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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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3
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1
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26.11 (3.18)
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2.42 (0.39)
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4.41 (0.79)
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0.75 (0.74)
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37.35 (6.15)
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5.67 (3.06)
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6.16 (3.20)
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− 0.491 (0.240)
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8
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18.83 (2.38)
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2.69 (0.35)
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2.11 (0.66)
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3.26 (0.64)
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37.01 (5.64)
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6.99 (2.43)
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6.97 (2.51)
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− 0.525 (0.148)
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4
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1
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26.47 (2.89)
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3.79 (0.44)
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6.31 (0.81)
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− 0.35 (0.79)
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40.93 (6.09)
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11.11 (4.63)
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5.57 (2.44)
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− 0.461 (0.219)
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8
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20.45 (2.56)
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3.85 (0.42)
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3.92 (0.68)
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2.18 (0.68)
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38.69 (5.22)
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13.38 (3.93)
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6.87 (2.11)
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− 0.526 (0.155)
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M
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3
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1
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35.42 (4.93)
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3.07 (0.41)
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4.02 (0.98)
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2.43 (0.98)
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36.08 (5.00)
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5.03 (2.59)
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5.15 (2.67)
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− 0.528 (0.217)
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8
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24.41 (3.63)
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3.29 (0.37)
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2.02 (0.75)
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4.51 (0.75)
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35.89 (4.68)
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6.10 (1.99)
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6.37 (1.86)
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− 0.518 (0.131)
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4
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1
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36.90 (4.17)
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4.44 (0.48)
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6.45 (0.83)
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0.95 (0.88)
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39.43 (5.90)
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9.22 (4.10)
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4.88 (2.37)
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− 0.503 (0.232)
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8
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25.41 (3.47)
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4.44 (0.46)
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4.05 (0.71)
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3.14 (0.70)
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37.68 (5.15)
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12.52 (4.04)
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6.13 (2.05)
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− 0.522 (0.141)
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- Values in brackets represent sampling standard deviations over 160 replicates
- Parameter setups 3 and 4 are fully described in Table 1. In setup 3, direct (\(dir\)) and maternal (\(mat\)) genetic variances in the base population are equal, while in parameter setup 4, \(\sigma_{{BV_{dir} }}^{2} = 2 \cdot \sigma_{{BV_{mat} }}^{2}\). In both setups, the direct-maternal genetic correlation in the base population equals − 0.5.
- L is within-maternal-line selection; M is mass selection; \(n_{D}\) is the number of drones mating each queen; F is the inbreeding coefficient; \(\frac{{P_{{\left[ {24} \right]}} }}{{\sigma_{P} }}\) is the standardized performance of colonies in year 24; \(\frac{{BV_{dir}^{{Q_{{\left[ {23} \right]}} }} }}{{\sigma_{{BV_{dir} }} }}\) and \(\frac{{BV_{mat}^{{Q_{{\left[ {23} \right]}} }} }}{{\sigma_{{BV_{mat} }} }}\) are the direct and maternal standardized breeding values of queens born in year 23, respectively; \(V\left( {P_{{\left[ {24} \right]}} } \right)\) 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; \(r_{{BV_{dir} , BV_{{mat_{{\left[ {23} \right]}} }} }}\) is the genetic correlation between direct and maternal effects from queens born in year 23.
