> And isn't it also true that polyandry makes passing a trait to a colony-level phenotype even less probable? 

> From the perspective of breeding for high levels of hygienic behaviour, multiple matings by queens creates additional challenges. A colony can appear to be hygienic if only a fraction of the workers are hygienic (Arathi et al., 2000), belonging to a few hygienic patrilines among the patrilines present in the colony (Pérez-Sato et al., 2009). As a result daughter queens reared from a hygienic colony may belong to non-hygienic patrilines.

However:

> Natural mating to many males leads to colonies that are characterized by high levels of genetic diversity in the workers, which has been shown to have a beneficial impact on colony productivity (Mattila and Seeley, 2007), exploitation of food sources (Mattila et al., 2008) and disease infections (Tarpy and Seeley, 2006). 

Journal of Apicultural Research 53(5): 563-568 (2014)

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