Abstract
We consider the problem of inferring an ancestral state from observations at the leaves of a tree, assuming the state evolves along the tree according to a two-state symmetric Markov process. We establish a general branching rate condition under which maximum parsimony, a common reconstruction method requiring only the knowledge of the tree topology (but not of the substitution rates or other parameters), succeeds better than random guessing uniformly in the depth of the tree. We thereby generalize previous results of [13, 37]. Our results apply to both deterministic and i.i.d. edge weights.
Highlights
We consider the problem of inferring an ancestral state from observations at the leaves of a tree, assuming the state evolves along the tree according to a two-state symmetric Markov process
Ancestral reconstruction In biology, the inferred evolutionary history of organisms is depicted by a phylogenetic tree, that is, a rooted tree whose branchings indicate past speciation events with the leaves representing living species
On each edge, the state of the feature changes according to a Markov process; at bifurcations, two independent copies of the feature evolve along the outgoing edges starting from the state at the branching point
Summary
Ancestral reconstruction In biology, the inferred evolutionary history of organisms is depicted by a phylogenetic tree, that is, a rooted tree whose branchings indicate past speciation events with the leaves representing living species. The parsimony principle dictates that one assigns to each vertex x (ancestor to the observed cutset π) a state σx such that the overall number of changes along the edges of T π, namely, (x,y)∈Eπ 1{σx = σy}, is minimized, where we let by default σz = σz for all z ∈ π. In case both 0 and 1 can be obtained in this way as root state, a uniformly random value in {0, 1} is returned. Λ > 6, which is consistent with the results of [13, Theorem 2.3]
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