Theoretical and Practical Considerations when using Retroelement Insertions to Estimate Species Trees in the Anomaly Zone
Authors: Molloy Erin K , Gatesy John , Springer Mark S 
Published: October 2021

Abstract
A potential shortcoming of concatenation methods for species tree estimation is their failure to account for incomplete lineage sorting. Coalescent methods address this problem but make various assumptions that, if violated, can result in worse performance than concatenation. Given the challenges of analyzing DNA sequences with both concatenation and coalescent methods, retroelement insertions (RIs) have emerged as powerful phylogenomic markers for species tree estimation. Here, we show that two recently proposed quartet-based methods, SDPquartets and ASTRAL_BP, are statistically consistent estimators of the unrooted species tree topology under the coalescent when RIs follow a neutral infinite-sites model of mutation and the expected number of new RIs per generation is constant across the species tree. The accuracy of these (and other) methods for inferring species trees from RIs has yet to be assessed on simulated data sets, where the true species tree topology is known. Therefore, we evaluated eight methods given RIs simulated from four model species trees, all of which have short branches and at least three of which are in the anomaly zone. In our simulation study, ASTRAL_BP and SDPquartets always recovered the correct species tree topology when given a sufficiently large number of RIs, as predicted. A distance-based method (ASTRID_BP) and Dollo parsimony also performed well in recovering the species tree topology. In contrast, unordered, polymorphism, and Camin–Sokal parsimony (as well as an approach based on MDC) typically fail to recover the correct species tree topology in anomaly zone situations with more than four ingroup taxa. Of the methods studied, only ASTRAL_BP automatically estimates internal branch lengths (in coalescent units) and support values (i.e., local posterior probabilities). We examined the accuracy of branch length estimation, finding that estimated lengths were accurate for short branches but upwardly biased otherwise. This led us to derive the maximum likelihood (branch length) estimate for when RIs are given as input instead of binary gene trees; this corrected formula produced accurate estimates of branch lengths in our simulation study provided that a sufficiently large number of RIs were given as input. Lastly, we evaluated the impact of data quantity on species tree estimation by repeating the above experiments with input sizes varying from 100 to 100,000 parsimony-informative RIs. We found that, when given just 1000 parsimony-informative RIs as input, ASTRAL_BP successfully reconstructed major clades (i.e., clades separated by branches $&gt;0.3$ coalescent units) with high support and identified rapid radiations (i.e., shorter connected branches), although not their precise branching order. The local posterior probability was effective for controlling false positive branches in these scenarios. [Coalescence; incomplete lineage sorting; Laurasiatheria; Palaeognathae; parsimony; polymorphism parsimony; retroelement insertions; species trees; transposon.]