Fast coalescent-based computation of local branch support from quartet frequencies

Species tree reconstruction is complicated by effects of incomplete lineage sorting, commonly modeled by the multi-species coalescent model (MSC). While there has been substantial progress in developing methods that estimate a species tree given a collection of gene trees, less attention has been paid to fast and accurate methods of quantifying support. In this article, we propose a fast algorithm to compute quartet-based support for each branch of a given species tree with regard to a given set of gene trees. We then show how the quartet support can be used in the context of the MSC to compute (1) the local posterior probability (PP) that the branch is in the species tree and (2) the length of the branch in coalescent units. We evaluate the precision and recall of the local PP on a wide set of simulated and biological datasets, and show that it has very high precision and improved recall compared with multi-locus bootstrapping. The estimated branch lengths are highly accurate when gene..., , , ## Simulations

There are two simulated datasets that we used in this paper.

### ASTRALII dataset.

This dataset contains estimated gene trees, true gene trees, true species trees, and inferred species trees with ASTRAL, RAxML, and NJST. Each archive contains a directory structure corresponding to:

* model conditions (e.g., `model.200.10000000.0.0000001`), and under each of them, it includes one folder per replicate `[rep]`.
* `k` is either 1000, 200, or 50, and is the number of genes.
* `method` is either `astral`, `njst`, `concat` and refers to the method used for inferring the species tree.
* Two types of gene trees `[gt]` are used: true gene trees `true` and estimated gene trees `half`. Note that `_[gt]` is not specified for `concat` method because it is irrelevant.

##### Files:

* `ASTRALII-BL.tar.gz`: The branch length estimations.
* `model.200.10000000.0.0000001/01/astral-bl-[k]-[gt].txt`: A file where each row is an internal branch and branch lengths are given...