Table 2.

Mating table for two preference/two trait model

		Males
Females		x1	x2	x3	x4	x5	x6	x7	x8	x9	x10	x11	x12	x13	x14	x15	x16
	x1	$\frac{\alpha p\left(x_1{x}_1\right)}{Z_1}$	$\frac{\alpha \left(x_1{x}_2\right)}{Z_1}$	$\frac{\alpha \left(x_1{x}_3\right)}{Z_1}$	$\frac{\left(x_1{x}_4\right)}{Z_1}$	$\frac{\alpha p\left(x_1{x}_5\right)}{Z_1}$	$\frac{\alpha \left(x_1{x}_6\right)}{Z_1}$	$\frac{\alpha \left(x_1{x}_7\right)}{Z_1}$	$\frac{\left(x_1{x}_8\right)}{Z_1}$	$\frac{\alpha p\left(x_1{x}_9\right)}{Z_1}$	$\frac{\alpha \left(x_1{x}_{10}\right)}{Z_1}$	$\frac{\alpha \left(x_1{x}_{11}\right)}{Z_1}$	$\frac{\left(x_1{x}_{12}\right)}{Z_1}$	$\frac{\alpha p\left(x_1{x}_{13}\right)}{Z_1}$	$\frac{\alpha \left(x_1{x}_{14}\right)}{Z_1}$	$\frac{\alpha \left(x_1{x}_{15}\right)}{Z_1}$	$\frac{\left(x_1{x}_{16}\right)}{Z_1}$
	X2	$\frac{\alpha p\left(x_2{x}_1\right)}{Z_1}$	$\frac{\alpha \left(x_2{x}_2\right)}{Z_1}$	$\frac{\alpha \left(x_2{x}_3\right)}{Z_1}$	$\frac{\left(x_2{x}_4\right)}{Z_1}$	$\frac{\alpha p\left(x_2{x}_5\right)}{Z_1}$	$\frac{\alpha \left(x_2{x}_6\right)}{Z_1}$	$\frac{\alpha \left(x_2{x}_7\right)}{Z_1}$	$\frac{\left(x_2{x}_8\right)}{Z_1}$	$\frac{\alpha p\left(x_2{x}_9\right)}{Z_1}$	$\frac{\alpha \left(x_2{x}_{10}\right)}{Z_1}$	$\frac{\alpha \left(x_2{x}_{11}\right)}{Z_1}$	$\frac{\left(x_2{x}_{12}\right)}{Z_1}$	$\frac{\alpha p\left(x_2{x}_{13}\right)}{Z_1}$	$\frac{\alpha \left(x_2{x}_{14}\right)}{Z_1}$	$\frac{\alpha \left(x_2{x}_{15}\right)}{Z_1}$	$\frac{\left(x_2{x}_{16}\right)}{Z_1}$
	X3	$\frac{\alpha p\left(x_3{x}_1\right)}{Z_1}$	$\frac{\alpha \left(x_3{x}_2\right)}{Z_1}$	$\frac{\alpha \left(x_3{x}_3\right)}{Z_1}$	$\frac{\left(x_3{x}_4\right)}{Z_1}$	$\frac{\alpha p\left(x_3{x}_5\right)}{Z_1}$	$\frac{\alpha \left(x_3{x}_6\right)}{Z_1}$	$\frac{\alpha \left(x_3{x}_7\right)}{Z_1}$	$\frac{\left(x_3{x}_8\right)}{Z_1}$	$\frac{\alpha p\left(x_3{x}_9\right)}{Z_1}$	$\frac{\alpha \left(x_3{x}_{10}\right)}{Z_1}$	$\frac{\alpha \left(x_3{x}_{11}\right)}{Z_1}$	$\frac{\left(x_3{x}_{12}\right)}{Z_1}$	$\frac{\alpha p\left(x_3{x}_{13}\right)}{Z_1}$	$\frac{\alpha \left(x_3{x}_{14}\right)}{Z_1}$	$\frac{\alpha \left(x_3{x}_{15}\right)}{Z_1}$	$\frac{\left(x_3{x}_{16}\right)}{Z_1}$
	X4	$\frac{\alpha p\left(x_4{x}_1\right)}{Z_4}$	$\frac{\alpha \left(x_4{x}_2\right)}{Z_1}$	$\frac{\alpha \left(x_4{x}_3\right)}{Z_1}$	$\frac{\left(x_4{x}_4\right)}{Z_1}$	$\frac{\alpha p\left(x_4{x}_5\right)}{Z_1}$	$\frac{\alpha \left(x_4{x}_6\right)}{Z_1}$	$\frac{\alpha \left(x_4{x}_7\right)}{Z_1}$	$\frac{\left(x_4{x}_8\right)}{Z_1}$	$\frac{\alpha p\left(x_4{x}_9\right)}{Z_1}$	$\frac{\alpha \left(x_4{x}_{10}\right)}{Z_1}$	$\frac{\alpha \left(x_4{x}_{11}\right)}{Z_1}$	$\frac{\left(x_4{x}_{12}\right)}{Z_1}$	$\frac{\alpha p\left(x_4{x}_{13}\right)}{Z_1}$	$\frac{\alpha \left(x_4{x}_{14}\right)}{Z_1}$	$\frac{\alpha \left(x_4{x}_{15}\right)}{Z_1}$	$\frac{\left(x_1{x}_{16}\right)}{Z_1}$
	x5	$\frac{\alpha \left(x_5{x}_2\right)}{Z_2}$	$\frac{\alpha \left(x_5{x}_2\right)}{Z_2}$	$\frac{\left(x_5{x}_3\right)}{Z_2}$	$\frac{\left(x_5{x}_4\right)}{Z_2}$	$\frac{\alpha \left(x_5{x}_5\right)}{Z_2}$	$\frac{\alpha \left(x_5{x}_6\right)}{Z_2}$	$\frac{\left(x_5{x}_7\right)}{Z_2}$	$\frac{\left(x_5{x}_8\right)}{Z_2}$	$\frac{\alpha \left(x_5{x}_9\right)}{Z_2}$	$\frac{\alpha \left(x_5{x}_{10}\right)}{Z_2}$	$\frac{\left(x_5{x}_{11}\right)}{Z_2}$	$\frac{\left(x_5{x}_{12}\right)}{Z_2}$	$\frac{\alpha \left(x_5{x}_{13}\right)}{Z_2}$	$\frac{\alpha \left(x_5{x}_{14}\right)}{Z_2}$	$\frac{\left(x_5{x}_{15}\right)}{Z_2}$	$\frac{\left(x_5{x}_{16}\right)}{Z_2}$
	x6	$\frac{\alpha \left(x_6{x}_2\right)}{Z_2}$	$\frac{\alpha \left(x_6{x}_2\right)}{Z_2}$	$\frac{\left(x_6{x}_3\right)}{Z_2}$	$\frac{\left(x_6{x}_4\right)}{Z_2}$	$\frac{\alpha \left(x_6{x}_5\right)}{Z_2}$	$\frac{\alpha \left(x_6{x}_6\right)}{Z_2}$	$\frac{\left(x_6{x}_7\right)}{Z_2}$	$\frac{\left(x_6{x}_8\right)}{Z_2}$	$\frac{\alpha \left(x_6{x}_9\right)}{Z_2}$	$\frac{\alpha \left(x_6{x}_{10}\right)}{Z_2}$	$\frac{\left(x_6{x}_{11}\right)}{Z_2}$	$\frac{\left(x_6{x}_{12}\right)}{Z_2}$	$\frac{\alpha \left(x_6{x}_{13}\right)}{Z_2}$	$\frac{\alpha \left(x_6{x}_{14}\right)}{Z_2}$	$\frac{\left(x_6{x}_{15}\right)}{Z_2}$	$\frac{\left(x_6{x}_{16}\right)}{Z_2}$
	x7	$\frac{\alpha \left(x_7{x}_2\right)}{Z_2}$	$\frac{\alpha \left(x_7{x}_2\right)}{Z_2}$	$\frac{\left(x_7{x}_3\right)}{Z_2}$	$\frac{\left(x_7{x}_4\right)}{Z_2}$	$\frac{\alpha \left(x_7{x}_5\right)}{Z_2}$	$\frac{\alpha \left(x_7{x}_6\right)}{Z_2}$	$\frac{\left(x_7{x}_7\right)}{Z_2}$	$\frac{\left(x_7{x}_8\right)}{Z_2}$	$\frac{\alpha \left(x_7{x}_9\right)}{Z_2}$	$\frac{\alpha \left(x_7{x}_{10}\right)}{Z_2}$	$\frac{\left(x_7{x}_{11}\right)}{Z_2}$	$\frac{\left(x_7{x}_{12}\right)}{Z_2}$	$\frac{\alpha \left(x_7{x}_{13}\right)}{Z_2}$	$\frac{\alpha \left(x_7{x}_{14}\right)}{Z_2}$	$\frac{\left(x_7{x}_{15}\right)}{Z_2}$	$\frac{\left(x_7{x}_{16}\right)}{Z_2}$
	x8	$\frac{\alpha \left(x_8{x}_2\right)}{Z_2}$	$\frac{\alpha \left(x_8{x}_2\right)}{Z_2}$	$\frac{\left(x_8{x}_3\right)}{Z_2}$	$\frac{\left(x_8{x}_4\right)}{Z_2}$	$\frac{\alpha \left(x_8{x}_5\right)}{Z_2}$	$\frac{\alpha \left(x_8{x}_6\right)}{Z_2}$	$\frac{\left(x_8{x}_7\right)}{Z_2}$	$\frac{\left(x_8{x}_8\right)}{Z_2}$	$\frac{\alpha \left(x_8{x}_9\right)}{Z_2}$	$\frac{\alpha \left(x_8{x}_{10}\right)}{Z_2}$	$\frac{\left(x_8{x}_{11}\right)}{Z_2}$	$\frac{\left(x_8{x}_{12}\right)}{Z_2}$	$\frac{\alpha \left(x_8{x}_{13}\right)}{Z_2}$	$\frac{\alpha \left(x_8{x}_{14}\right)}{Z_2}$	$\frac{\left(x_8{x}_{15}\right)}{Z_2}$	$\frac{\left(x_8{x}_{16}\right)}{Z_2}$
	x9	$\frac{\alpha \left(x_9{x}_2\right)}{Z_3}$	$\frac{\left(x_9{x}_2\right)}{Z_3}$	$\frac{\alpha \left(x_9{x}_3\right)}{Z_3}$	$\frac{\left(x_9{x}_4\right)}{Z_3}$	$\frac{\alpha \left(x_9{x}_5\right)}{Z_3}$	$\frac{\left(x_9{x}_6\right)}{Z_3}$	$\frac{\alpha \left(x_9{x}_7\right)}{Z_3}$	$\frac{\left(x_9{x}_8\right)}{Z_3}$	$\frac{\alpha \left(x_9{x}_9\right)}{Z_3}$	$\frac{\left(x_9{x}_{10}\right)}{Z_3}$	$\frac{\alpha \left(x_9{x}_{11}\right)}{Z_3}$	$\frac{\left(x_9{x}_{12}\right)}{Z_3}$	$\frac{\alpha \left(x_9{x}_{13}\right)}{Z_3}$	$\frac{\left(x_9{x}_{14}\right)}{Z_3}$	$\frac{\alpha \left(x_9{x}_{15}\right)}{Z_3}$	$\frac{\left(x_9{x}_{16}\right)}{Z_3}$
	x10	$\frac{\alpha \left(x_{10}{x}_2\right)}{Z_3}$	$\frac{\left(x_{10}{x}_2\right)}{Z_3}$	$\frac{\alpha \left(x_{10}{x}_3\right)}{Z_3}$	$\frac{\left(x_{10}{x}_4\right)}{Z_3}$	$\frac{\alpha \left(x_{10}{x}_5\right)}{Z_3}$	$\frac{\left(x_{10}{x}_6\right)}{Z_3}$	$\frac{\alpha \left(x_{10}{x}_7\right)}{Z_3}$	$\frac{\left(x_{10}{x}_8\right)}{Z_3}$	$\frac{\alpha \left(x_{10}{x}_9\right)}{Z_3}$	$\frac{\left(x_{10}{x}_{10}\right)}{Z_3}$	$\frac{\alpha \left(x_{10}{x}_{11}\right)}{Z_3}$	$\frac{\left(x_{10}{x}_{12}\right)}{Z_3}$	$\frac{\alpha \left(x_{10}{x}_{13}\right)}{Z_3}$	$\frac{\left(x_{10}{x}_{14}\right)}{Z_3}$	$\frac{\alpha \left(x_{10}{x}_{15}\right)}{Z_3}$	$\frac{\left(x_{10}{x}_{16}\right)}{Z_3}$
	x11	$\frac{\alpha \left(x_{11}{x}_2\right)}{Z_3}$	$\frac{\left(x_{11}{x}_2\right)}{Z_3}$	$\frac{\alpha \left(x_{11}{x}_3\right)}{Z_3}$	$\frac{\left(x_{11}{x}_4\right)}{Z_3}$	$\frac{\alpha \left(x_{11}{x}_5\right)}{Z_3}$	$\frac{\left(x_{11}{x}_6\right)}{Z_3}$	$\frac{\alpha \left(x_{11}{x}_7\right)}{Z_3}$	$\frac{\left(x_{11}{x}_8\right)}{Z_3}$	$\frac{\alpha \left(x_{11}{x}_9\right)}{Z_3}$	$\frac{\left(x_{11}{x}_{10}\right)}{Z_3}$	$\frac{\alpha \left(x_{11}{x}_{11}\right)}{Z_3}$	$\frac{\left(x_{11}{x}_{12}\right)}{Z_3}$	$\frac{\alpha \left(x_{11}{x}_{13}\right)}{Z_3}$	$\frac{\left(x_{11}{x}_{14}\right)}{Z_3}$	$\frac{\alpha \left(x_{11}{x}_{15}\right)}{Z_3}$	$\frac{\left(x_{11}{x}_{16}\right)}{Z_3}$
	x12	$\frac{\alpha \left(x_{12}{x}_2\right)}{Z_3}$	$\frac{\left(x_{12}{x}_2\right)}{Z_3}$	$\frac{\alpha \left(x_{12}{x}_3\right)}{Z_3}$	$\frac{\left(x_{12}{x}_4\right)}{Z_3}$	$\frac{\alpha \left(x_{12}{x}_5\right)}{Z_3}$	$\frac{\left(x_{12}{x}_6\right)}{Z_3}$	$\frac{\alpha \left(x_{12}{x}_7\right)}{Z_3}$	$\frac{\left(x_{12}{x}_8\right)}{Z_3}$	$\frac{\alpha \left(x_{12}{x}_9\right)}{Z_3}$	$\frac{\left(x_{12}{x}_{10}\right)}{Z_3}$	$\frac{\alpha \left(x_{12}{x}_{11}\right)}{Z_3}$	$\frac{\left(x_{12}{x}_{12}\right)}{Z_3}$	$\frac{\alpha \left(x_{12}{x}_{13}\right)}{Z_3}$	$\frac{\left(x_{12}{x}_{14}\right)}{Z_3}$	$\frac{\alpha \left(x_{12}{x}_{15}\right)}{Z_3}$	$\frac{\left(x_{12}{x}_{16}\right)}{Z_3}$
	x13	(x13x1)	(x13x2	(x13x3)	(x13x4)	(x13x5)	(x13x6)	(x13x7)	(x13x8)	(x13x9)	(x13x10)	(x13x11)	(x13x12)	(x13x13)	(x13x14)	(x13x15)	(x13x16)
	x14	(x14x1)	(x14x2)	(x14x3)	(x14x4)	(x14x5)	(x14x6)	(x14x7)	(x14x8)	(x14x9)	(x14x10)	(x14x11)	(x14x12)	(x14x13)	(x14x14)	(x14x15)	(x14x16)
	x15	(x15x1)	(x15x2)	(x15x3)	(x15x4)	(x15x5)	(x15x6)	(x15x7)	(x15x8)	(x15x9)	(x15x10)	(x15x11)	(x15x12)	(x15x13)	(x15x14)	(x15x15)	(x15x16)
	x16	(x16x1)	(x16x2)	(x16x3)	(x16x4)	(x16x5)	(x16x6)	(x16x7)	(x16x8)	(x16x9)	(x16x10)	(x16x11)	(x16x12)	(x16x13)	(x16x14)	(x16x15)	(x16x16)
	Z1 = αp(x1 + x5 + x9 + x13) + α(x2 + x3 + x6 + x7 + x10 + x11 + x14 + x15) + x4 + x8 + x12 + x16
	Z2 = α(x1 + x2 + x5 + x6 + x9 + x10 + x13 + x14) + x3 + x4 + x7 + x8 + x11 + x12 + x15 + x16
	Z3 = α(x1 + x3 + x5 + x7 + x9 + x11 + x13 + x15) + x2 + x4 + x6 + x8 + x10 + x12 + x14 + x16