Skip to main content

Table 2 Phenotypic and genetic evolution of the population over 20 years for the parameter setups without an initial direct–maternal correlation

From: A simulation study of a honeybee breeding scheme accounting for polyandry, direct and maternal effects on colony performance

Selection strategy

Setup

\(n_{D}\)

F (%)

\(\frac{{P_{{[{24}]}} }}{{\sigma_{P} }}\)

\(\frac{{BV_{dir}^{{Q_{{[ {23} ]}} }} }}{{\sigma_{{BV_{dir} }} }}\)

\(\frac{{BV_{mat}^{{Q_{{[ {23} ]}} }} }}{{\sigma_{{BV_{mat} }} }}\)

\(V\left( {P_{{[ {24} ]}} } \right)\)

\(V\left( {BV_{dir}^{{Q_{{[ {23} ]}} }} } \right)\)

\(V\left( {BV_{mat}^{{Q_{{[ {23} ]}} }} } \right)\)

\(r_{{BV_{dir} , BV_{{mat_{{[ {23} ]}} }} }}\)

L

1

1

25.68 (2.56)

4.24 (0.49)

5.92 (0.81)

3.45 (0.72)

40.09 (6.29)

5.47 (2.23)

5.88 (2.67)

− 0.089 (0.275)

8

19.49 (2.19)

4.63 (0.39)

4.62 (0.63)

5.10 (0.64)

40.88 (5.93)

6.68 (2.20)

6.66 (2.15)

− 0.030 (0.197)

16

18.57 (2.14)

4.82 (0.42)

4.60 (0.60)

5.43 (0.63)

39.31 (6.19)

6.89 (1.91)

6.38 (2.02)

− 0.074 (0.203)

2

1

27.15 (3.36)

5.81 (0.54)

7.74 (0.80)

3.11 (0.79)

43.72 (7.50)

10.04 (4.41)

5.73 (2.58)

− 0.022 (0.265)

8

20.23 (2.18)

6.11 (0.48)

6.07 (0.65)

4.79 (0.67)

42.64 (6.54)

12.50 (3.64)

6.48 (2.14)

− 0.036 (0.206)

M

1

1

38.72 (4.97)

5.27 (0.50)

6.20 (0.90)

5.27 (0.87)

38.00 (5.57)

4.40 (1.87)

4.55 (2.22)

− 0.062 (0.283)

8

26.58 (3.63)

5.53 (0.49)

5.11 (0.70)

6.47 (0.75)

37.72 (5.27)

5.92 (1.89)

5.76 (1.83)

− 0.060 (0.185)

16

25.51 (3.23)

5.56 (0.44)

4.93 (0.77)

6.61 (0.67)

38.51 (5.00)

5.95 (7.89)

5.98 (1.60)

− 0.054 (0.182)

2

1

38.94 (5.01)

6.76 (0.55)

7.96 (0.86)

4.88 (0.79)

40.82 (6.24)

7.98 (3.58)

4.47 (1.83)

− 0.085 (0.289)

8

27.30 (4.05)

7.11 (0.53)

6.68 (0.73)

6.12 (0.68)

41.08 (6.06)

11.01 (3.17)

5.84 (1.98)

− 0.064 (0.205)

  1. Values in brackets represent sampling standard deviations over 160 replicates
  2. 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.
  3. 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.