With the development of sequencing techniques, genetic sequencing data has been extensively used in evolutionary studies. The phylogenetic reconstruction problem, which is the reconstruction of evolutionary history from biomolecular sequences, is a fundamental problem. The evolutionary relationship between organisms is often represented by phylogeny, which is a tree or network representation. The most widely-used approach for reconstructing phylogenies from sequencing data involves two phases: multiple sequence alignment and phylogenetic reconstruction from the aligned sequences. As the amount of biomolecular sequence data increases, it has become a major challenge to develop efficient and accurate computational methods for phylogenetic analyses of large-scale sequencing data. Due to the complexity of the phylogenetic reconstruction problem in modern phylogenetic studies, the traditional sequence-based phylogenetic analysis methods involve many over-simplified assumptions. In this thesis, we describe our contribution in relaxing some of these over-simplified assumptions in the phylogenetic analysis.Insertion and deletion events, referred to as indels, carry much phylogenetic information but are often ignored in the reconstruction process of phylogenies. We take into account the indel uncertainties in multiple phylogenetic analyses by applying resampling and re-estimation. Another over-simplified assumption that we contributed to is adopted by many commonly used non-parametric algorithms for the resampling of biomolecular sequences, all sites in an MSA are evolved independently and identically distributed (i.i.d). Many evolution events, such as recombination and hybridization, may produce intra-sequence and functional dependence in biomolecular sequences that violate this assumption. We introduce SERES, a resampling algorithm for biomolecular sequences that can produce resampled replicates that preserve the intra-sequence dependence. We describe the application of the SERES resampling and re-estimation approach to two classical problems: the multiple sequence alignment support estimation and recombination-aware local genealogical inference. We show that these two statistical inference problems greatly benefit from the indel-aware resampling and re-estimation approach and the reservation of intra-sequence dependence.A major drawback of SERES is that it requires parameters to ensure the synchronization of random walks on unaligned sequences. We introduce RAWR, a non-parametric resampling method designed for phylogenetic tree support estimation that does not require extra parameters. We show that the RAWR-based resampling and re-estimation method produces comparable or typically better performance than the traditional bootstrap approach on the phylogenetic tree support estimation problem.We further relax the commonly used assumption of phylogeny. Evolutionary history is usually considered as a tree structure. Evolutionary events that cause reticulated gene flow are ignored. Previous studies show that alignment uncertainty greatly impacts downstream tree inference and learning. However, there is little discussion about the impact of MSA uncertainties on the phylogenetic network reconstruction. We show evidence that the errors introduced in MSA estimation decrease the accuracy of the inferred phylogenetic network, and an indel-aware reconstruction method is needed for phylogenetic network analysis.In this dissertation, we introduce our contribution to phylogenetic estimation using biomolecular sequence data involving complex evolutionary histories, such as sequence insertion and deletion processes and non-tree-like evolution.
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