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Modern phylogenetic methods allow inference of ancestral molecular sequences given an alignment and phylogeny relating present-day sequences. This provides insight into the evolutionary history of molecules, helping to understand gene function and to study biological processes such as adaptation and convergent evolution across a variety of applications. Here, we propose a dynamic programming algorithm for fast joint likelihood-based reconstruction of ancestral sequences under the Poisson Indel Process (PIP). Unlike previous approaches, our method, named ARPIP, enables the reconstruction with insertions and deletions based on an explicit indel model. Consequently, inferred indel events have an explicit biological interpretation. Likelihood computation is achieved in linear time with respect to the number of sequences. Our method consists of two steps, namely finding the most probable indel points and reconstructing ancestral sequences. First, we find the most likely indel points and prune the phylogeny to reflect the insertion and deletion events per site. Second, we infer the ancestral states on the pruned subtree in a manner similar to FastML. We applied ARPIP (Ancestral Reconstruction under PIP) on simulated data sets and on real data from the Betacoronavirus genus. ARPIP reconstructs both the indel events and substitutions with a high degree of accuracy. Our method fares well when compared to established state-of-the-art methods such as FastML and PAML. Moreover, the method can be extended to explore both optimal and suboptimal reconstructions, include rate heterogeneity through time and more. We believe it will expand the range of novel applications of ancestral sequence reconstruction. [Ancestral sequences; dynamic programming; evolutionary stochastic process; indel; joint ancestral sequence reconstruction; maximum likelihood; Poisson Indel Process; phylogeny; SARS-CoV.]., (© The Author(s) 2022. Published by Oxford University Press on behalf of the Society of Systematic Biologists.)

Recently we presented a frequentist dynamic programming (DP) approach for multiple sequence alignment based on the explicit model of indel evolution Poisson Indel Process (PIP). This phylogeny-aware approach produces evolutionary meaningful gap patterns and is robust to the 'over-alignment' bias. Despite linear time complexity for the computation of marginal likelihoods, the overall method's complexity is cubic in sequence length. Inspired by the popular aligner MAFFT, we propose a new technique to accelerate the evolutionary indel based alignment. Amino acid sequences are converted to sequences representing their physicochemical properties, and homologous blocks are identified by multi-scale short-time Fourier transform. Three three-dimensional DP matrices are then created under PIP, with homologous blocks defining sparse structures where most cells are excluded from the calculations. The homologous blocks are connected through intermediate 'linking blocks'. The homologous and linking blocks are aligned under PIP as independent DP sub-matrices and their tracebacks merged to yield the final alignment. The new algorithm can largely profit from parallel computing, yielding a theoretical speed-up estimated to be proportional to the cubic power of the number of sub-blocks in the DP matrices. We compare the new method to the original PIP approach and demonstrate it on real data., (© The Author(s) 2019. Published by Oxford University Press on behalf of NAR Genomics and Bioinformatics.)