species tree (with some pendant edge lengths) obtained by pruning. Indeed, this is why we have introduced such trees. We will use them to easily extend results where one individual is sampled per species to the multiple sampling situation, in Proposition 13 and Corollary 14.

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(-1200,0)[ ![(a) A gene tree with multiple lineages sampled from several species within a species tree. The taxa are $\mathcal X =
  \{x_1, x_2, x_3, x_4, x_5\}$ with $\delta = (3,1,1,2,1)$ lineages sampled from them. (b) The extended version of the species tree with taxa $\mathcal X^* = \{x_{11}, x_{12}, \dots,
  x_{51}\}$ and one lineage sampled per taxon. Under the multispecies coalescent, the probability of any clade $\mathcal A_g \subset \mathcal X^*_g$ is the same for both the species trees in (a) and in (b).[]{data-label="F:intra"}](intraA.eps "fig:"){width=".48\textwidth"}]{} (-950,290)

(2436.0, 0.0)\[l\]

$x_1$ $x_2$ $x_3$ $x_4$ $x_5$

(100,1204)(0,0) (0,0)[ ![(a) A gene tree with multiple lineages sampled from several species within a species tree. The taxa are $\mathcal X =
  \{x_1, x_2, x_3, x_4, x_5\}$ with $\delta = (3,1,1,2,1)$ lineages sampled from them. (b) The extended version of the species tree with taxa $\mathcal X^* = \{x_{11}, x_{12}, \dots,
  x_{51}\}$ and one lineage sampled per taxon. Under 