Table 3.

Phenotypic and genetic evolution of the population over 20 years for the parameter setups with an initial negative direct-maternal correlation

Selection strategy	Setup	$n_D$	F (%)	$\frac{P_{[24]}}{{\sigma }_P}$	$\frac{B{V}_{\mathit{dir}}^{Q_{[23]}}}{{\sigma }_{B{V}_{\mathit{dir}}}}$	$\frac{B{V}_{\mathit{mat}}^{Q_{[23]}}}{{\sigma }_{B{V}_{\mathit{mat}}}}$	$V\left(P_{[24]}\right)$	$V\left(B{V}_{\mathit{dir}}^{Q_{[23]}}\right)$	$V\left(B{V}_{\mathit{mat}}^{Q_{[23]}}\right)$	$r_{B{V}_{\mathit{dir}},B{V}_{ma{t}_{[23]}}}$
L	3	1	26.11 (3.18)	2.42 (0.39)	4.41 (0.79)	0.75 (0.74)	37.35 (6.15)	5.67 (3.06)	6.16 (3.20)	− 0.491 (0.240)
		8	18.83 (2.38)	2.69 (0.35)	2.11 (0.66)	3.26 (0.64)	37.01 (5.64)	6.99 (2.43)	6.97 (2.51)	− 0.525 (0.148)
	4	1	26.47 (2.89)	3.79 (0.44)	6.31 (0.81)	− 0.35 (0.79)	40.93 (6.09)	11.11 (4.63)	5.57 (2.44)	− 0.461 (0.219)
		8	20.45 (2.56)	3.85 (0.42)	3.92 (0.68)	2.18 (0.68)	38.69 (5.22)	13.38 (3.93)	6.87 (2.11)	− 0.526 (0.155)
M	3	1	35.42 (4.93)	3.07 (0.41)	4.02 (0.98)	2.43 (0.98)	36.08 (5.00)	5.03 (2.59)	5.15 (2.67)	− 0.528 (0.217)
		8	24.41 (3.63)	3.29 (0.37)	2.02 (0.75)	4.51 (0.75)	35.89 (4.68)	6.10 (1.99)	6.37 (1.86)	− 0.518 (0.131)
	4	1	36.90 (4.17)	4.44 (0.48)	6.45 (0.83)	0.95 (0.88)	39.43 (5.90)	9.22 (4.10)	4.88 (2.37)	− 0.503 (0.232)
		8	25.41 (3.47)	4.44 (0.46)	4.05 (0.71)	3.14 (0.70)	37.68 (5.15)	12.52 (4.04)	6.13 (2.05)	− 0.522 (0.141)

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 ($\mathit{dir}$) and maternal ($\mathit{mat}$) genetic variances in the base population are equal, while in parameter setup 4, ${\sigma }_{B{V}_{\mathit{dir}}}^2=2·{\sigma }_{B{V}_{\mathit{mat}}}^2$. 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; $\frac{B{V}_{\mathit{dir}}^{Q_{\left[23\right]}}}{{\sigma }_{B{V}_{\mathit{dir}}}}$ and $\frac{B{V}_{\mathit{mat}}^{Q_{\left[23\right]}}}{{\sigma }_{B{V}_{\mathit{mat}}}}$ 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; $V\left(B{V}_{\mathit{dir}}^{Q_{23}}\right)$ and $V\left(B{V}_{\mathit{mat}}^{Q_{23}}\right)$ are the direct and maternal genetic variances of queens born in year 23; $r_{B{V}_{\mathit{dir}},B{V}_{ma{t}_{\left[23\right]}}}$ is the genetic correlation between direct and maternal effects from queens born in year 23.