Table 1. Simulated variance and inbreeding effective sizes (N _e(V) and N _e(I)) and predicted (N _e(pre)) effective size of populations with various proportion (ϕ) of worker-produced males, when the progeny number in each gametic pathway follows a Poisson distribution.

Nf	Nm	μwm2	ϕ	Effective size
				Ne(V)	Ne(I)	Ne(pre)
100	100	2	0.2	140.5	142.1	139.0
			0.4	128.1	127.2	126.1
			0.8	101.3	98.6	96.0
		5	0.2	126.3	127.3	125.6
			0.4	105.5	104.3	103.0
			0.8	68.2	65.9	65.1
150	50	2	0.2	117.3	113.2	112.6
			0.4	95.7	92.6	92.5
			0.8	66.1	60.3	59.3
		5	0.2	103.2	99.3	96.1
			0.4	75.7	71.8	69.6
			0.8	41.9	38.4	37.3
50	150	2	0.2	100.1	97.7	97.0
			0.4	99.9	97.2	96.8
			0.8	94.8	92.4	91.7
		5	0.2	93.4	93.1	92.5
			0.4	91.3	87.5	86.8
			0.8	74.4	71.1	70.3

Abbreviations: N_f, number of queens; N_m, number of males; μ_wm2, average number of male progeny per laying worker.