> So... my question is for those who have raised queens, what's a minimum number of queen lines you have used without ending up with lots of spotty brood from inbreeding?

Sorry, but I don't think anyone is giving the right answer to this question. First of all, the correct term is heterozygosity vs homozygosity. If honeybee eggs are homozygous at the sex allele, the bee is male and the workers eat it. However, this is an extreme scenario and unlikely to occur in field conditions. On the other hand, colonies benefit from heterozygosity, so inbreeding is to be avoided. Kaspar Bienefeld wrote in 2016:

> Responsible breeding means not optimizing for short-term breeding progress at whatever cost, but rather ensuring that the population is sustainably improved over a long time frame. This can be realized by introducing unselected individuals of the same subspecies in a controlled manner and/or applying selection methods based on long term strategies. Until recently, such concepts have been met with modest interest in the fields of plant and animal breeding. This is due to the fact that current gains remain in the foreground and addressing disadvantages for subsequent generations are typically a drastically lower priority. Reducing inbreeding and experiencing long-term selection success depend upon, above all, the size of the breeding population. 

Bienefeld, K. (2016). Breeding Success or Genetic Diversity in Honey Bees?. Bee World, 93(2), 40-44. Chicago	

On the other hand, despite a maximal inbreeding scenario, honeybees maintained heterozygosity:

> Inbreeding (the mating between closely related individuals) often has detrimental effects that are associated with loss of heterozygosity at overdominant loci, and the expression of deleterious recessive alleles. Here, we utilise a unique inbred population of clonal (thelytokous) honey bees, Apis mellifera capensis, to determine which loci reduce individual fitness when homozygous. This asexual population arose from a single worker ancestor approximately 20 years ago, and has persisted for at least 100 generations. Thelytokous parthenogenesis results in a 1/3 of loss of heterozygosity with each generation. Yet, this population retains heterozygosity throughout its genome due to selection against homozygotes.

Smith, N. M., & al (2018). Strikingly high levels of heterozygosity despite 20 years of inbreeding in a clonal honey bee. Journal of evolutionary biology.

Without understanding these aspects, one cannot really make assertions about the risk/benefit of closed breeding populations.

PLB

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