Progressive multiple sequence alignment with indel evolution

Sequence alignment is crucial in genomics studies. However, optimal multiple sequence alignment (MSA) is NP-hard. Thus, modern MSA methods employ progressive heuristics, breaking the problem into a series of pairwise alignments guided by a phylogeny. Changes between homologous characters are typically modelled by a Markov substitution model. In contrast, the dynamics of indels are not modelled explicitly, because the computation of the marginal likelihood under such models has exponential time complexity in the number of taxa. But the failure to model indel evolution may lead to artificially short alignments due to biased indel placement, inconsistent with phylogenetic relationship