Estimation of Cross-Species Introgression Rates Using Genomic Data Despite Model Unidentifiability

Abstract

Full likelihood implementations of the multispecies coalescent with introgression (MSci) model treat genealogical fluctuations across the genome as a major source of information to infer the history of species divergence and gene flow using multilocus sequence data. However, MSci models are known to have unidentifiability issues, whereby different models or parameters make the same predictions about the data and cannot be distinguished by the data. Previous studies have focused on heuristic methods based on gene trees and do not make an efficient use of the information in the data. Here we study the unidentifiability of MSci models under the full likelihood methods. We characterize the unidentifiability of the bidirectional introgression (BDI) model, which assumes that gene flow occurs in both directions. We derive simple rules for arbitrary BDI models, which create unidentifiability of the label-switching type. In general, an MSci model with k BDI events has 2k unidentifiable modes or towers in the posterior, with each BDI event between sister species creating within-model parameter unidentifiability and each BDI event between non-sister species creating between-model unidentifiability. We develop novel algorithms for processing Markov chain Monte Carlo (MCMC) samples to remove label-switching problems and implement them in the BPP program. We analyze real and synthetic data to illustrate the utility of the BDI models and the new algorithms. We discuss the unidentifiability of heuristic methods and provide guidelines for the use of MSci models to infer gene flow using genomic data.

Inference of Gene Flow between Species under Misspecified Models

“…With multiple sequences per species ( ), all eight parameters of the MSci model, ( fig. 1 d ) are identifiable ( Yang and Flouri 2022 ). The results are summarized in figure 3 .…”

“…Nevertheless, the information concerning ϕ A→B is mostly determined by the number of sequences reaching the hybridization node Y and by the difficulty with which one can tell the parental path taken by each B sequence at Y . There is thus little difference in information content about ϕ A→B between models I and B. Computationally, model B is much more expensive due to sampling an extra parameter in the Markov chain Monte Carlo (MCMC) algorithm and to MCMC mixing issues (Yang and Flouri, 2022).…”

“…Commonly used heuristic methods for inferring gene flow such as the D statistic (Green et al, 2010;Durand et al, 2011) may not be informative about the direction of gene flow as they do not use all information in the data. The computational strengths and statistical deficiencies of heuristic methods have been reviewed by Hibbins and Hahn (2021), Jiao et al (2021), Huang et al (2022), and Yang and Flouri (2022). We assume that multiple sequences are sampled per species per locus, but will also consider the special case of only one sequence per species.…”

“…We assume that multiple sequences are sampled per species per locus, but will also consider the special case of only one sequence per species. Sampling only one sequence per species leads to unidentifiability or severe reduction in information about gene flow (Degnan, 2018;Yang and Flouri, 2022).…”

Detection of Ghost Introgression from Phylogenomic Data Requires a Full-Likelihood Approach

“…However, these heuristic methods have a significant drawback: networks may not always be identifiable. This means that the information derived solely from gene tree topologies may be insufficient to differentiate between networks representing different biological hypotheses about speciation and introgression (Pardi and Scornavacca 2015;Zhu and Degnan 2017;Yang and Flouri 2022).…”