AbstractMotivationAdmixture, the interbreeding between previously distinct populations, is a pervasive force in evolution. The evolutionary history of populations in the presence of admixture can be modeled by augmenting phylogenetic trees with additional nodes that represent admixture events. While enabling a more faithful representation of evolutionary history, admixture graphs present formidable inferential challenges. A key challenge is the need for admixture graph inference algorithms that are accurate while being completely automated and computationally efficient. Given the challenge of exhaustively evaluating all topologies, search heuristics have been developed to enable efficient inference. One heuristic, implemented in the popular method TreeMix, consists of adding admixture edges to an initial tree while optimizing a suitable objective function.ResultsHere, we present a demographic model (with one admixed population incident to a leaf) where TreeMix and any other starting-tree-based maximum likelihood heuristic using its likelihood function is guaranteed to get stuck in a local optimum and return the incorrect network topology. To address this issue, we propose a new search strategy based on reorientating the admixture graph that we term the maximum likelihood network orientation (MLNO) problem. We augment TreeMix with an exhaustive search for MLNO, referred to as OrientAGraph. In evaluations using previously published admixture graphs, OrientAGraph outperforms TreeMix on 4/8 models (there are no differences in the other cases). Overall, OrientAGraph finds graphs with higher likelihood scores and topological accuracy while remaining computationally efficient. Lastly, our study reveals important directions for improving maximum likelihood admixture graph estimation.AvailabilityOrientAGraph is available on Github (https://github.coin/ekinolloy/OrientAGraph) under the GNU General Public License v3.0.