Evaluating Variations on the Star Algorithm for Relative Efficiency and Sample Sizes Needed to Reconstruct Species Trees

Abstract

Many methods for inferring species trees from gene trees have been developed when incongruence among gene trees is due to incomplete lineage sorting. A method called STAR , assigns values to nodes in gene trees based only on topological information and uses the average value of the most recent common ancestor node for each pair of taxa to construct a distance matrix which is then used for clustering taxa into a tree. This method is very efficient computationally, scaling linearly in the number of loci and quadratically in the number of taxa, and in simulations has shown to be highly accurate for moderate to large numbers of loci as well as robust to molecular clock violations and misestimation of gene trees from sequence data. The method is based on a particular choice of numbering nodes in the gene trees; however, other choices for numbering nodes in gene trees can also lead to consistent inference of the species tree. Here, expected values and variances for average pairwise distances and differences between average pairwise distances in the distance matrix constructed by the STAR algorithm are used to analytically evaluate efficiency of different numbering schemes that are variations on the original STAR numbering for small trees.

Coalescent methods for estimating species trees from phylogenomic data

“…The STAR and STEAC methods can quickly infer phylogenies even for large-scale phylogenomic data (Liu et al, 2009a). When the true gene trees are given, STAR and STEAC are statistically consistent in estimating species trees (Liu et al, 2009b;Allman et al, 2013;Degnan, 2013). Both methods are robust to a limited amount of horizontal transfer as well as deviations from the molecular clock assumption, because some small values of coalescence times due to horizontal transfer or rate variation in a small number of genes do not have major effects on the average ranks and average coalescence times when the number of genes is moderate or large.…”

Discordance of Species Trees with Their Most Likely Gene Trees: A Unifying Principle

“…2013 ), and simulation-based assessments of the performance of particular species tree methods at parameter settings that produce AGTs ( Kubatko and Degnan 2007 ; Ewing et al 2008 ; Huang and Knowles 2009 ; Liu and Edwards 2009 ; Liu et al 2009 ; DeGiorgio and Degnan 2010 ; Hird et al 2010 ; Liu, Yu, and Edwards 2010 ; Liu, Yu, and Pearl 2010 ; O’Meara 2010 ; Wang and Degnan 2011 ; Helmkamp et al . 2012 ; Jewett and Rosenberg 2012 ; Sánchez-Gracia and Castresana 2012 ; Degnan 2013a ). AGTs represent the basis for inconsistency of the “democratic vote” method for species tree inference, in which the most commonly observed gene tree is taken as an estimate of the species tree; many other methods, including concatenation ( Kubatko and Degnan 2007 ), greedy consensus ( Degnan et al 2009 ), matrix representation with parsimony ( Wang and Degnan 2011 ), and the minimize-deep-coalescences algorithm ( Than and Rosenberg 2011 ), have analogous regions of the parameter space in which species tree estimates converge on incorrect estimates as increasingly large numbers of gene trees are accumulated.…”

Consistency and inconsistency of consensus methods for inferring species trees from gene trees in the presence of ancestral population structure

“…This consistency stems from the consistency of neighbor-joining and the observation that under the multispecies coalescent, for species X, Y, and Z, if the divergence time of species X and Y is smaller than that for X and Z and for Y and Z, then the expected rank in the gene tree is smaller for the coalescence of lineages from X and Y than for X and Z and for Y and Z. The consistency results still hold with arbitrary rankings in which a non-negative real number is assigned to the root and internal nodes are assigned ranks using a function that monotonically decreases as the number of edges between the node and the root increases [Allman et al, 2013, Degnan, 2013]. We show that in the presence of ancestral structure, STAR is a misleading estimator for the topology of fixed species tree σ with n ≥ 3 taxa under model 𝒮( σ , D , N , M , Ψ ).…”

“…A ranking is a non-negative real number assignment in which the root is given a positive real value a , and internal nodes are assigned ranks using a function that monotonically decreases with distance along each path from the root to a leaf [Allman et al, 2013, Degnan, 2013]. For example, for the topology (((AB)C)D), we could assign a ranking in which the root node has rank 4, the node connecting clade {AB} to C has rank 3, and the node connecting A and B has rank 2.…”