Abstract
The multispecies coalescent with introgression (MSci) model accommodates both the coalescent process and cross-species introgression/hybridization events, two major processes that create genealogical fluctuations across the genome and gene-tree–species-tree discordance. Full likelihood implementations of the MSci model take such fluctuations as a major source of information about the history of species divergence and gene flow, and provide a powerful tool for estimating the direction, timing and strength of cross-species introgression using multilocus sequence data. However, introgression models, in particular those that accommodate bidirectional introgression (BDI), are known to cause unidentifiability issues of the label-switching type, whereby different models or parameters make the same predictions about the genomic data and thus cannot be distinguished by the data. Nevertheless, there has been no systematic study of unidentifiability when full likelihood methods are applied. Here we characterize the unidentifiability of arbitrary BDI models and derive simple rules for its identification. In general, an MSci model with k BDI events has 2k unidentifiable towers in the posterior, with each BDI event between sister species creating within-model unidentifiability and each BDI between non-sister species creating cross-model unidentifiability. We develop novel algorithms for processing Markov chain Monte Carlo (MCMC) samples to remove label switching and implement them in the BPP program. We analyze genomic sequence data from Heliconius butterflies as well as synthetic data to illustrate the utility of the BDI models and the new algorithms.
Competing Interest Statement
The authors have declared no competing interest.
Footnotes
ZY and TF conceived the research, designed and conducted the experiment, and wrote the paper