Table 2.

Split probabilities for gene trees arising on the 5-taxon species trees under the multispecies coalescent model.

	σbal	σpc
sab	$1-\frac{2}{15}X{Y}^{3}Z-\frac{2}{3}X$	$1-\frac{1}{45}{\mathit{XYZ}}^6-\frac{1}{9}XY-\frac{2}{3}X$
sac, sbc	$-\frac{2}{15}X{Y}^{3}Z+\frac{1}{3}X$	$\frac{1}{30}{\mathit{XYZ}}^6-\frac{1}{6}XY+\frac{1}{3}X$
sad, sae, sbd, sbe	$\frac{1}{30}X{Y}^{3}Z+\frac{1}{6}\mathit{XYZ}$	$-\frac{1}{45}{\mathit{XYZ}}^6+\frac{2}{9}XY$
scd, sce	$\frac{1}{30}X{Y}^{3}Z-\frac{1}{6}\mathit{XYZ}+\frac{1}{3}YZ$	$\frac{1}{30}{\mathit{XYZ}}^6-\frac{1}{6}XY+\frac{1}{3}Y$
sde	$1+\frac{1}{5}X{Y}^{3}Z-\frac{1}{3}\mathit{XYZ}-\frac{2}{3}YZ$	$1-\frac{1}{45}{\mathit{XYZ}}^6-\frac{1}{9}XY-\frac{2}{3}Y$

	σcat
sab	$1-\frac{1}{45}X{Y}^3{Z}^6-\frac{1}{9}X{Y}^3-\frac{2}{3}X$
sac, sbc	$-\frac{1}{45}X{Y}^3{Z}^6-\frac{1}{9}X{Y}^3+\frac{1}{3}X$
sad, sbd	$-\frac{1}{45}X{Y}^3{Z}^6+\frac{1}{18}X{Y}^3+\frac{1}{6}XY$
sae, sbe	$\frac{1}{30}X{Y}^3{Z}^6+\frac{1}{6}XY$
scd	$-\frac{1}{45}X{Y}^3{Z}^6+\frac{1}{18}X{Y}^3-\frac{1}{6}XY+\frac{1}{3}Y$
sce	$\frac{1}{30}X{Y}^3{Z}^6-\frac{1}{6}XY+\frac{1}{3}Y$
sde	$1+\frac{1}{30}X{Y}^3{Z}^6+\frac{1}{6}X{Y}^3-\frac{1}{3}XY-\frac{2}{3}Y$