the correct permutation to recover P $^{ma}$. Otherwise, restart this iteration with a different a . If a is the root, choose two other terminal nodes b and c such that the most recent common ancestor of b and c is m . Again by assumptions A, B, and D, we can apply Lemma 3.1 to b and c to obtain a stochastic matrix V and a diagonal matrix U such that P mb = RV and diag π m = RUR ⊺ for some permutation matrix R . Then P ma = RU − $^{1}$( V − $^{1}$) $^{⊺}$J $^{ba}$. Once more if P ma ∈ M , we infer the correct matrix R and we know P $^{ma}$. Otherwise, restart this iteration with a different a . So we are able to determine P ma for a terminal node a and its neighbour m . The induction step is then to remove the edge { m,a } from the tree, and make m a terminal node in two subtrees, or one subtree if m happens to be the root. For any subtree, J im = J $^{ia}$( P $^{ma}$) − 1 for any terminal node of the subtree i . This step can be repeated until all subtrees have two taxa and the full model is recovered on all edges. We will now show that Theorem 3.1 is still applicable in almost all cases if we further restrict the model to be continuous-time. We state this explicitly as some care is required because the matrix logarithm can have multiple roots. Continuous- time models provide more information than discrete-time models, for instance for questions concerning genetic distance and relative rates of evolution. Theorem 3.2. Make the assumptions of Theorem 3.1. Additionally assume that for every { u,v } ∈ E , where v is further from the root than u , there exists a unique mapping Q uv = log P uv where every off-diagonal element of Q uv is non-negative. Also replace assumption D with the assumption that Q uv is strand-symmetric. Then the full model is identifiable from the joint distribution of states at the terminal nodes of the tree. 18 3.4 Continuous-Time Models