In 2019 we published several results on ancestral reconstruction, notably in Molecular Biology and Evolution, Systematic Biology and Bioinformatics. The reconstruction of ancestral scenarios is widely used to study the evolution of characters along a phylogenetic tree, for example to infer ancestral molecular characters and their changes in time, or in phylogeography to trace back the geographical locations and moves of species. Standard methods are based on parsimony and likelihood. In the likelihood framework one assumes a probabilistic evolutionary model and commonly uses the marginal posterior probabilities of the character states, and the joint reconstruction of the most likely scenario. Both approaches are somewhat unsatisfactory. Marginal reconstructions provide users with state probabilities, but these are difficult to interpret and use, while joint reconstructions select a unique state for every tree node and thus do not reflect the uncertainty of inferences.
We propose a fast and simple approach, which is in between these two extremes. We use decision-theory concepts and the Brier criterion to associate each node in the tree to a set of likely states. In the tree regions where the uncertainty is low, a unique state is predicted for the nodes. In the uncertain parts, typically around the tree root, several states are predicted. The algorithm has linear time complexity and applies to very large trees. To visualize the results, we cluster the neighboring nodes associated to the same states and use graph visualization tools.
This project was performed in collaboration with the University of Tokyo (Wataru Iwasaki).