Table 2.

Production of queens.

mating	frequency	viability of ab offspring	proportion of MM offspring	proportion of MP offspring	proportion of PP offspring
MM × M	$R_{MM\times M}$	$V_{ab|MM\times M}^{\mathrm{female}}$	1	0	0
MM × P	$R_{MM\times P}$	$V_{ab|MM\times P}^{\mathrm{female}}$	0	1	0
MP × M	$R_{MP\times M}$	$V_{ab|MP\times M}^{\mathrm{female}}$	1/2	1/2	0
MP × P	$R_{MP\times P}$	$V_{ab|MP\times P}^{\mathrm{female}}$	0	1/2	1/2
PP × M	$R_{PP\times M}$	$V_{ab|PP\times M}^{\mathrm{female}}$	0	1	0
PP × P	$R_{PP\times P}$	$V_{ab|PP\times P}^{\mathrm{female}}$	0	0	1