Table 5.

Formulae for the expected numbers of triplets after three events

Model $M\in ℳ$
Triplet $\Delta \in T$	(2,2,2)	(3,2,2)	(2,3,2)
{t1,t1,t1}	-	u′(1+v)3(1+w)3	-
{t1,t1,t2}	2uv(1+v)(1+w)3	2(3u′+u)v(1+v)(1+w)3	2u(3v′+v)
			×(1+2v′+v)(1+w)3
{t1,t2,t2}	-	-	-
{t2,t2,t2}	-	-	(1+u)v′(1+w)3
{t2;t2;t3}	2(1+u)vw(1+w)	2(1+2u′+u)vw(1+w)	2(1+u)(3v′+v)w(1+w)
{t2,t3,t3}	-	-	-
{t3,t3,t3}	-	-	-
{t1,t1,t3}	2u(1+v)2w(1+w)	2(3u′+u)(1+v)2w(1+w)	2u(1+2v′+v)2w(1+w)
{t1,t3,t3}	-	-	-
{t1,t2,t3}	-	-	-
model $M\in ℳ$
triplet $\Delta \in T$	(2,2,3)	(2,3,3)	(3,2,3)
{t1,t1,t1}	-	-	u′(1+v)3
			×(1+2w′+w)3
{t1,t1,t2}	2uv(1+v)	2u(3v′+v)(1+2v′+v)	2(3u′+u)v(1+v)
	×(1+2w′+w)3	×(1+2w′+w)3	×(1+2w′+w)3
{t1,t2,t2}	-	-	-
{t2,t2,t2}	-	(1+u)v′	-
		×(1+2w′+w)3
{t2;t2;t3}	2(1+u)v	2(1+u)(3v′+v)	2(1+2u′+u)v
	×(3w′+w)(1+2w′+w)	×(3w′+w)(1+2w′+w)	×(3w′+w)(1+2w′+w)
{t2,t3,t3}	-	-	-
{t3,t3,t3}	(1+u)(1+v)w′	(1+u)(1+2v′+v)w′	(1+2u′+u)(1+v)w′
{t1,t1,t3}	2u(1+v)2	2u(1+2v′+v)2	2(3u′+u)(1+v)2
	×(3w′+w)(1+2w′+w)	×(3w′+w)(1+2w′+w)	×(3w′+w)(1+2w′+w)
{t1,t3,t3}	-	-	-
{t1,t2,t3}	-	-	-
model $M\in ℳ$
triplet $\Delta \in T$	(3,3,2)	(3,3,3)
{t1,t1,t1}	u′(1+2v′+v)3(1+w)3	u′(1+2v′+v)3(1+2w′+w)3
{t1,t1,t2}	2(3u′+u)(3v′+v)(1+2v′+v)(1+w)3	2(3u′+u)(3v′+v)(1+2v′+v)(1+2w′+w)3
{t1,t2,t2}	-	-
{t2,t2,t2}	(1+2u′+u)v′(1+w)3	(1+2u′+u)v′(1+2w′+w)3
{t2;t2;t3}	2(1+2u′+u)(3v′+v)w(1+w)	2(1+2u′+u)(3v′+v)(3w′+w)(1+2w′+w)
{t2,t3,t3}	-	-
{t3,t3,t3}	-	(1+2u′+u)(1+2v′+v)w′
{t1,t1,t3}	2(3u′+u)(1+2v′+v)2w(1+w)	2(3u′+u)(1+2v′+v)2(3w′+w)(1+2w′+w)
{t1,t3,t3}	-	-
{t1,t2,t3}	-	-

u= probability that two progeny survive after the first polyploidization event. u^′= probability that three survive. Similarly v and v^′ are the probabilities that two or three progeny survive, respectively, after the second event. w and w^′ are the probabilities that two or three progeny survive after the third event