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In eusocial Hymenoptera, queens and their helper offspring should favour different sex investment ratios. Queens should prefer a 1:1 investment ratio, as they are equally related to offspring of both sexes ( r  = 0.5). In contrast, helpers should favour an investment ratio of 3:1 towards the production of female brood. This conflict arises because helpers are more closely related to full sisters ( r  = 0.75) than brothers ( r  = 0.25). However, helpers should invest relatively more in male brood if relatedness asymmetry within their colony is reduced. This can occur due to queen replacement after colony orphaning, multiple paternity and the presence of unrelated alien helpers. We analysed an unprecedentedly large number of colonies ( n  = 109) from a UK population of  Lasioglossum malachurum , an obligate eusocial sweat bee, to tease apart the effects of these factors on colony-level investment ratios. We found that multiple paternity, unrelated alien helpers and colony orphaning were all common. Queen-right colonies invested relatively more in females than did orphaned colonies, producing a split sex ratio. However, investment ratios did not change due to multiple paternity or the presence of alien helpers, reducing inclusive fitness pay-offs for helpers. Queen control may also have been important: helpers rarely laid male eggs, and investment in female brood was lower when queens were large relative to their helpers. Genetic relatedness between helpers and the brood that they rear was 0.43 in one year and 0.37 in another year, suggesting that ecological benefits, as well as relatedness benefits, are necessary for the maintenance of helping behaviour. Significance statement How helping behaviour is maintained in eusocial species is a key topic in evolutionary biology. Colony-level sex investment ratio changes in response to relatedness asymmetries can dramatically influence inclusive fitness benefits for helpers in eusocial Hymenoptera. The extent to which helpers in primitively eusocial colonies can respond adaptively to different sources of variation in relatedness asymmetry is unclear. Using data from 109 colonies of the sweat bee  Lasioglossum malachurum , we found that queen loss, but not multiple paternity or the presence of alien helpers, was correlated with colony sex investment ratios. Moreover, we quantified average helper-brood genetic relatedness to test whether it is higher than that predicted under solitary reproduction ( r  = 0.5). Values equal to and below  r  = 0.5 suggest that relatedness benefits alone cannot explain the maintenance of helping behaviour. Ecological benefits of group living and/or coercion must also contribute.

Split sex ratios and genetic relatedness in a primitively eusocial sweat bee