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Multiple sequence alignment (MSA) is a crucial precursor to many downstream biological analyses, such as phylogeny estimation [Morrison, 2006], RNA structure prediction [Shapiro et al., 2007], protein structure prediction [Jumper et al., 2021], etc. Obtaining an accurate MSA can be challenging, especially when the dataset is large (i.e., more than 1000 sequences). A key technique for large-scale MSA estimation is to add sequences into an existing alignment. For example, biological knowledge can be used to form a reference alignment on a subset of the sequences, and then the remaining sequences can be added to the reference alignment. Another case where adding sequences into an existing alignment occurs is when new sequences or genomes are added to databases, leading to the opportunity to add the new sequences for each gene in the genome into a growing alignment. A third case is for de novo multiple sequence alignment, where a subset of the sequences is selected and aligned, and then the remaining sequences are added into this "backbone alignment" [Nguyen et al., 2015; Park et al., 2023; Shen et al., 2022; Liu and Warnow, 2023; Park and Warnow, 2023; Yamada et al., 2016]. Thus, adding sequences into existing alignments is a natural problem with multiple applications to biological sequence analysis. A few methods have been developed to add sequences into an existing alignment, with MAFFT--add [Katoh and Frith, 2012] perhaps the most well-known. However, several multiple sequence alignment methods that operate in two steps (first extract and align the backbone sequences and then add the remaining sequences into this backbone alignment) also provide utilities for adding sequences into a user-provided alignment. We present EMMA, a new approach for adding "query" sequences into an existing "constraint" alignment. By construction, EMMA never changes the constraint alignment, except through the introduction of additional sites to represent homologies between the query sequences. EMMA uses a divide-and-conquer technique combined with MAFFT--add (using the most accurate setting, MAFFT-linsi--add) to add sequences into a user-provided alignment. We evaluate EMMA by comparing it to MAFFT-linsi--add, MAFFT--add (the default setting), and WITCH-ng-add. We include a range of biological and simulated datasets (nucleotides and proteins) ranging in size from 1000 to almost 200,000 sequences and evaluate alignment accuracy and scalability. MAFFT-linsi--add was the slowest and least scalable method, only able to run on datasets with at most 1000 sequences in this study, but had excellent accuracy (often the best) on those datasets. We also see that EMMA has better recall than WITCH-ng-add and MAFFT--add on large datasets, especially when the backbone alignment is small or clade-based.

Species tree estimation is a basic step in many biological research projects, but is complicated by the fact that gene trees can differ from the species tree due to processes such as incomplete lineage sorting (ILS), gene duplication and loss (GDL), and horizontal gene transfer (HGT), which can cause different regions within the genome to have different evolutionary histories (i.e., "gene tree heterogeneity"). One approach to estimating species trees in the presence of gene tree heterogeneity resulting from ILS operates by computing trees on each genomic region (i.e., computing "gene trees") and then using these gene trees to define a matrix of average internode distances, where the internode distance in a tree T between two species x and y is the number of nodes in T between the leaves corresponding to x and y. Given such a matrix, a tree can then be computed using methods such as neighbor joining. Methods such as ASTRID and NJst (which use this basic approach) are provably statistically consistent, very fast (low degree polynomial time) and have had high accuracy under many conditions that makes them competitive with other popular species tree estimation methods. In this study, inspired by the very recent work of weighted ASTRAL, we present weighted ASTRID, a variant of ASTRID that takes the branch uncertainty on the gene trees into account in the internode distance. Our experimental study evaluating weighted ASTRID shows improvements in accuracy compared to the original (unweighted) ASTRID while remaining fast. Moreover, weighted ASTRID shows competitive accuracy against weighted ASTRAL, the state of the art. Thus, this study provides a new and very fast method for species tree estimation that improves upon ASTRID and has comparable accuracy with the state of the art while remaining much faster. Weighted ASTRID is available at https://github.com/RuneBlaze/internode.