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http://www.glenn-apiaries.com/principles.html
Hygienic behavior
Hygienic behavior is probably the most successful achievement in breeding bees. It's been very well studied and proven to be effective against chalkbrood, American foulbrood, and varroa.genetics of hygienic behavior
Hygienic behavior is controlled by two recessive genes. One gene allows the worker to detect and uncap a cell that contains diseased brood. The other gene makes the workers remove the brood and discard it. It's possible for a hive to contain one of these genes and not the other, in which case the hive won't be hygienic. It's also possible for different individual bees to have one, but not the other gene.
For a recessive trait to be expressed, a worker needs to be homozygous for the gene. Homozygous means that it gets the same allele from the mother and father. Heterozygous means that the bee has one of the alleles and so is a carrier, but the trait is not expressed.
In this example we're starting with a queen homozygous for the hygienic traits and mating her to non hygienic drones. The offspring will not express the hygienic trait, but they will be heterozygous and so be carriers of the trait. It's important to remember that when you're dealing with recessive traits, it will not show up in the first or F1 generation. But if you have patience and continue with the program, you'll be successful in getting the trait into the following generations.
After a few generations of selecting and breeding from the colonies that express the trait, it can become fixed in the population. Then all the bees in that population will express the trait. We have reached this point with artificial insemination and closed populations.
Resistance to tracheal mites has recently been found to be a grooming behavior. The bees use their middle legs to groom the mites away from their tracheal opening. It's also been found that the trait is controlled by dominant genes. It hasn't been determined if there are more than one gene involved. In this example, we'll assume there's just one gene controlling it. Here we'll say that we're starting with a single drone that carries the resistant gene.