of the arrhenotokous form is specifically adapted to promote outbreeding.
Similarly to gregarious parasitoids, the offspring of nest building wasps also are likely to meet sibs early in life. Females of the hunting wasp Euodynerus foraminatus build nests in which they store prey and lay eggs. Males develop faster than females and up to 66 per cent of the females in a nest mate with their brothers [56, 57]; this species undoubtedly has sl-CSD. However, Cowan and Stahlhut  recently have shown that the diploid males in E. foraminatus are normally fertile and able to transmit their genes to their daughters. It seems that diploidy does not entail many costs in these males. This case appears unique, but shows that one needs to be cautious in generalising that diploid males produced by CSD are an evolutionary dead end. For another cavity nesting Vespid, the potter wasp Ancistrocerus antilope, the other Vespoidea in Table 1, extremely high levels (>90 per cent) of inbreeding have been found in natural populations . The same study also reported that around 25 per cent of the males collected from trap nests in the field were diploid. If CSD is the mechanism causing this diploidy, the two findings could point to a similar 'immunity for male diploidy' as in E. foraminatus.
It must be emphasised that for none of the solitary species in Table 1 life histories or mating and oviposition behaviour have been studied with special reference to CSD. For example, little is known about avoidance of sib mating in solitary parasitoid species in general, simply because it remains relatively uninvestigated. Moreover, although the mechanisms promoting sib mating avoidance in the gregarious Bracon case are likely adaptations to CSD, the aforementioned mechanisms that contribute to temporal or spatial segregation of sibs in solitary species are not necessarily specific adaptations to CSD. Laying small clutches, for example, may serve as a bet-hedging strategy in the first place, while laying male eggs in small hosts a matter of optimal host use. The Cotesia genus, in which species with and without CSD occur, could provide a good system to study the adaptive significance of life history traits and behaviour with respect to CSD. The example of E. foraminatus shows that asking if and how CSD species reduce the probability of matched matings may lead to surprising new findings.
Diploid males have now been detected in more than 40 species of ants, bees and social wasps. Although this study doubles the number of cases compared to previous reviews [3, 7, 34], contrary to non-social Hymenoptera, sl-CSD has been confirmed only for a small number of social Hymenoptera (Table 2). This may be attributed to difficulties of breeding social hymenopterans in the laboratory. The proportion of diploid males that have been found among the progeny of social Hymenoptera can be remarkably high, indicating either high levels of inbreeding or small variation in the sex determination locus. For the primitively social wasp Liostenogaster flavolineata, for example, Strassmann et al.  found 11 of 71 males to be diploid and in some Formica ant species (F. aquilona, F. rufa and F. polyctena) 10 per cent of all males are diploid . In the primitive eusocial bee Hallictus poeyi proportions of diploids that are male are estimated to range from 9.1 to 50 per cent . Populations may differ significantly in their DMP. For example, Roubic et al.  found that, within populations of the colonial genera Euglossa and Eulaema of Euglossine bees in Panama, an estimated 12–100 per cent of all males are diploid, yet Takahashi et al.  found almost no diploid males within Brazilian populations of Euglossine bees .
In social hymenoptera, diploid males are produced at the expense of workers or female reproductives and are therefore expected to impose severe disadvantages for colony growth and survival. Plowright and Pallett , for example, found that colonies of the bumble bee Bombus atratus in which 50 per cent of the diploid progeny were male grew significantly slower than colonies producing only workers. Also, incipient monogynous colonies (bearing a single reproductive queen) of the fire ant Solenopsis invicta with DMP have a significantly slower colony growth and exhibit higher mortality than those that do not produce diploid males . While diploid males are often sterile, diploid males of Polistes dominules wasps are capable of mating and produce triploid offspring. In this species DMP may thus result in a delayed fitness cost for two generations .
A number of traits appear to have evolved in social Hymenoptera that reduce the risk of sib-mating. Additionally, there are several other traits that may diminish the costs of DMP. In the following section an overview of these traits is presented for various species known to produce diploid males.
Avoidance of sib-matings
Social Hymenoptera show several behavioural and morphological traits that reduce the probability of mating amongst siblings and most species have inbreeding levels not significantly different from zero . Most species avoid inbreeding by dispersal of both sexes, and males and females will often leave the nest at different times [66, 67]. Both sexes of Apis and Melipona bees, for example, are known to fly great distances in order to mate in population-wide mating swarms . Alternative sexual dispersal behaviour is found in the ants Harpagoxenus sublaevis and Doronomyrmex kutteri. In these species, the males leave their natal nest and disperse to find unmated queens, while the females walk only a short way from the nest to exhibit a so-called "female calling" behaviour to attract mates [69, 70]. Workers of a number of Bombus species reduce the risk of inbreeding by actively removing young males from the colony, thereby preventing them from mating with their own sisters. Males are attacked when they are 4–5 days old and eventually killed if they do not leave the colony . In the primitively social bee Lasioglossum zephyrum, the male bees recognise and avoid mating female kin through olfactory signals .
Removal of diploid male larvae
Some social Hymenoptera remove diploid males in an early stage, thereby avoiding rearing costs . Woyke  showed that diploid male larvae of the honeybee Apis mellifera are removed and cannibalised almost immediately after hatching. The hydrocarbon patterns of diploid male larvae of A. mellifera differ from those of diploid worker and haploid drone larvae and may be used by workers to distinguish between the three types of larvae . The diploid males of another honeybee, A. cerana are also removed, one day after hatching . In the African swarm-founding wasp Polybiodes tabidus and Formica ants, diploid males are only detected at times when the colony produces sexual offspring, suggesting that in non-sexual brood males are eliminated at early developmental stages [60, 76].
Removal of diploid male-producing queens
In contrast with the larvae of the honeybee, which are situated in open cells, the larvae of Melipona bees are reared in sealed cells. Melipona bees are therefore not able to detect and remove diploid males. Diploid males of M. quadrifasciata have normal survival as immatures . However, when a M. quadrifasciata queen produces diploid males, the workers kill the queen and rear a replacement .
Polyandry and polygyny
If all queens in a population of social Hymenoptera are singly mated, under random mating, a number of females within the population will mate with a male sharing their sex allele and produce diploid progeny of which half will be males. If females mate with multiple males, more females within the population will produce diploid males, but the proportion of males among the diploid progeny per female will be lower. Thus, in polyandrous populations, although the absolute proportion of diploid males will be the same, the variance in DMP among colonies is reduced .
The load hypothesis predicts that the load of diploid males will select for monandry or polyandry depending on the relationship between DMP and female fitness [16, 78–80]. In case of a linear relationship between DMP and female fitness, sl-CSD in not expected to select for polyandry, but under some non-linear relationships it may. Antolin and colleagues , for example, showed theoretically that multiple mating reduces genetic load if populations contain only few sex alleles. In social hymenoptera several factors influencing the relationship between DMP and a queen's fitness, like the timing of the removal of diploid males  and the timing of sexual production during colony growth  have been suggested to promote polyandry. The load hypothesis predicts selection for polyandry when, for example, colonies of social Hymenoptera can tolerate moderate, but not high frequencies of diploid males, because high levels of diploid males would almost always result in the death of a colony. As a result, the fitness of multiple mated queens within colonies that produce, for example, 25 per cent diploid males could be higher than the average of single mated queens producing 50 per cent or 0 per cent diploid males. At this moment there is, however, no empirical evidence that polyandry has specifically evolved in response to DMP.
In polygynous colonies, the DMP by some queens can be buffered by the presence of workers produced by other queens in the nest. In addition, polygynous colonies often reproduce by fission or budding, and may therefore skip the vulnerable early exponential phase of colony growth, in which the load of diploid males might be fatal . Around 1940, the fire ant Solenopsis invicta was introduced from South-America to North-America; diploid males are far more common in the introduced population than in the native populations, probably due to loss of sex alleles [15, 81]. In the introduced range, several polygynous populations have apparently evolved independently in only a few decades from the originally monogynous founder population. While diploid males are very common in polygynous colonies, they are absent in monogynous colonies . Ross and Fletcher  showed that monogynous colonies which adopted queens rear diploid males in the laboratory and the absence of diploid males in monogynous colonies in the field can thus not be explained by elimination of diploid males at early stages. This suggests that monogynous incipient colonies of S. invicta producing diploid males do not survive . While DMP producing queens are likely to benefit greatly from joining a multi-queen colony, it is unclear what role DMP has had in the evolution or maintenance of polygyny in the imported fire ant [18, 81].
The load hypothesis predicts an association between monogyny and monandry when colonies with moderate frequencies of diploid males have high mortality . Pamilo et al  investigated this hypothesis in several Formica ant species. In accordance with the theory up to 10 per cent of all males are diploid in species of Formica ant with highly polygynous colonies (F. aquilona, F. truncorum and F. polyctena), while no diploid males were found in two mainly monandrous/monogynous species (F. exsecta and F. pratensis). However, in three other monogynous/weakly polygynous species (F. rufa, F. lugubris, F. truncorum) diploid males were found in fairly high frequencies, which indicates that diploid males are not necessarily an unbearable load.