given in [@adr2011], so we omit repeating that here. Because we focus in this paper on the probabilities of observing gene trees or clades on gene trees under that model, we fix the following notation.

Under the multispecies coalescent model on a fixed species tree $\sigma$ on taxa $\mathcal X$, the probabilities of a gene tree $T$, and a clade $\mathcal C_g$ on gene trees are denoted ${\mathbb P}_\sigma(T)$ and ${\mathbb P}_\sigma(\mathcal C_g)$, respectively.

If more than one lineage is sampled per species, a generalization of our results on species tree identifiability still holds. For this extension, we require the following definitions. (See Fig. \[F:intra\] for an example.)

\[def:extended\] Let $\mathcal X = \{x_{1}, \dots, x_{n}\}$ be a taxon set, with $|\mathcal X| = n$. Let $\delta = (\delta_1, \dots, \delta_n)$ be the number of individuals sampled from species $x_i$, $i = 1, \dots,
  n$. With $x_{ij}$, $1\le j\le\delta_i$, denoting the individuals in taxon $x_i$, $\mathcal X^*=\{x_{ij}\}$ is the set of all sampled individuals, so $|\mathcal X^*|=\sum_{i=1}^n \delta_i$.

An *extended species tree* $\sigma^* = (
  \psi^*,\lambda,\delta)$ on $\mathcal X$ is a species tree $(\psi^*,\lambda)$ on $\mathcal X^*$ such that for each $1\le i\le
  n$ all the leaves $x_{ij}$, $1\le j\le 