Covariance Decomposition for Distance Based Species Tree Estimation

TL;DR

This paper derives the covariance matrix of pairwise species-distance estimates under a combined coalescent and substitution model, enabling improved confidence estimation in species tree inference.

Contribution

It provides an exact covariance decomposition for distance estimates, revealing dominant noise sources under different mutation regimes, and introduces a Gaussian-sampling method for reliable confidence assessment.

Findings

Substitutional noise dominates at very low and high mutation rates.

Coalescent variance is primary at intermediate mutation rates.

The Gaussian-sampling approach improves confidence estimate reliability.

Abstract

In phylogenomics, species-tree methods must contend with two major sources of noise; stochastic gene-tree variation under the multispecies coalescent model (MSC) and finite-sequence substitutional noise. Fast agglomerative methods such as GLASS, STEAC, and METAL combine multi-locus information via distance-based clustering. We derive the exact covariance matrix of these pairwise distance estimates under a joint MSC-plus-substitution model and leverage it for reliable confidence estimation, and we algebraically decompose it into components attributable to coalescent variation versus sequence-level stochasticity. Our theory identifies parameter regimes where one source of variance greatly exceeds the other. For both very low and very high mutation rates, substitutional noise dominates, while coalescent variance is the primary contributor at intermediate mutation rates. Moreover, the interval over which coalescent variance dominates becomes narrower as the species-tree height increases. These results imply that in some settings one may legitimately ignore the weaker noise source when designing methods or collecting data. In particular, when gene-tree variance is dominant, adding more loci is most beneficial, while when substitution noise dominates, longer sequences or imputation are needed. Finally, leveraging the derived covariance matrix, we implement a Gaussian-sampling procedure to generate split support values for METAL trees and demonstrate empirically that this approach yields more reliable confidence estimates than traditional bootstrapping.