For each simulated year t, we calculated the mean true breeding value B¯t of the breeding colonies of that year. The corresponding values for the passive population could not be retrieved directly, because no worker groups were simulated for the passive queens [14, page 4]. Thus, we reconstructed the average passive colonies’ breeding values P¯t from the available average breeding and passive queens’ breeding values B¯tQ and P¯tQ as:

which reflects that a colony’s breeding value is equal to the average breeding values of the queen and of the drones that the queen mated with. Values for B¯t and P¯t were determined for the direct, maternal, and total breeding values, where the total breeding value of a colony was equal to the sum of its direct and maternal breeding values. The realized annual genetic progress rates and the realized genetic lag between the breeding population and the passive population were then calculated as:

In order to examine how well the observed values correspond to the results given in Table 2, we needed to access values for S1 and S2 from the simulations. Therefore, for each year t17, we denoted by B¯1,t the mean breeding value of those colonies of year t that were selected to produce breeding queens in year t+2 and by B¯2,t the mean breeding value of those colonies that were selected to produce drone producing queens in year t+3. Then, for j=1,2:

With these resulting values for ΔB¯t, ΔP¯t, D¯t, S¯1,t, and S¯2,t, we investigated, how well the simulated data represented the relations of Table 2.

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