Directional selection in a population yields reduced genetic variance due to the Bulmer effect. While this effect has been thoroughly investigated in mammals, it is poorly studied in social insects with biological peculiarities such as haplo-diploidy or the collective expression of traits. In addition to natural adaptation to climate change, parasites, and pesticides, honeybees increasingly experience artificial selection pressure through modern breeding programs. Besides selection, many honeybee breeding schemes introduce controlled mating. We investigated which individual effects selection and controlled mating have on genetic variance. We derived formulas to describe short-term changes of genetic variance in honeybee populations and conducted computer simulations to confirm them. Thereby, we found that the changes in genetic variance depend on whether variance is measured between queens (inheritance criterion), worker groups (selection criterion) or both (performance criterion). All three criteria showed reduced genetic variance under selection. In the selection and performance criteria, our formulas and simulations showed an increased genetic variance through controlled mating.
This newly described effect counterbalanced and occasionally outweighed the Bulmer effect. It could not be observed in the inheritance criterion. A good understanding of the different notions of genetic variance in honeybees therefore appears crucial to interpret population parameters correctly.

The dataset results from stochastic honeybee breeding simulations performed with the program BeeSim (Link). Average outcome values for all simulation settings were collected and afterwards aggregated in an R object called "simulation_data".

The file "simulation_data.rda" contains a single R object called simulation_data. In R it can be loaded with the command load("[path]/simulation_data.rda"), where [path] stands for the path to the file.

simulation_data is stored in form of a 7D array.

• The first dimension has three entries, signifying the three different orders of introduction of controlled mating and selection
• The second dimension has three entries, signifying the three different numbers nd of selected dams.
• The third dimension has three entries, signifying the three different numbers ns of pseudo sires.
• The fourth dimension has two entries, signifying the two different genetic correlations r_md between maternal and direct effects.
• The fifth dimension has seven entries, signifying direct and maternal breeding values of queens and worker groups and their three relevant combinations (inheritance criterion, performance criterion, and selection criterion).
• The sixth dimension has 20 entries, signifying the 20 simulated years
• The seventh dimension has two entries, signifying population means and population variances.

The dimension names of simulation_data can be retrieved by the command dimnames(simulation_data)