I have a question about queen breeding - not the specifics of the mechanics. ;)  I am wondering what the theoretical minimum number of queen lines you would need to have an apiary be self-sufficient without resulting in inbreeding.  

David Tarpy just gave a great talk about how inbreeding manifests at the Ohio State Beeks fall conference.  It will manifest as spotty brood.  This link talks a bit about how: http://www.theabk.com.au/articles/2017/5/4/poor-queen-viability-due-to-inbreeding  and this is the kind of spotty brood that is cleared up by requeening.  ;)  As opposed to the kind that needs treatment or other more intensive management.  

In short, bee gender is determined by heterozygous alleles at several key spots on their chromosomes.  If a sister and brother mate who have identical alleles at those spots on their chromosome, those alleles will be homozygous.  So some of the worker bee daughters of that pairing will result in a _diploid_ drone, which is to say non-female, but with 2 copies of the identical allele.  

If a queen is mating ONLY with brothers with identical copies of the sex-linked allele, then this would be 100% of her fertilized eggs.  If a queen mated with 20 drones, and 1 of them was her brother with an identical sex-linked allele, then 1 in 20 of her fertilized eggs will become diploid drones.  

And the workers eject diploid drones.... creating a spotty brood pattern.

So... what's a queen breeder to do?  Really I want a small number of queen mothers, like 4.  But.... I need queen fathers too!!!!  If I have 8 colonies, and they are not related, and this year colonies 1-4 are the mother and 5-8 are the fathers... well, then I have to think about next year.  ;)  The Russian queen breeders have a system with 3 blocks of queens, and the queen mother apiary is rotated between those 3 blocks to tap into different fathers.  

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?  Any strategies for keeping a queen line going in a sustainable manner?  I'm especially interested in how many colonies were used and the likely density of beeks in your area.

I am assuming open mating because I am not interested in II at this point in my beeK career...

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