Probabilistic Techniques in Mathematical Phylogenetics

提出从概率的角度研究系统发育重建问题。推断一组生物的物种形成历史是进化生物学的一个基本问题。这段历史用系统发育来表示，即有根的树，其中叶子对应当前的物种，分支表明物种形成事件。分子序列在这种系统发育上的随机演化是树上马尔可夫模型的一个实例。在这个项目中，PI将进一步发展吉布斯测度理论与系统发育重建问题之间的联系。将特别强调插入和删除的模型，目的是提供多序列比对问题的概率分析。与信息理论问题的联系也将被考虑。组装生命之树是生物学中的一个基本问题，它为进化、适应和物种形成的研究提供了见解。从现有物种收集的DNA序列数据分析中可以推断出许多关于过去进化事件的信息。分子序列进化的一个显著特征是随机性的显著作用。近年来，概率论，即随机性的数学研究，为评估统计方法在大规模系统发育中重建进化过程的能力提供了关键的新见解。这个项目的主题是进一步研究这些联系。特别是，将考虑更现实的进化模型。新的系统发育分析技术将被开发和实施。

It is proposed to investigate the phylogenetic reconstruction problem from a probabilistic perspective. Inferring the speciation history of a group of organisms is a fundamental problem in evolutionary biology. This history is represented by a phylogeny, i.e., a rooted tree where the leaves correspond to current species and branchings indicate speciation events. The stochastic evolution of molecular sequences on such a phylogeny is an instance of a Markov model on a tree. In this project, the PI will further develop connections between the theory of Gibbs measures on trees and the phylogenetic reconstruction problem. A particular emphasis will be given to models of insertions and deletions with the objective of providing a probabilistic analysis of the multiple sequence alignment problem. Connections to information theory problems will also be considered.Assembling the Tree of Life is a fundamental problem in biology which provides insights in the study of evolution, adaptation, and speciation. Much information about past evolutionary events can be inferred from the analysis of DNA sequence data collected from existing species. A notable feature of the evolution of molecular sequences is the significant role played by randomness. In recent years, probability theory, the mathematical study of randomness, has provided key new insights in assessing the power of statistical methods to reconstruct evolutionary processes in large-scale phylogenetics. The main theme of this project is to further investigate these connections. In particular, more realistic models of evolution will be considered. New phylogenetic analysis techniques will be developed and implemented.