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Abstract Likelihood-based tests of phylogenetic trees are a foundation of modern systematics. Over the past decade, an enormous wealth and diversity of model-based approaches have been developed for phylogenetic inference of both gene trees and species trees. However, while many techniques exist for conducting formal likelihood-based tests of gene trees, such frameworks are comparatively underdeveloped and underutilized for testing species tree hypotheses. To date, widely used tests of tree topology are designed to assess the fit of classical models of molecular sequence data and individual gene trees and thus are not readily applicable to the problem of species tree inference. To address this issue, we derive several analogous likelihood-based approaches for testing topologies using modern species tree models and heuristic algorithms that use gene tree topologies as input for maximum likelihood estimation under the multispecies coalescent. For the purpose of comparing support for species trees, these tests leverage the statistical procedures of their original gene tree-based counterparts that have an extended history for testing phylogenetic hypotheses at a single locus. We discuss and demonstrate a number of applications, limitations, and important considerations of these tests using simulated and empirical phylogenomic data sets that include both bifurcating topologies and reticulate network models of species relationships. Finally, we introduce the open-source R package SpeciesTopoTestR (SpeciesTopology Tests in R) that includes a suite of functions for conducting formal likelihood-based tests of species topologies given a set of input gene tree topologies. 

Abstract Long-term balancing selection typically leaves narrow footprints of increased genetic diversity, and therefore most detection approaches only achieve optimal performances when sufficiently small genomic regions (i.e., windows) are examined. Such methods are sensitive to window sizes and suffer substantial losses in power when windows are large. Here, we employ mixture models to construct a set of five composite likelihood ratio test statistics, which we collectively term B statistics. These statistics are agnostic to window sizes and can operate on diverse forms of input data. Through simulations, we show that they exhibit comparable power to the best-performing current methods, and retain substantially high power regardless of window sizes. They also display considerable robustness to high mutation rates and uneven recombination landscapes, as well as an array of other common confounding scenarios. Moreover, we applied a specific version of the B statistics, termed B2, to a human population-genomic data set and recovered many top candidates from prior studies, including the then-uncharacterized STPG2 and CCDC169–SOHLH2, both of which are related to gamete functions. We further applied B2 on a bonobo population-genomic data set. In addition to the MHC-DQ genes, we uncovered several novel candidate genes, such as KLRD1, involved in viral defense, and SCN9A, associated with pain perception. Finally, we show that our methods can be extended to account for multiallelic balancing selection and integrated the set of statistics into open-source software named BalLeRMix for future applications by the scientific community.