Table 1. Possible events in facultative sexual coalescent simulation.

kj samples split by sex in deme j: $p\left(k_{\text{j}}|x_{\text{j}},{\sigma }_{\text{j}}\right)=\left(\begin{array}{c}{x}_{\text{j}}\\ k_{\text{j}}\end{array}\right){\sigma }_{\text{j}}^{{\text{k}}_{\text{j}}}{\left(1-{\sigma }_{\text{j}}\right)}^{{\text{x}}_{\text{j}}-{\text{k}}_{\text{j}}}$
Event	Description	Configuration change in a deme	Probability
1	New single samples remain single	$\left(x_{\text{j}},y_{\text{j}}\right)\to \left(x_{\text{j}}-k_{\text{j}},y_{\text{j}}+2k_{\text{j}}\right)$	1–all other probabilities
2	One of the paired samples is re-created	$\left(x_{\text{j}},y_{\text{j}}\right)\to \left[x_{\text{j}}-k_{\text{j}}+1,y_{\text{j}}+2\left(k_{\text{j}}-1\right)\right]$	$\frac{k_{\text{j}}{y}_{\text{j}}}{N_{\text{d}}}+\left(\begin{array}{c}2k_{\text{j}}\\ 2\end{array}\right)\frac{1}{2N_{\text{d}}}$
3	A new single sample coalesces with an existing single sample	$\left(x_{\text{j}},y_{\text{j}}\right)\to \left(x_{\text{j}}-k_{\text{j}}+1,y_{\text{j}}+2k_{\text{j}}-1\right)$	$\frac{k_{\text{j}}{y}_{\text{j}}}{N_{\text{d}}}+\left(\begin{array}{c}2k_{\text{j}}\\ 2\end{array}\right)\frac{1}{2N_{\text{d}}}$
4	A new single sample coalesces with an existing paired sample	$\left(x_{\text{j}},y_{\text{j}}\right)\to \left(x_{\text{j}}-k_{\text{j}},y_{\text{j}}+2k_{\text{j}}-1\right)$	$\frac{2k_{\text{j}}\left(x_{\text{j}}-k_{\text{j}}\right)}{N_{\text{d}}}$
5	Two existing single samples form a new paired sample	$\left(x_{\text{j}},y_{\text{j}}\right)\to \left[x_{\text{j}}-k_{\text{j}}+1,y_{\text{j}}+2\left(k_{\text{j}}-1\right)\right]$	$\left(\begin{array}{c}{y}_{\text{j}}\\ 2\end{array}\right)\frac{1}{2N_{\text{d}}}$
6	Two existing single samples coalesce	$(x_{\text{j}},y_{\text{j}})\to \left[x_{\text{j}}-k_{\text{j}},y_{\text{j}}+2k_{\text{j}}-1\right]$	$\left(\begin{array}{c}{y}_{\text{j}}\\ 2\end{array}\right)\frac{1}{2N_{\text{d}}}$
7	Two remaining paired samples doubly coalesce asexually	$\left(x_{\text{j}},y_{\text{j}}\right)\to \left(x_{\text{j}}-k_{\text{j}}-1,y_{\text{j}}+2k_{\text{j}}\right)$	$\left(\begin{array}{c}{x}_{\text{j}}-k_{\text{j}}\\ 2\end{array}\right)\frac{1}{N_{\text{d}}}$
8	One remaining paired sample coalesces with a single sample	$\left(x_{\text{j}},y_{\text{j}}\right)\to \left(x_{\text{j}}-k_{\text{j}},y_{\text{j}}+2k_{\text{j}}-1\right)$	$\frac{\left(x_{\text{j}}-k_{\text{j}}\right)y_{\text{j}}}{N_{\text{d}}}$
9	Paired sample coalesces via gene conversion	$\left(x_{\text{j}},y_{\text{j}}\right)\to \left(x_{\text{j}}-k_{\text{j}}-1,y_{\text{j}}+2k_{\text{j}}+1\right)$	$\gamma \left(x_{\text{j}}-k_{\text{j}}\right)$
10	A sample migrates to another deme	$\left(x_{\text{j}},y_{\text{j}}\right)\to \left(x_{\text{j}}-k_{\text{j}},y_{\text{j}}+2k_{\text{j}}\right)$	$m\left(x_{\text{j}}+y_{\text{j}}+k_{\text{j}}\right)$
		(before migration)

The listed probabilities for events 1–4 are conditional on sex having occurred and are otherwise zero.