Correction to: The performance of coalescent-based species tree estimation methods under models of missing data

Abstract

The question of interest in [1] is whether several species tree estimation methods that operate by combining gene trees (e.g., ASTRAL [5], ASTRID [3], and NJst [2]) remain statistically consistent when data are missing due to random taxon deletion, under the assumption that the gene trees are generated by the multi-species coalescent (MSC) model [6] and so can differ from the true species tree due to incomplete lineage sorting (ILS). Furthermore, they prove that as the number of gene trees increases, NJst and ASTRID will converge to a tree other than the true species tree. [...]neither NJst nor ASTRID are statistically consistent under the combination of MSC and Miid taxon deletion, and in fact are positively misleading. [4] showed that when L = ∞, E = 0, and p ∈ (0, 1) (where p gives the probability of taxon presence under Miid), the expected internode distance matrix under the combined MSC + Miid model is additive for a tree with a topology different from σ; in particular, it will display quartet tree (ac, bd) (which is the tree with the leaves for a, c separated from the leaves for b, d by one or more edges) whereas σ displays (ab, cd). [...]by continuity of the expected distances, when E > 0 is sufficiently small and L is finite but sufficiently large, the expected distance matrix will be sufficiently close to the additive matrix inducing quartet tree (ac, bd) that both neighbor joining and BME within FastME will return a tree that displays (ac, bd).