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Selection strategy
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Setup
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\(n_{D}\)
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F (%)
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\(\frac{{P_{{[{24}]}} }}{{\sigma_{P} }}\)
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\(\frac{{BV_{dir}^{{Q_{{[ {23} ]}} }} }}{{\sigma_{{BV_{dir} }} }}\)
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\(\frac{{BV_{mat}^{{Q_{{[ {23} ]}} }} }}{{\sigma_{{BV_{mat} }} }}\)
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\(V\left( {P_{{[ {24} ]}} } \right)\)
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\(V\left( {BV_{dir}^{{Q_{{[ {23} ]}} }} } \right)\)
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\(V\left( {BV_{mat}^{{Q_{{[ {23} ]}} }} } \right)\)
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\(r_{{BV_{dir} , BV_{{mat_{{[ {23} ]}} }} }}\)
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L
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1
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1
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25.68 (2.56)
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4.24 (0.49)
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5.92 (0.81)
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3.45 (0.72)
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40.09 (6.29)
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5.47 (2.23)
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5.88 (2.67)
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− 0.089 (0.275)
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8
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19.49 (2.19)
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4.63 (0.39)
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4.62 (0.63)
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5.10 (0.64)
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40.88 (5.93)
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6.68 (2.20)
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6.66 (2.15)
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− 0.030 (0.197)
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16
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18.57 (2.14)
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4.82 (0.42)
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4.60 (0.60)
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5.43 (0.63)
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39.31 (6.19)
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6.89 (1.91)
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6.38 (2.02)
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− 0.074 (0.203)
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2
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1
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27.15 (3.36)
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5.81 (0.54)
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7.74 (0.80)
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3.11 (0.79)
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43.72 (7.50)
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10.04 (4.41)
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5.73 (2.58)
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− 0.022 (0.265)
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8
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20.23 (2.18)
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6.11 (0.48)
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6.07 (0.65)
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4.79 (0.67)
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42.64 (6.54)
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12.50 (3.64)
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6.48 (2.14)
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− 0.036 (0.206)
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M
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1
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1
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38.72 (4.97)
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5.27 (0.50)
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6.20 (0.90)
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5.27 (0.87)
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38.00 (5.57)
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4.40 (1.87)
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4.55 (2.22)
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− 0.062 (0.283)
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8
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26.58 (3.63)
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5.53 (0.49)
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5.11 (0.70)
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6.47 (0.75)
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37.72 (5.27)
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5.92 (1.89)
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5.76 (1.83)
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− 0.060 (0.185)
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16
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25.51 (3.23)
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5.56 (0.44)
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4.93 (0.77)
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6.61 (0.67)
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38.51 (5.00)
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5.95 (7.89)
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5.98 (1.60)
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− 0.054 (0.182)
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2
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1
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38.94 (5.01)
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6.76 (0.55)
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7.96 (0.86)
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4.88 (0.79)
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40.82 (6.24)
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7.98 (3.58)
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4.47 (1.83)
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− 0.085 (0.289)
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8
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27.30 (4.05)
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7.11 (0.53)
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6.68 (0.73)
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6.12 (0.68)
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41.08 (6.06)
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11.01 (3.17)
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5.84 (1.98)
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− 0.064 (0.205)
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- Values in brackets represent sampling standard deviations over 160 replicates
- Parameter setups 1 and 2 are fully described in Table 1. In setup 1, direct (\(dir\)) and maternal (\(mat\)) genetic variances in the base population are equal (\(\sigma_{{BV_{dir} }}^{2} = \sigma_{{BV_{mat} }}^{2}\)), while in parameter setup 2, \(\sigma_{{BV_{dir} }}^{2} = 2 \cdot \sigma_{{BV_{mat} }}^{2}\). In both setups, the direct-maternal genetic correlation in the base population is null.
- L is within-maternal-line selection; M is mass selection; \(n_{D}\) is number of drones mating each queen; F is the inbreeding coefficient; \(\frac{{P_{{[ {24} ]}} }}{{\sigma_{P} }}\) is the standardized performance of colonies in year 24; \(\frac{{BV_{dir}^{{Q_{{[ {23} ]}} }} }}{{\sigma_{{BV_{dir} }} }}\) and \(\frac{{BV_{mat}^{{Q_{{[ {23}]}} }} }}{{\sigma_{{BV_{mat} }} }}\) are the direct and maternal standardized breeding values of queens born in year 23, respectively; \(V\left( {P_{{[ {24} ]}} } \right)\) is the phenotypic variance of colonies performing in year 24; \(V\left( {BV_{dir}^{{Q_{23} }} } \right)\) and \(V\left( {BV_{mat}^{{Q_{23} }} } \right)\) are the direct and maternal genetic variances of queens born in year 23; \(r_{{BV_{dir} , BV_{{mat_{{[ {23}]}} }} }}\) is the genetic correlation between direct and maternal effects from queens born in year 23.
