Greetings
I am sorry, but most of the discussions about bee breeding are sadly informed. Breeding bees is not like breeding dogs. The honeybee is essentially a wild animal and nature has provided a number of mechanisms to ensure that it remains such. Recent work on the subject highlights this fact:

Most bee breeding programmes have focussed on honey production, 
temperament and disease resistance. Sadly, few bee breeding programmes
have been successful in the long term, constrained by limited progress in trait
improvement, the detrimental effects of inbreeding and poor returns on investment.

Honeybee breeding requires identifying colonies that show superior traits and
ensuring that the alleles that contribute to these traits are passed on to the next
generation. However, the relationships between genes and desired commercial
traits are more complex in honeybees than in other livestock.

One of the most extensively studied behaviours—foraging behaviour—has
revealed a complex genetic architecture, which is influenced by multiple loci of
moderate to small effect.

A negative genetic correlation between two traits (e.g. between hoarding and
time to sting; see Collins et al., 1984) means that a beneficial change in one trait
will lead to a detrimental change in the other. A trade-off between two traits will
reduce the rate or even limit the extent to which the traits can be improved by a
breeding scheme.

The accuracy of any estimate of breeding merit is limited by the accuracy with
which the phenotype of interest can be measured. Many commercially important
traits of honeybees are behavioural.

Honeybee mating biology means that queens mate with drones sourced
from a large geographic range. Jensen et al. (2005) noted that only 18% of
matings occur between drones and queens from the same apiary. This makes
it extremely difficult to reproductively isolate selected lines from unselected
and wild colonies.

Identification of the paternal genetic contribution to the phenotype of a
queen’s colony is further hindered by multiple mating. Since only a fraction
of the colony’s paternal genome is passed on to offspring queens, neither the
remaining drone contributions nor the emergent properties arising from the
interactions between the patrilines are inherited. 

The Genetic Architecture of Honeybee Breeding
Peter R. Oxley and Benjamin P. Oldroyd 2010
ADVANCES IN INSECT PHYSIOLOGY VOL. 39

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